MATHEMATICS - larberthigh.com24432]General_Practice_Papers_Pa… · The managers of the “Eskimo Engineering” company are experimenting with new logos. They decide to use the initial

Please note … the format of this practice examination is different from the current format. The paper timings are different and calculators can be used throughout.

General Mathematics - Practice Examination A

MATHEMATICS Standard Grade - General Level

First name and initials Surname

Read Carefully 1. Answer as many questions as you can. 2. Write your answers in the spaces provided . 3. Full credit will be given only where the solution contains appropriate working. 4. You may use a calculator

Time allowed - 1 hours 30 minutes

FORMULAE LIST

Circumference of a circle: C = πd Area of a circle: A = πr2 Curved surface area of a cylinder: A = 2πr h Volume of a cylinder: V = πr 2h Volume of a triangular prism: V = Ah

b

a

Theorem of Pythagoras:

a2 = b2 + c2 c Trigonometrical ratios in a right angled

hypotenuseadjacentcos

hypotenuseoppositesin

adjacentoppositetan

=

=

=

o

o

o

x

x

x

xo

hypotenuse triangle:

opposite adjacent Gradient: vertical

height horizontal distance

Gradient = vertical height

horizontal distance

1. Solve the following equation 3x + 2 = 18 − x (3) 2. The radius of the earth is metres. 61084 ×⋅ Write this number out in full. (2) 3. John has a £1 coin which he is going to spend in the “snacks” machine. The cost of the

items are as follows : Crisps 25p Chump Bar 10p Orange Drink 35p

The machine is not giving any change. Complete the table to show four more ways for John to spend exactly £1.

Crisps Chump Drink

1 4 1

(4) 4. The managers of the “Eskimo Engineering” company are experimenting with new logos. They decide to use the initial letters of the company name. They want the design to have half-turn symmetry about the

RA KU

Example

dot so that it can be used

either way up. Complete the design. (4)

5. Simplify 3(4x + 3) − 7x (3 ) 6. AB is a diameter of the circle and BD is a tangent at point B. Angle BAD = 27o. Calculate the size of the of the angle marked xo. (3)

RA KU

A

B D

27o

xo

7. (a) The cost per hour of making different types of television programmes is shown below : Type of programme Cost (£)

Drama 656 000 Sitcoms 312 000 Family entertainment 245 000 Documentary 145 000 Chat show 143 000 Sport 51 000 Current affairs 44 000

What is the mean cost per hour of producing a television programme ? (2) (b) This year 227 760 hours of television will be broadcast. If you sat down to watch this continuously, how long would it take ? Give your answer in years. (2)

8. Gerry won £1500 in the National Lottery and decided to open a Building Society account.

He invested his money in an account which offered a rate of 7 % per annum.

How much money will he have if he closes his account at the end of 6 months ? (3) 9. A helicopter takes off and follows a path given by y = 3 + 2x.

At the same time a hanglider is descending and is following a path given by x + y = 12.

(a) Draw a graph to show these two flight paths and write down the coordinates of the point of intersection of the paths. (5)

(b) Although the flight paths intersect, the helicopter and the hanglider do not meet. Give a reason for this. (1)

KU RA

10. At a garage the cost £C, of car repairs is given by the formula

C = 30 + p + 18t

where p is the cost in £ of new parts and t is the time spent in hours on repairs. (a) Find the total cost of repairs if new parts cost £27 and the repairs take 2 hours. (2)

(b) If new parts cost £58 and the total cost is £97, how long was spent on repairs ? (3) 11. A jeweller makes earrings in the shape of similar triangles as shown below. 3⋅6 cm 4⋅5 cm 5⋅4 cm

If the ratio of the sides is 6 : 4 and the area of the small triangle is 2.16 cm2, find the area of the largest triangle. (4)

RA KU

RA KU 12. Tony has made a small coffee table in his woodwork class, by cutting the corners off a 70 cm square piece of wood .

The top of the table is shown. He wants to complete the table by putting A finishing strip round the outside edge. What length of strip will he need ? (5)

50 cm

50 cm

70 cm

70 cm Give your answer correct to 1 - decimal place. 13. Karen is buying a new TV & video. She has seen it advertised in two stores in the town for a cash price of £750. Both stores offer payment terms.

TV & Video Package £750

or 10% deposit and 12 payments of

£58

TV & VIDEO ~ £750

Or

Deposit of £50 and 18 payments of £40

Which firm is cheaper and by how much ? (7)

KU RA 14.

Mr and Mrs Redwood have a tree in their garden which they want to cut down. They are wondering if there is any chance it could hit the house as it falls. They don't know the height of the tree.

Their son George makes some measurements and then draws a sketch of the situation

10 m

39o

Tree

The angle of elevation of the top of the tree from the house is 39o and the distance

along the ground between the tree and the house is 10 m. Can the tree be cut down safely ? (4)

15. The cost of a mirror (£C ) varies directly as the square of its length (s cm). A mirror of length 50 cm costs £35. (a) Find a formula connecting C and s. (4)

(b) Find the cost of a mirror of length 30 cm. (2)

16. Coronet Wallcoverings make several designs for wallpaper borders one of

which is shown below. The pattern is made up of circle shapes and cross shapes. (a) Complete the table below. (2)

Number of circle shapes (C) 2 3 4 5 6 7 Number of cross shapes (N) 2 6

(b) Write down a formula connecting the number of cross shapes, N, and the number

of circle shapes, C . N = (2) (c) How many cross shapes would there be if there were 12 circle shapes ? (2) (d) How many circle shapes would there be in a pattern which had 36 cross shapes ? (3) (e) Each pattern in the design is 40 cm long. A roll of the border is 10 m long. How many cross shapes would there be in a full roll of the border ? (4) 17. Mr. D. Glazing, a salesman, has to drive from London

to Manchester – a distance of 200 miles – to attend a meeting at midday. If he leaves the house at 9.15 am and travels by motorway, can he get to the meeting in time without breaking the speed limit ?

KU RA

1 pattern 40 cm

Speed Limit

miles per hour

(4)

End of Question Paper


Time allowed - 1 hours 30 minutes

Read Carefully 1. Answer as many questions as you can. 2. Write your answers in the spaces provided . 3. Full credit will be given only where the solution contains appropriate working. 4. You may use a calculator

First name and initials Surname

Class Teacher

General Mathematics - Practice Examination BPlease note … the format of this practice examination is different from the current format. The paper timings are different and calculators can be used throughout.

FORMULAE LIST Circumference of a circle: C = πd Area of a circle: A = πr2 Curved surface area of a cylinder: A = 2πr h Volume of a cylinder: V = πr 2h Volume of a triangular prism: V = Ah

Theorem of Pythagoras: Trigonometrical ratios in a right angled

triangle: Gradient: Gradient =

a

bc a2 + b2 = c2

xo adjacent

opposite hypotenuse



adjacentoppositetan

=

=

=

o

o

o

x

x

x

horizontal distance

vertical height

distancehorizontalheightvertical

1. Solve algebraically the inequality 2(5x − 2) < 16 (3) 2. The planet Venus is 108 million kilometres from the sun. Write this number in standard form (2) 3. Barbara and Ken are getting married. They have a list of the presents they would like

in Littletrees department store. Here is part of the list :

Barbara ~Ken Wedding List Item cost(£)

clock radio 7 set of glasses 15

6 mugs 8 small lamp 12

set of towels 20 toaster 10

set of pots 18 cutlery set 15

Mr & Mrs Payne would like to buy them gifts which exactly total £30. Show in the table five different ways that they could spend their money.

cutlery pots toaster towels lamp mugs glasses radio √ √ √

(5) 4. O is the centre of the circle. Write down the sizes of the angles marked a and b. (3)

KU RA

O

a

b 47o .

5. The cost, £C, of arranging a celebration dinner at the

Boat House Hotel is given by C = 50 + 25n + 20b where n is the number of people and

b is the number of bottles of champagne ordered. (a) (i) Find the total cost of a dinner if 40 people attended and 8 bottles of champagne were ordered. (2)

(ii) What was the mean cost per person ? (3)

(b) A bowling club with 110 members has £3200 to spend on a celebration dinner. How many bottles of champagne can they order ? (3) 6. Mike is moving house and decides to pack his collection of Maths books into cardboard

boxes measuring 60 cm by 45 cm by 35 cm. All his books are the same size and measure 15 cm by 20 cm by 5 cm. (a) What is the maximum number of books he can pack into a box ? (3) (b) If each book weighs 800g and the empty box weighs 300g, what is the total weight of the box, in kilograms, when it is full of books ? (3)

KU RA

at The Boat House

7. Mike needs to hire a van for his move to a new house. He makes enquiries from 2 firms and finds that the costs are as follows VG Van Hire : £50 + £1 per mile Hasty Hires : £30 + £1.50 per mile (a) Complete the tables for the costs for each firm. (4) (b) Draw the graphs for both firms on the same grid below. (3) (c) If Mike estimates he will travel 25 miles altogether, which firm should he choose ?

(1) (d) If he thinks his total mileage will be 150 miles which firm will be best ? (1)

VG Van Hire Number of miles 10 20 30 40 50 60 Cost (£) 60 90

Hasty Hires Number of miles 10 20 30 40 50 60 Cost (£) 45 75

KU RA

8. Factorise fully 12x − 4y

(2)

9. Three local stores are running special offers on bottles of cola. Mark is having his friends to visit and wants 6 bottles of cola. (a) Which of the above stores would offer him the best value for money if a bottle

of cola is normally priced at £1.24 ? (Give reasons for your answer) (7) (b) How much will he save on the cost of buying 6 bottles at the normal price if

he buys his cola from the best value store ? (2) 10. Philip sees an advert for loans in a Sunday newspaper. The repayments for the loan are 48 monthly

instalments of £94.66. (a) What is the total amount that Philip has to repay ? (2)

(b) How much extra does he pay ? (1) (c) What percentage is this of the original loan ? (2) (give your answer to the nearest 1%)

3 for the price of

2

3bottles for

£2.51 Buy one get the second

½ price

Special Offer

COLA

£3000 for less than £95 a month

KU RA

11. The heat output (U kW) of a radiator is in direct proportion to the surface area (A cm2). The heat output of radiator A , which measures 120 cm by 75 cm, is 3 kW.

radiator A radiator B

Calculate the heat output for radiator B which measures 72 cm by 50 cm. (6)

12. The average speed of the Eurostar between London and Paris is 90 miles per hour. The length of the journey is 498 miles. If I leave London at 7.15 am, what time will I arrive in Paris, given that France

is 1 hour ahead of UK time ? (4) 13. The diagram shows a section of a drain whose

diameter is 1 metre. The surface width of the water in the drain is 70 cm. (a) Write down the length of OA in

centimetres. (1)

(b) Calculate how far the water level

is below the centre of the pipe, O. (Give your answer to the nearest centimetre) (4)

KU RA

O

A C

14. The basic design for a floor tile is shown below. The designer wants to make a larger

tile that has 2 lines of reflection symmetry. Complete his design. (4)

15. The strip for fastening babies’ nappies is printed with colourful animals. It is

manufactured in one long piece and then cut to size. Part of one of the strips is shown below.

(a) Complete the table for the pattern shown (3) (b) Write down a formula for the number of birds, B, when you know the

number of fish, F. (2) (c) How many birds would there be if there were 20 fish ? (2)

(d) How many fish would there be for 30 birds ? (3)

number of fish (F) 2 3 4 5 6 10 number of birds (B) 3 9

KU RA

Two satellites A and B are orbiting the Earth. They are both observed at a distance of 23,200 miles from a fixed position on Earth (P). The angle between them is 6 o as shown in the diagram which is not to scale.

(a) What type of triangle is PAB ? (1) (b) Calculate the distance between A and B. (Give your answer correct to the nearest mile) (6)

17. (a) Calculate (i) (1 + 2 + 3) (1)

(ii) (13 + 23 + 33) (2) (b) Describe any relationship between the two answers. (1)

(c) Calculate (i) (1 + 2 + 3 + 4) (1)

(ii) (13 + 23 + 33 + 43) (2) (d) Describe this relationship. (1)

End of Question Paper

A

B 23200 mls

23200 mls

6 o

P

.

.

16. KU RA

General Mathematics - Practice Examination C Please note … the format of this practice examination is

different from the current format. The paper timings are different and calculators can be used throughout.

Class

First name and initials

Read Carefully 1. Answer as ma2. Write your ans3. Full credit will 4. You may use a


Time Allowed - 1 hour 30 minutes

Teacher

Surname

ny questions as you can. wers in the spaces provided . be given only where the solution contains appropriate working. calculator


c b a2 + b2 = c2

a




adjacentoppositetan

=

=

=

o

o

o

x

x

xtriangle: hypotenuse

xo


height

horizontal distance Gradient = distancehorizontal

heightvertical

1. A certain form of bacteria, when examined under a microscope, is found to be 00120 ⋅ cm in length. Write this number in scientific notation. (2) 2. The table below shows the temperatures in 5 British cities on January 4th 1998 at 9 am.

City Temperature Aberdeen -5 °C Cardiff 1 °C

Glasgow -1 °C London 4 °C

Manchester 2 °C

(a) By how many degrees was London warmer than Glasgow ? (1) (b) By noon on January 4th the temperature in Glasgow had risen by 9°C. What was the noon temperature in Glasgow ?

RAKU

(1) 3. Maggie earns a salary of £12,600 per year. She is told that she will be receiving a salary increase of 7%. (a) Calculate Maggie's new salary. (3) (b) Maggie is paid monthly and when she receives her wageslip she sees

that her gross monthly pay is £1062 Has Maggie been paid correctly ? You must give a reason for your answer.

(3)

RAKU 4. (a) On the grid below, plot the following points and join them up to

form a triangle. (2) P (3 , 2) Q (3 , -3) R( -2 , -3)

4

3

2 1

y

(b)

5. Solve algebra

-5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

Calculate the len

ically

5x – 4 =

-2

-3

-4

gth of side PR. (3)

2x + 20 (3)

RAKU6. The diagram shown is of a new design for a bedspread. For each bedspread, a diamond is cut out of a plain sheet of cloth and patterned material is sewn in its place. (a) Calculate the area of the diamond.

112 cm 260 cm (3)

160 cm

(b) Calculate the area of plain cloth remaining after the diamond has been removed. (2)

(c) What percentage of the bedspread is plain material ? (3) 7. Simplify :- (a) 4 (3) 20)5(6 −−+ aa (b) 3 (2) )2( −bb

KU RA

8. Complete the diagram below, by reflecting the flag in the dotted lines of symmetry.

(3) 9. In the diagram below CB is a tangent to the circle. Angle OAB is 50° and the line OC is parallel to AB.

Calculate the size of the angle x. (3)

C B

A O 50°

x

RAKU

10. While on holiday Paul decides to calculate the height of his hotel.

He draws a sketch to help him.

Paul positions himself 43 ⋅ metres away from a marked spot on the ground and he measures his own height to be 160 centimetres.

The hotel is 102 metres from the spot on the ground.

m43 ⋅

hotel

me

160 cm

x 102 m

Assuming Paul uses a method involving similar triangles, what height will he calculate the hotel to be ?

You must not use a scale drawing. (4)

11. A painter and decorator knows that he needs 42 litres of paint to paint a room. He must use a mixture of blue and red paint in the ratio 3 : 4.

How many litres of red paint will the painter need ? (3)

12. The distance time graph shows details of a coach journey on a weekend outing.

(a) How far did the coach travel before it stopped for the first time ? (1) (b) Calculate the total driving time for the driver ? (2)

(c) Hence calculate the average speed of the coach for the whole journey, giving your answer in miles per hour. (do not include the stops). (3)

RAKU

50

100

150

0

Distance (Miles)

0 1 2 3 4 Time (hours)

RAKU 13.

50 cm

80 cm

The doormat shown above is made up from a rectangle and two semi circles.

(a) A coloured border is to be put around the edge of the mat without any overlap.

Calculate the length of piping required for the border. (3) (b) Calculate the area of the mat in square metres. (5)

(c) If the material used to make the mat costs £3.40 per square metre, and the

coloured edging costs 90p per metre, find the total cost of making the mat. (4)

RAKU

14. An engineer planning a new suspension bridge decides to use the following design for the sides.

The side of the bridge is made up of steel hexagon shapes with bolts to hold them together. The number of bolts needed depends on the number of hexagons used. (a) Complete the table to help the engineer plan the bridge.

(3)

Number of hexagons (h) 1 2 3 4 5 10 Number of bolts (B) 6 11

(b) Find a formula connecting the number of hexagons (h) with the number of bolts (B). (2)

(c) Is it possible for the engineer to build the bridge using 120 bolts ? (3) You must explain your answer with appropriate working.

15. Barry needs new glasses. He has seen a pair of frames that he likes in three different opticians.

Barry must also have an eye test which normally costs £12.

Obviously Barry wants the cheapest deal.

Which Opticians should Barry choose ? Your answer must be accompanied with the appropriate working. (6)

16. A skateboard ramp has been designed to have the following dimensions :- The ramp can only be used in competitions if the angle marked x is

between 20 and 30 degrees.

Can this ramp be used in a competition ? (4)

RAKU

S A L E 20% discount on all frames Frames - £110 Lenses - £26

Lenses and

Frames £120

Lenses £30 Frames £100

Free Eye Test

15 m x°

7 m

You must show all your working. END OF QUESTION PAPER

Please note … the format of this practice examination is the same as the current format. The paper timings are the same, as are the marks allocated. Calculators may only be used in Paper 2.

General Mathematics - Practice Examination D


Class


Read Carefully 1. Answer as many2. Write your answe3. Full credit will be4. You may not us

Time Allowed - 35 minutes

questions as yors in the spaces

given only where a calculator

Paper I

Teacher

Surname

u can. provided . e the solution contains appropriate working.

FORMULAE LIST


c b a2 + b2 = c2

a

Theorem of Pythagoras: Trigonometrical ratios in a right angled oppositeotriangle:

hypotenuse

xo


height


heightvertical



adjacenttan

=

=

=

o

o

x

x

x

1. Carry out the following calculations. (a) 40% of £120

KU 2 1 1 1 3 4

RE

(b) 6 + 734219 ⋅−⋅ (c) 710 ⋅ 50× (d) 43 796. ÷ 2. Mike decided to play 9 holes on his local golf course. A score of +2 would mean that he was 2 shots above par for a certain hole. A score of –1 would mean that he was 1 shot below par for a certain hole. For the nine holes Mike's "scores to par" were as follows:- +1 , -2 , 0 , +3 , +1 , -1 , +1 , +2 , +4 Calculate Mike’s average score “to par” for a hole. 3. Julie works in her local supermarket. She works a basic week of 30 hours. She is paid £3.80 per hour. All overtime is paid at double time. (a) One week Julie works 35 hours. Calculate her gross pay. (b) Julie works different shifts every day. Shown opposite is her shifts for a particular week. Julie slept in on Friday morning and was 30 minutes late for work. Assuming she does not get paid for her missing minutes, calculate her wages for this week.

JULIE WATT MONDAY 0900 - 1200TUESDAY 1200 - 1900WEDNESDAY 1030 - 1800THURSDAY 0930 - 1430FRIDAY 0900 - 1700

3

KU 2 2 2

RE 4. A secondary school has a roll of 574 pupils. 7

4 of them are boys.

How many boys are there ? 5. A wooden shelving unit is made by joining side panels and shelves,

as shown below.

(a) Complete the following table.

Number of side panels (P) 2 3 4 5 20 Number of shelves (S) 6 12

The shelves shown in the diagram have three side panels and six shelves.

(b) Write down a formula for the number of shelves, S, when you know the

number of side panels , P.

KU

2 2 3 5

RE 6. (a) Solve algebraically 4x – 7 ≤ 13.

(b) Factorise fully 9a - 12b 2

7. If 9 litres of petrol costs £6.21.

Find the cost of 20 litres of petrol.

8. A supermarket displays tins of beans as shown below. This display has 3

rows and 6 tins

Each tin is 12 cm high. The manager wants the display to be 1 08⋅ metres high.

How many tins of beans will there be in the completed display ? [END OF QUESTION PAPER]

General Mathematics Practice Exam D Marking Scheme - Paper 1 1. (a) ans: £48 5 KU • know how to find a commonly 1 used whole number percentage of a quantity • correct answer 2 (b) ans: 21.72 • add and subtract decimal numbers 1 (c) ans: 35.5

multiply a decimal number by 10 1• (d) ans: 6.28

1• divide a decimal number by a single whole number

2. ans: 1 3 KU 1 know how to find an average • 2 add numbers • divide 3• 3. (a) ans: £152 4 KU 1 calculate basic pay • 2 interpret information • calculate overtime 3• 4 calculate gross pay • (b) ans: £114 3 RE 1 interpret table : total hours • 2 subtracting late time • state or calculate wages 3• 4. ans: 328 2 KU 1 know how to find a simple fraction •

of a quantity 2 calculate a simple fraction of a quantity • 5. (a) ans: 3 , 9 , 57 2 RE 1 continue pattern • 2 extend pattern •

1•

2•

1•

1•

1•

1•

•3•

1••

3••

1••

3•

1•

2•

1••

0.4 × 120

£48

21.72

35.5 6.28 (a) know to add numbers and divide

by 9 2 9 1 (a) 30 × £3.80 = £114 2 5 hours overtime 5 × 2 × £3.80 = £38 4 114 + 38 = £152 (b) total 30½ hours 2 paid for 30 hours £114 (or consistent answer)

574 × 4 ÷ 7

328

(a) 3 and 9 shelves 2 57 shelves

Illustration(s) for awarding each mark Give 1 mark for each

(b) ans: S = 3P - 3 2 RE 1 generalise pattern •

•

5x ≤

••

2

1•2•

••

3•

••

3•

4•

5•

1••

1• 20x4 ≤2• 5x ≤

1•2• 2

1••

3•

1••

3•

•

5•

Give 1 mark for each Illustration(s) for awarding each mark

2 3P – 3 or equivalent

3 3(3a - 4b)

2 £6.21 ÷ 9 = 0.69

0.69 × 20 = £13.80

know to divide 1.08 m by 12 cm 2 9 rows of tins needed appropriate evidence eg 2 rows 1 + 2 3 rows 1 + 2 + 3 4 4 rows 10 tins 5 rows 15 tins 9 rows needs 45 tins 21 - KU 12 - RE

Total 33

2 generalise pattern 6. (a) ans: 2 KU 1 collect constants 2 solve inequality for x

(b) ans: 3(3a - 4b) 2 KU common factor terms in brackets 7. ans: £13.80 3 KU 1 knowing to use proportion 2 dividing to find 1 litre calculating answer 8. ans: 45 tins 5 RE 1 strategy 2 9 rows of tins needed strategy

strategy carry out strategy

Please note … the format of this practice examination is the same as the current format. The paper timings are the same, as are the marks allocated. Calculators may only be used in this paper.

General Mathematics - Practice Examination D MATHEMATICS

Standard Grade - General Level

Class


Read Carefully 1. Answer as many2. Write your answe3. Full credit will be4. You may use a


questions as yrs in the space

given only whecalculator

Paper II

Teacher

Surname

ou can. s provided . re the solution contains appropriate working.

FORMULAE LIST


c b a2 + b2 = c2

a


hypotenuse

xo


height

horizontal distance

Gradient = distancehorizontalheightvertical



adjacenttan

=

=

=

o

o

x

x

x

RE KU

1 1 1

1. Two judges, Judge 1 and Judge 2, were scoring athletes in a competition. Each judge awarded points out of 5. The scattergraph shows the marks for five of the athletes who took part.

0 1 2 3 4 5

5

4

3

2

1

Scores Judge 2

Judge 1

(a) Susan was given a score of 34 ⋅ by Judge 1 and 4 6⋅ by Judge 2. Mark Susan’s score with an X on the scattergraph. (b) Draw a line of best fit on the scattergraph. (c) John was scored by Judge 1. 73 ⋅

From your scattergraph estimate the score that Judge 2 may have awarded him.

4

KU RE 3

2. Mr Andrew has a safe deposit box at the local bank.

1 2 4 The lock on it has a 3 digit code. Each digit can either be 1, 2, 3 or 4 . For example, the code on the right is 412.

On Mr Andrew’s lock : answer

• the second digit is a multiple of 2

• the last digit is a prime number greater than 2

• no number is repeated. Write down all the possible codes for Mr Andrew’s lock. 3. A circular table cloth has to be designed so that it completely covers a square table

with side 2 metres. The designer wishes to use the minimum amount of material. The diagram below shows the designers initial plan.

2 m

table

What is the diameter of the smallest possible tablecloth which the designer could make ? Round your answer to 1 decimal place.

4. (a) On the grid below, plot the points

F(-6,0), G(-1,3) and H(4,6). (b) Find the gradient of the line FG. 5. The shoe sizes of pupils in a maths class were recorded on a frequency table.

Shoe size Frequency Shoe size × Frequency

4 5 6 7 8

3 7 8 5 2

25

12 35 48 35

(a) Complete the table and calculate the mean. (b) What was the range of the distribution ?

0 5

-5

-5

5

x

y

2 2 1

KU RE 1

25 m

12 m 8 m

4

KU RE

6. A rectangular garden is shown below. GRASS The garden has a rectangular shaped lawn with a circular flower bed in the centre.

The diameter of the flower bed is 8 metres as shown. Calculate the area of grass in the garden.

7. An Army helicopter leaves it’s base B, on a bearing of 055° and travels 50km to

a secret location S. It picks up supplies and travels 75 km in a south-easterly direction.

(a) Using a scale of 1cm to 10 km, make a scale drawing of it’s journey.

(b) Use your scale drawing to find the bearing that the helicopter should take in order to return directly to the army base.

8. The diagram shown is a design for a kite. Calculate the length x cm. Do not use a scale drawing.

B

55°

32 cm

x cm

3 2 5

KU RE

9. The pie chart shown below shows the results of a survey of “Favourite TV Channels”.

The total number of people surveyed was 1600.

Use the pie chart to calculate the number channel. Round your answer to the neares

10. The shape below is rotated 90° clockwise Draw the shape in it’s new position.

120°

Sky Sports

Sky 1

VH-1

X

KU RE

Movie Channel

of people who preferred watch the movie t whole number.

about X.

3 3

KU

4 3

RE 11. READ THIS INFORMATION CAREFULLY The surface area of a sphere can be calculated using the formula

A = 4πr ²

Where r is the radius of the sphere The figure opposite shows a model helium balloon which is spherical in shape. The balloon has a radius of 12 centimetres. Calculate the area of material needed to make the balloon.

3 5

RE

KU 12. The wishing well shown in the diagram has a cylindrical spindle which, when turned, moves the bucket up and down the well.

An enlarged version of the spindle is shown below. The diameter of the spindle is 15 cm.

15 cm (a) Calculate the circumference of the end of the spindle.

(b) When the bucket is at the top, with its handle touching the spindle, the rope has wrapped around the spindle exactly 7 times. The bucket measures 45cm from the top of the handle to its base, as shown.

The distance to the bottom of the well is 3 8⋅ metres. Can the bucket sit on the bottom of the well ? You must give a reason for your answer.

45cm

[END OF QUESTION PAPER]


General Mathematics - Practice Examination E


Class



Pegasys 2005




Paper I

Teacher

Surname



c b a2 + b2 = c2

a


hypotenuse

xo


height


heightvertical

Pegasys 2005



adjacenttan

=

=

=

o

o

x

x

x

32

6254 ⋅−⋅

40083 ×⋅

756 ÷⋅

RE KU 1. Carry out the following calculations. (a) 66 % of £4⋅20 (2) (b) 11 (1) (c) 0 (1) (d) 49 (1) 2. Calculate the perimeter of this garden. (5) 14 m

8 m garden 8 m 3. (a) Factorise 18a – 27b (2)

(b) Solve algebraically the equation

3(2x + 1) = 4x (3)

Pegasys 2005

∠

73

KU RE 4. In the diagram AB = AC and BAD = 114o as shown.

(a) Find ∠CAB. (2) B

(b) Find ∠ABC. (2) 114o

D C A 5. (a) When John, a cyclist, had travelled a distance of 15 km he had completed

of his journey. What was the total length of his journey? (2)

(b) John travelled at an average speed of 10 km/h. Calculate the time taken for the whole journey, giving your answer in

hours and minutes. (3) 6. Sam’s class held a competition to find out who could hold their breath the longest.

The results, in seconds, are shown below: 34 56 82 65 44 61 78 32 45 52 51 63 49 47 39 56 25 43 47 41

(a) Construct a stem-and-leaf diagram to illustrate this data. (3)

(b) What is the median number of (2) seconds for this data?

Pegasys 2005

KU RE 7. Two shops are selling the same model of computer for the same price. One shop asks for a £200 deposit and 12 equal payments of £100. The other shop asks for a £500 deposit and 10 equal payments. How much should each payment be? (4)

END OF QUESTION PAPER

Pegasys 2005

General Mathematics Practice Exam E Marking Scheme - Paper 1

Give 1 mark for each • Illustrations for awarding each mark 1(a)

1(b) 1(c) 1(d)

• knowing to work out 32

• carry out calculation correctly • carry out calculation correctly • carry out calculation correctly • carry out calculation correctly

• 32 of £4⋅20

• £2⋅80 • 5⋅78 • 332 • 7⋅08

5 marks KU2.

• know to use Pythagoras’ Theorem to find sloping side (say x) • square and add numbers correctly • use Pythagoras correctly • know to add lengths • adding correctly

• 222 68 +=x • 10036642 =+=x• x = 10 m • Perimeter = 14 + 8 + 8 + 10 • 40 m

5 marks RE3(a) 3(b)

• correct common factor • correct bracket • expand bracket correctly • gather like terms correctly • solve equation

• and • 9(2a – 3b)

2 marks KU• 6x + 3 = 4x • 2x = −3 • 512

3 ⋅−−= orx 3 marks KU

4(a) 4(b)

• know to subtract 114o from 180o • subtract correctly • know to subtract from 180o • know to half above answer

• 180 – 114 • 66o • 180 – 66 = 114 • 114 ÷ 2 = 57o

4 marks KU5(a)

5(b)

• know to find 71 by dividing by 3

• know to find whole journey by multiplying by 7 • know to divide answer to (a) by speed • dividing correctly • writing answer in hours and minutes

• 15 ÷ 3 = 5 km

• 5 × 7 = 35 km 2 marks RE

• 35 ÷ 10 (or equivalent from (a)) • 3⋅5 hours • 3 hours 30 minutes

3 marks KU

Pegasys 2005

Marking Instructions for General Level - Paper 1 (cont.)

Give 1 mark for each • Illustrations for awarding each mark 6(a) 6(b)

• correct stem and showing key • correct leaves • putting leaves in correct order • finding 10th and 11th pieces of data (must be shown) • averaging the above two numbers

• • and • see below for diagram

3 marks KU • finding 47 and 49 • (47 + 49) ÷ 2 = 48

2 marks KU

7.

• know to work out total cost of computer • working out total cost correctly • know to subtract £500 from total cost • divides remainder by 10

• 200 + (12 × 100) • £1400 • 1400 – 500 = £900 • 900 ÷ 10 = £90

4 marks RE

Diagram for Question 6(a)

2

3 4 5 6 7 8

5 2 4 9 1 3 4 5 7 7 9 1 2 6 6 1 3 5 8 2 6 / 3 means 63 seconds

Pegasys 2005


General Mathematics - Practice Examination E


Class



Pegasys 2005



given only whercalculator

Paper II

Teacher

Surname


FORMULAE LIST



triangle: Gradient: Gradient =


vertical height

horizontal distance

opposite

adjacent

hypotenuse

xo

c b a2 + b2 = c2

a

oppositeo

Pegasys 2005



adjacenttan

=

=

=

o

o

x

x

x

1. Complete the pattern below so that it has rotational symmetry

of order 4 about point X: (3) 2. Erin has annual tax free allowances of £3500.

Erin pays income tax at the rate of 24% on the first £13 800 of taxable income and at the rate of 46% on the remainder. (a) Calculate the amount of income tax paid on the first £13 800 of taxable income. (2) (b) Calculate Erin’s gross income if she pays in total £6233 in income tax (5)

X

RE KU

Pegasys 2005

3. In a class there are 16 boys and 13 girls.

Four boys wear glasses and three girls wear glasses. A pupil is picked at random from the class. (a) What is the probability that the pupil is a boy? (2) (b) What is the probability that the pupil wears glasses? (2) (c) What is the probability that the pupil is a boy who wears glasses? (1) (d) A girl is picked at random from the class.

What is the probability that she wears glasses? (1)

4.

A window is in t

he shape of a rectangle and a semicircle , as shown. The

Calculate the area of the window in cm2.

rectangular part of the window is 80 cm

long and 1⋅5 m high.

(5)

80 cm

1⋅5 m

RE KU

Pegasys 2005

Pegasys 2005

A B

C

D

8 m KU RE

5. Nayeem’s horses’ field can be split into a right-angled triangle and an isosceles triangle as shown in the diagram.

15 m (a) AB = 8 m and BC = 15 m. Show that AC is 17 metres long. (3)

(b) Calculate the size of angle ACB, to the nearest degree. (3) (c) Given that AD is parallel to BC, state the size of angle DAC. (1)

(d) Hence calculate the length of DC correct to 1 decimal place. (5) 6. Anna was on holiday in Austria.

£1 = 21 ATS £1 = 3100 Lire

On a day trip to Italy, Anna noticed that she could pay for her lunch in either Austrian Schillings (ATS) or Italian Lire. Anna’s bill was either 9000 Lire or 78 ATS. Using the exchange rates shown, which currency gives Anna the best value for her money, and how much would she save by taking this option? (3)

KU RE 7. George went paragliding.

For the last part of his flight he glided in a perfect straight line until he landed.

The equation of this straight line is y = 1400 – 10x .

(a) Complete the table below for y = 1400 – 10x. (2)

Distance from take-off point (x)

Pegasys 2005

Height (y) 20 40 60 80

(b) Using the table in (a) draw the graph of the line y = 1400 – 10x on the grid below. (2)

y

1200

1000 Vertical height

above ground (in metres)

800

600

400 200 x 0 20 40 60 80 100 120 140 160 Horizontal distance from take-off point (in metres) (c) Write down the coordinates of the point where George landed. (2)

8. Elizabeth was on holiday in the Dolomites.

One of the roads where she was staying had lots of hair-pin bends. She noticed that the height of the road,above sea level, at each successive bend followed a pattern. The pattern is shown in the table below. (All heights are in metres above sea level) (a) Complete the table: (2)

No. of hair-pin bend (n) 1 2 3 4 5 10 Height above sea level (h) 1820 1832 1844

KU RE

(b) Find a formula connecting the number of the hair-pin bend and its height above sea level. (2)

(c) Elizabeth thought she saw a sign for a hair-pin bend with a height of 2000 m.

Was she correct? All working must be shown. (3)

(d) There are 28 hair-pin bends in total.

Calculate the height of this last bend above sea level. (2)

Pegasys 2005

21⋅ 5⋅

5⋅ 9⋅

21 ⋅

51 ⋅

KU RE 9. Michael is rolling hay into the

shape of a cylinder with diameter m and height 1 m, m

as shown in the diagram. m (a) Calculate the volume of this cylinder, in m3, correct to 2 decimal places. (3)

(b) The cylinder of hay is then wrapped in thin plastic sheeting.

Given that all the surfaces of the cylinder are covered, calculate the total surface area of the wrapping in square metres. (4)

(c) Jason makes bales of the same volume but makes them into the shape

of a cuboid instead.

If the length and breadth of the cuboid are 1 m and 0 m respectively, Calculate the height of the cuboid. (3)

10. Anton has a 4-digit security code for his mobile phone. 1st 2nd 4th 3rd The first digit is a 4 and the rest are

prime numbers less than 7. All of the digits are different.

List all six possible security codes for Anton’s phone. (3)

END OF QUESTION PAPER Pegasys 2005


General Mathematics - Practice Examination F


Class



Pegasys 2005




Paper I

Teacher

Surname



c b a2 + b2 = c2

a


hypotenuse

xo


height


heightvertical

Pegasys 2005



adjacenttan

=

=

=

o

o

x

x

x

1. Carry out the following calculations. (a) 12 % of £952 (2) 2

1

xxx −+ 32 2

(b) 38⋅7 + 3⋅51 (1) (c) 2⋅7 × 300 (1) (d) 63 ÷ 0⋅9 (1) 2. Calculate the size of ∠BCD in the diagram below. (3) 3. (a) Solve 6(x – 2) – 2(x – 8) = 0 . (3)

(b) Find the value of when x = 9. (3)

D 33o

C

B

A

RE KU

Pegasys 2005

Pegasys 2005

4. PQRS is a rectangle with diagonals intersecting at T. Calculate the length of ST. (4)

5. Calculate 4( writing your answer as an ordinary number. (2) )1073()101 24 ×⋅+×⋅

76

1211

32

1411

KU RE

R Q

T 10 cm

P S 24 cm

6. (a) What is the smallest number that 3, 7, 12 and 14 will all divide into? (1) (b) Hence write these fractions in order, starting from the smallest. (2)

Pegasys 2005

7. James puts his savings of £3400 into the bank, and receives interest at a rate of 4% per annum. (a) How much money will James have in his account at the end of the first year? (2) (b) James needs £3800 to buy a motorbike. For how many years does he have to invest his money so that he will have enough saved up? (3)

8. A survey is carried out to find out how many children are in each family. The results for one street are shown below.

KU RE

Number of children per family 0 1 2 3 4 5 Number of families 3 10 13 10 6 2

(a) Calculate the mean number of children per family. (3) (b) What percentage of these families has more than two children? (3)


General Mathematics Practice Exam F Marking Scheme - Paper 1


1(b) 1(c) 1(d)

• knowing to work out 81 (or otherwise)

• carry out calculation correctly • carry out calculation correctly • carry out calculation correctly • carry out calculation correctly

• 81 of £952

• £119 • 42⋅21 • 810 • 70

5 marks KU2.

• know angle in semi-circle is right-angle • calculate 3rd angle in triangle • calculate required angle

• ∠ABC = 90o • ∠ACB = 180 – (90 + 33) = 57o • ∠BCD = 180 – 57 =123o

3 marks RE

3(a) 3(b)

• multiply out of brackets correctly • gather like terms • solve for x • substitute number into expression • evaluates square and square root correctly • answer

• 6x – 12 – 2x + 16 = 0 • 4x = –4 • x = –1

3 marks KU• ( ) ( ) 99392 −+2 • 2×81 + 3×9 – 3 • 186

3 marks KU4.

• divide up diagram to make right-angled triangle • knows to use Pythagoras’ Theorem • uses Pythagoras correctly • answer

• • • ST2 = 52 + 122 • ST = 13 cm

4 marks RE5.

• removes standard form correctly • answer

• 41000 + 370 • 41370

2 marks KU6(a) 6(b)

• answer • puts fractions over common denominators • orders fractions from smallest to largest

• 84 1 mark KU

• 8466

8456

8477

8472

• 1211

76

1411

32

2 marks RE

12

T

5 S

Pegasys 2005



7(b)

• knows how to calculate interest • adds interest on to amount invested • attempts to calculate interest for further years • calculates amounts correctly • correct conclusion

• 0⋅04 × 3400 = 136 (or otherwise) • £3536

2 marks KU• 1⋅04 × 3536 = 3677⋅44 (or otherwise) 1⋅04 × 3677⋅44 = 3824⋅54 • as above • must invest for 3 years

3 marks RE8(a) 8(b)

• attempting to find total no. of children • finding total no. of houses • answer • knowing to choose 3, 4 or 5 children in family • knows to divide total by 50 • answer

• 0×3 + 1×10 + 2×13 + 3×10 + 4×6 + 5×2 = 100 • 3 + 10 + 13 + 14 + 8 + 2 = 50 • 100 ÷ 50 = 2

3 marks KU• 10 + 6 + 2 = 18 • 18 ÷ 50 • 36%

3 marks RE Total marks: KU 19 RE 15

Pegasys 2005


General Mathematics - Practice Examination F MATHEMATICS

Standard Grade - General Level

Class



Pegasys 2005




Paper II

Teacher

Surname


FORMULAE LIST


c b a2 + b2 = c2

a


hypotenuse

xo


height

horizontal distance


Pegasys 2005



adjacenttan

=

=

=

o

o

x

x

x

Pegasys 2005

KU RE 1. The shape ABCDEFGH is a regular octagon with diagonals crossing at O. 1. The shape ABCDEFGH is a regular octagon with diagonals crossing at O.

A B H C xo O G D F E (a) Calculate x, the angle shown at the centre of the shape. (2) (a) Calculate x, the angle shown at the centre of the shape. (2) (b) The octagon is rotated through 135o. (b) The octagon is rotated through 135o. What are the two possible images of triangle BOC under this rotation? (3) What are the two possible images of triangle BOC under this rotation? (3) 2. Mary’s business cards are cut from an A4 page, as shown. 2. Mary’s business cards are cut from an A4 page, as shown. Mary Higgins

Costume Designer

027 777 7777

5⋅1 cm

29⋅7 cm 8⋅7 cm 21⋅1 cm If one thousand of these cards are printed, calculate the total amount If one thousand of these cards are printed, calculate the total amount of waste paper accrued from making these cards. (4) of waste paper accrued from making these cards. (4)

Pegasys 2005

KU RE 3. Alan’s dad told him that the tree at the bottom of his garden was more than 20 metres tall. Alan thinks it is less than 20 metres.

32o 150 cm

30 m Alan measures the angle to the top of the tree with a clinometer. Who is correct, Alan or his dad? (Do not use a scale drawing). (4)

4. Two cylinders, each of radius 9 cm and height 20 cm, fit exactly into a rectangular box. (a) State the dimensions of the box. (3)

(b) Calculate the volume of empty space in the box. (4)

Pegasys 2005

MILEAGE CHART

Clea

rwat

er

Coco

a Be

ach

Crys

tal R

iver

Key

Larg

o

Key

Wes

t

Kiss

imm

ee

Mia

mi

Napl

es

Orla

ndo

Clearwater 143 60 314 410 70 275 165 106Cocoa Beach 143 140 249 345 65 191 220 50Crystal River 60 140 350 450 85 325 210 90Key Largo 314 249 350 96 284 55 144 294Key West 410 345 450 96 380 160 236 390Kissimmee 70 65 85 284 380 215 176 20Miami 275 191 325 55 160 215 107 232Naples 165 220 210 144 236 176 107 269Orlando 106 50 90 294 390 20 232 269

KU RE 5. The Harris family are going on holiday to Florida. They use the mileage chart shown to plan their journeys. (a) They hire a car in Key West and travel first to Miami, then on to Orlando and back to Key West. Calculate the total distance travelled. (2)

Easy Hire Mileage allowance: 75 miles per day For each additional mile: $0⋅20

(b) They hire the car for 7 days with Easy Hire.

How much extra do they have to pay the car hire company? (3)

(c) The Harris’ spend 15 hours 45 minutes travelling in the car, in total. Calculate the average speed of the car, to 1 decimal place. (2)

Pegasys 2005

KU RE 6. Lydia is making a prize-winning grid to raise money for charity. The grid is a rectangle, 20 squares long by 10 squares broad. There are 12 winning squares altogether.

What is the probability of picking a winning square? (3)

7. An isosceles triangle is cut from a square of length 30 cm, as shown.

20 cm 30 cm (a) Calculate the area of the isosceles triangle. (2) (b) Calculate the percentage of the square left over after the triangle is cut away. (3)

Pegasys 2005

KU RE

8. Caroline has designed some crazy paving for her garden path. Each paving stone is in the shape of a cross. Each cross is joined to the next on three sides, as shown below. (a) Complete the table: (2)

No. of paving stones (p) 2 3 4 5 14 No. of edges joined (e) 3 9

(b) Find a formula for calculating the number of edges joined (e), when you know the number of paving stones (p). (2) (c) Caroline completed the path with 117 edges joined altogether. How many paving stones were used? (2)

9. Factorise 18a – 27 (2)

10. 60 people were surveyed and asked for their favourite holiday destination. The results are shown in the pie chart. (a) How many people went to Italy on holiday? (2) (b) How many more people went to Spain than Italy? (3)

Italy

France

Spain 120o

RE KU


Pegasys 2005

General Mathematics - Practice Examination G



Class


Read Carefully 1. Answer as many2. Write your answ3. Full credit will be4. You may not us

© Pegasys 2005


questions as yoers in the spaces given only where a calculator

Paper I

Teacher

Surname




triangle: Gradient:

Gradient =



adjacentoppositetan

=

=

=

o

o

o

x

x

x


vertical height

horizontal distance

hypotenuse opposite

adjacent

xo

a2 + b2 = c2 c b

a

© Pegasys 2005

© Pegasys 2005

1. Carry out the following calculations. (a) 7⋅31 - 4⋅642 (1)

(b) 9⋅27 × 40 (1) (c) 25⋅2 ÷ 6 (1)

(d) (2) 187

65

+

KU RE

2. In the diagram below

• AC is parallel to DE • Angle CBE = 32o • Angle BDE = 47o.

Calculate the size of angle DBE. (3)

B A C32o 47o D E

3. (a) List all the prime numbers between 1 and 20 inclusive. (2)

(b) What is the probability that a number chosen at random from

the numbers 1 to 20 will be prime? (2) 4. A rope has to be fed through a pipe in the ground for the telephone wire to be connected

from the house to the telephone pole. All dimensions are shown in the diagram.

John has a 40 metre long rope to complete the job.

Is the rope long enough?

You must justify your answer with approp

25 m

30 m

Pipe

House

RE KU

© Pegasys 2005

Telephone Pole

(5) riate working.

5. The marks attained by 5 candidates in a test are shown.

(a) Complete the total scores for Susan, Frank and Jane. (2)

(b) The marks for the individual questions are shown below.

Construct a stem and leaf diagram to represent this data. (4)

(c) What is the median mark? (1) (d) The grades are calculated as follows using the total scores:

A 255 – 300 B 209 – 254 C 165 – 208 D 120 – 164 E 75 – 119

Write down the grades attained by each of the 5 students. (3)

Question John Aneela Susan Frank Jane 1 2 3 4 5 6

32 43 24 19 14 21

50 40 44 31 46 43

49 44 49 42 47 50

31 32 29 28 19 24

16 42 37 6

25 9

Total 153 254

RE KU

32 43 24 19 14 21

50 40 44 31 46 43

49 44 49 42 47 50

31 32 29 28 19 24

16 42 37 6

25 9

© Pegasys 2005

6. Complete the diagram so that it has rotational symmetry of order 4 about the point o. (3)


o

RE KU

© Pegasys 2005

General Mathematics Practice Exam G Marking Scheme - Paper 1

Give 1 mark for each • Illustrations for awarding each mark 1(a) 1(b) 1(c) 1(d)

• carry out calculation correctly • carry out calculation correctly • carry out calculation correctly • knows to find common denominator • carry out calculation correctly

• 2⋅668 • 370⋅8 • 4⋅2

• 18

715 +

• 921 ( )18

22

5 marks KU2.

• knows angle BED = 32o • knows angles in triangle add up to 180o • calculates correctly Candidate can also find angle ABD and use property of straight angle.

• • ∠ DBE = 180 – (47 + 32) • ∠ DBE = 101o

3 marks RE

3(a) 3(b)

• appears to know what a prime number is • lists all of the prime numbers between 1 & 20 • counts no. of prime numbers • divides this by 20 and simplifies

• 2, 3, 5, etc • 2, 3, 5, 7, 11, 13, 17, 19

2 marks KU• 8 prime numbers (or whatever they have in their own list)

• 52

208

= or 0⋅4

2 marks KU4.

• knows to use Pythagoras’ Theorem • Uses Pythagoras correctly • knows to square length of rope • squares correctly • correct conclusion

• 302 + 252 • 900 + 625 = 1525 • 402 • 1600 • rope is long enough since 1525 < 1600

5 marks RE5(a) 5(b) 5(c) 5(d)

• one or two correct totals • All three totals correct • Stem correct • Leafs correct • Leafs re-ordered • key present • Reads off median correctly • knows how to use table • 2 or 3 correct grades attained • 4 or 5 correct grades attained

• • Susan– 281, Frank – 163, Jane – 135

2 marks KU• See diagram at end of Marking Scheme • • •

4 marks KU• median = 32

1 mark KU• John – Grade D; Aneela – Grade B • Susan – Grade A; Frank – Grade D • Jane – Grade D

3 marks RE

© Pegasys 2005

Give 1 mark for each • Illustrations for awarding each mark 6. • Half turn symmetry correct

• 1st quarter turn symmetry correct • 2nd quarter turn symmetry correct

• See diagram below • •

3 Marks RE Question 5(b)

n = 30 3 1 represents 31 marks

0 6 9 1 9 4 9 6 2 4 1 9 8 4 5 3 2 1 1 5 7 4 3 0 4 6 3 9 4 9 2 7 25 0 0

0 6 9 1 4 6 9 9 2 1 4 4 5 8 9 3 1 1 2 2 7 4 0 2 2 3 3 4 4 6 7 9 95 0 0

Question 6 Total Marks for Paper I : KU 16 RE 14 © Pegasys 2005




Class



© Pegasys 2005





Paper II

Teacher

Surname



c b a2 + b2 = c2

a




adjacentoppositetan

=

=

=

o

o

o

x

x

xhypotenuse

xo

triangle: opposite

adjacent Gradient: vertical

height

horizontal distance

distancehorizontalheightvertical Gradient =

© Pegasys 2005

1. In the World’s Strongest Man contest the men have to carry a heavy weight

around the edge of a circle of circumference 30m.

Calculate the area of this circle. (4) 2. Adults in a community centre were asked to complete a questionnaire. The pie chart shows the number of males and females who took part in the survey.

(a) What percentage of people surveyed were male? (3) (b) Calculate the size of angle xo in the pie chart. (2)

xo

Male, 15

Female, 35

30 m

RE KU

© Pegasys 2005

3. (a) There are 4⋅546 litres in one gallon.

How many cubic metres (m3) are there in 3000 gallons? (4)

(b) Can 3000 gallons of oil fit in the tank shown below? (2)

4. The distance between Liverpool and Norwich is 240 miles. Sophie travelled between Liverpool and Norwich at an average speed of 50 mph.

How long, in hours and minutes, did it take Sophie to complete this journey? (3)

1⋅5 m

2⋅5 m

3⋅5 m

RE KU

© Pegasys 2005

5. (a) Solve the following equation 6x – 14 = 2(x + 5) (3)

(b) Factorise 27a2 + 18ab (3)

6. A painting was posted in a cylindrical tube of height 91cm and diameter 21cm .

Calculate the curved surface area of the tube. (3)

91 cm

21 cm

RE KU

© Pegasys 2005

7. (a) Complete the table below for y = 7 – 2x. (2) (b) Using the table above, draw the graph of the line y = 7 – 2x on the grid below. (2)

(c) On the same grid draw the graph of the line y = 3x – 3. (3)

(d) At what point do the two lines intersect? (1)

x – 1 3 5 y

y

–8

–4

8

4

–8 –4 0 4 8 x

RE KU

© Pegasys 2005

8. 30 × 29 × 28 × 27 × . . . × 3 × 2 × 1 is equal to 265252859812191058636308480000000

Write this number in scientific notation, giving your answer to 3 decimal places. (3)

9. Marie works 39 hours per week as a school secretary. Her basic rate of pay is £5⋅80 per hour with any overtime paid at time-and-a-half. In one particular week her gross salary was £287⋅10.

How many hours of overtime did she work? (4) 10. The distance between the tent pegs at A and B is 4⋅6 m and the angle of elevation

of the sides of the tent is 42o, as shown.

Calculate the height, h, of the tent. (4)

4⋅6 m

h

42o 42o B A

RE KU

© Pegasys 2005

11. (a) Karen is always forgetting part of her mobile telephone number. She only ever recalls the following information: The number is 086 * * * 6404 The missing 3 digits form a square number Two of these three digits are equal

List all possible combinations of the three missing digits. (3) (b) Karen also remembered that the three digits add up to 16, itself a square number.

Use this additional information to write down Karen’s telephone number. (2)

12. The box of Big Value Rice has a special offer. Calculate the missing percentage number which has been ripped from the label. (3)

% extra

Contents: 1035 g

Big Value Rice

free

RE KU

© Pega

Value Rice

Contents: 900 g

END OF QUESTION PAPER sys 2005

General Mathematics - Practice Examination H Please note … the format of this practice examination is the same as the current format. The paper timings are the same, as are the marks allocated. Calculators may only be used in Paper 2.

MATHEMATICS Standard Grad General Level

Class



Pegasys 2005




e - Paper I

Teacher

Surname



c b a2 + b2 = c2

a


hypotenuse

xo


height

horizontal distance


Gradient =

Pegasys 2005



adjacenttan

=

=

=

o

o

x

x

x

÷

65

KU RE1. Carry out the following calculations.

(a) 409⋅2 – 265⋅47

(1)

(b) 232⋅2 9

(1)

(c) 63⋅8 × 70 (1)

(d) of £72

(2)

2. The table below shows the average seasonal temperatures in Quebec.

Spring Summer Autumn Winter

Average temperature -2oC 19oC 13oC -13oC

(a) What is the difference between the highest and lowest average temperatures?

(2)

(b) One winter’s day the temperature in Quebec was 12 degrees below the average. What was the temperature that day? (1)

Pegasys 2005

Pegasys 2005

•

o

3. A dust mite is approximately 0⋅00023metres long. Write this number in standard form. 4. Complete the diagram below so that it has rotational symmetry of order 3 about the point O.

5. B ABCD is a rhombus.

A

• Angle DAC = 48 Calculate the size of angle ABC.

KUKU RE

(2)

O

(3)

C D

48o

(3)

( ) xyx 632 −+

17246 +=+ xx

6. (a) Multiply out the brackets and simplify: 3 .

Pegasys 2005

(b) Solve algebraically the equation: .

7. The senior school pupils in Maurice Academy have all been assigned a locker to keep their belongings safe. Each locker has a four digit security code. Each code must follow the same rules:

• S4 pupils begin with a 4 • S5 pupils begin with a 5 • S6 pupils begin with a 6 • All four digits must be different.

Kim, who is a sixth year pupil, has forgotten her number. She remembers that apart from one digit the rest are prime numbers less than 7. List all six possible codes for Kim’s locker.

1st digit

2nd digit

3rd digit

4th digit

REKU

(2)

(2)

32

0987

4 5 61

(3)

8. A bar gate bracelet is designed with 3 chain links between 2 solid bars as shown in the diagram below. (a) Complete the table below.

(b) Find a formula for calculating the number of chain links (c) when you know the number of bars (b). (c) How many bars would be in a bracelet which had 63 gold chain links? Working must be shown.

REKU

Number of bars (b) 2 3 4 5 6 10

Number of chains (c) 3 6 9

(2)

(2)

(3)


Pegasys 2005

General Mathematics Practice Exam H Marking Scheme - Paper 1

•

•

•65

•

••

•

••

•••

Give one mark for each ●

•

2

1(a) 1 carry out calculation correctly 1(b) 1 carry out calculation correctly 1(c) 1 carry out calculation correctly

1(d) 1 knowing how to find

2 carry out calculation correctly 2(a) 1 identifying highest & lowest temperatures

2 subtracting correctly 2(b) 1 subtracting 12 from winter temperature 3 1 number between 1 and 10 2 correct power of 10 4 1 knowing to rotate 1200 2 1st rotational symmetry correct 3 2nd rotational symmetry correct

Pegasys 2005

•

•

•

•61

• =× 512£

••

•

•• ×

1 143⋅73

1 25⋅8

1 4466

1 of £72 = £12 2 £60

5 marks KU

1 19 – (-13) 2 32oC

1 -25oC

3 marks KU

1 2⋅3 2 10-4

2 marks KU

3 marks RE

Illustrations for awarding mark

Give one mark for each ● 5 1 knowing AC is an axis of symmetry • 2 knowing diagonals are perpendicular • 3 calculating angle • 6(a) 1 breaking bracket correctly • 2 simplifying expression correctly • 6(b) 1 gathering like terms • 2 solving for x • 7 1 knowing 1st digit is 6 • 2 completing 3 lines correctly • 3 completing another 3 lines correctly • 8(a) 1 correct entries for 5 and 6 • 2 correct entry for 10 • 8(b) 1 and 2 correct formula • • 8(c) 1 substituting into formula • 2 and 3 solving for b • •

Pegasys 2005

•

•

•

• xyx 696 −+•

•

•4

13=x

•

•

• • 33 −= bc

• 6333 =−b• 663 =b• 22=b

1 angle CAB = 48o

2 angle ABD = 42o

3 angle ABC = 84o 3 marks RE

1 2 9y

1 4x = 13 2

4 marks KU 6 2 3 5 6 2 5 3 6 3 2 5 6 3 5 2 6 5 2 3 6 5 3 2 3 marks RE

1 12 & 15

2 27

1 & 2

1 2 3

7 marks RE

Illustrations for awarding mark

Total marks: KU 14 RE 16

General Mathematics - Practice Examination H Please note … the format of this practice examination is the same as the current format. The paper timings are the same, as are the marks allocated. Calculators may only be used in this paper.


Class



Pegasys 2005




Paper II

Teacher

Surname


FORMULAE LIST


c b a2 + b2 = c2

a


hypotenuse

xo


height

horizontal distance


Pegasys 2005



adjacenttan

=

=

=

o

o

x

x

x

13 += xy

13 += xy

1. Rachael won £4200 in Oldvillage Savings Bank a prize draw. She invested it with the Amount invested Annual rate of interest

Up to £2000 4⋅2% £2001 - £6000 4⋅4% £6001 - £10000 5⋅2% Over £10000 6⋅2%

Oldvillage Savings Bank. Calculate the interest she would receive after 8 months.

(4) 2. (a) Complete the table below for x -3 -1 0 1 3

y

(2) (b) Using the table above draw the line of on the grid below. y

10

-10 0 x 10 -10 (2)

Pegasys 2005

KU
RE

KU RE 3. Tazmin is making a fruit punch. She mixes orange juice, pineapple juice and lemonade in the ratio 2 : 3 : 5.

Tazmin wishes to make 2 litres of fruit punch. How many millilitres of orange juice will she need?

(4) 4. The ages of a group of adults travelling to a political rally are shown below. 22 28 18 34 33 31 27 27 19 45 27 44 34 35 37 30 43 37 34 28

(a) Illustrate this data in an ordered stem and leaf diagram. (4) (b) What is the median age of the group? (2)

Pegasys 2005

•

•

•

•

5. (a) The times recorded by a group of 5 snowboarders on a particular run were:

Calculate the mean time recorded by the snowboarders. (3) (b) A sixth boarder recorded a time of 37⋅21 seconds. How did his time compare to the mean time set by the others? (1)

6. The quadrilateral in the diagram is called an Isosceles Trapezium.

AD = BC

3⋅5cm A B the height of the trapezium is 4 centimetres AB is 3⋅5 centimetres long 4cm CD is 5 centimetres long Calculate the perimeter of the trapezium. D C 5cm

(4) 7. During 2005 Maurice Academy students ran their own General Election. 840 students voted in this election and the results are shown below. SNP and Labour gained exactly the same number of votes. (a) Write down the size of the angle (2) in the SNP sector. CONSERVATIVE

S N P (b) Calculate the number of students who voted SNP. LABOUR

(2)

Pegasys 2005

KU
RE
38⋅31secs 37⋅49secs 39⋅25secs 38⋅54secs 39⋅06secs

Pegasys 2005

8. A doorstop is in the shape of a triangular prism. The shape and measurements of the doorstop are shown in the diagram below.

(a) To be effective the angle of inclination (xo) must be between 10o and 15o. Will the doorstop shown above be effective?

(b) The doorstop shown above is made from hardwood.

1cm3 hardwood weighs 0⋅67grams. Calculate the weight of the doorstop to the nearest 10 grams.

9. (a) Factorise: 12x – 8y

(b) Solve the inequality: 4a – 5 > 11.

REKU

xo5 cm

3 cm

12 cm

(3)

(4)

(2)

(2)

KU RE 10. A rectangular field has a perimeter of 360 metres.

Its length is (2x –3) metres and its breadth is (x + 3) metres.

(2x - 3)m

(x +

3)m

(a) Using the information given above, construct an equation about the perimeter of this rectangle.

(2) (b) By solving the equation in (a), find the breadth of the field.

(2) 11. Two swimmers must complete a distance of 1500 metres.

Swimmer A decides to swim at a constant speed of 75 metres per minute without stopping. Swimmer B decides to swim at a faster speed of 80 metres per minute but rests for 10 seconds after every 150 metres.

If the two swimmers set off at the same time, who will finish first?

(5)

Pegasys 2005


General Mathematics - Practice Exam A Marking Scheme 1. 3x + 2 = 18 − x For 3x + x = 18 − 2 ……….(1) For 4x = 16 ……….(1) For x = 4 ……….(1) [ 3 marks KU ] 2. 4.6 × 106 = 4 800 000 ……….(1) ……….(1) [ 2 marks KU ] 3.

………. (1) each row [ 4 marks RA ]

4. ………. (2) each shape [ 4 marks RA ] 5. 3 (4x + 3) − 7x = 12x ………. (1)

+ 9 − 7x ………. (1) = 5x + 9 ………. (1) [ 3 marks KU ]

Crisps Chump Drink 1 4 1 2 5 0 4 0 0 0 10 0 0 3 2

6. For ∠ ABD = 90o (tangent) ……….(1) For ∠ ADB = 180o − (90+27)o = 63o ………. (1) For ∠ x = 180o − 63o = 117o ………. (1) [ 3 marks KU ]

7. (a) For mean = 15960007

……….(1)

= 228000 ……….(1) [ 2 marks KU ]

(b) For dividing by 24 i.e. 227760 ÷24 = 9490 ………. (1) For dividing by 365 9490 ÷ 365 = 26 years ………. (1) [ 2 marks RA ] 8. For calculating 1 years interest = £105 ………. (1) For calculating 6 months interest = £105 ÷ 2

= £52.50 ………. (1) For calculating total = £1500 + £52.50

= £1552.50 ………. (1) [ 3 marks KU ] 9. (a)

For point of intersection = (3, 9) ………. (1) [ 5 marks KU ] (b) For suggesting - different speeds, times, planes, or other suitable reason ………. (1) [ 1 mark RA ]

y

(2) each line

3

12

12 x

10. (a) For substituting into formula C = 30 + 27 + (18 × 2) ……….(1) For answer = £93 ……….(1) [ 2 marks KU ] (b) For 97 = 30 + 58 + 18t ………. (1) For 18t = 9 ………. (1) For t = ½ hr ………. (1) [ 3 marks RA ]

11. For k = 6

4 = 1 ………. (1) 5⋅ For k2 = 1 ………. (1) 5 2 252⋅ = ⋅ For Area = 2 × ………. (1) 25⋅ 2 16⋅

= cm4 86⋅ 2 ………. (1) [ 4 marks KU ]

12. For diagram ………. (1)

For using Pythagoras ………. (1) x2 = 102 + 102 ………. (1)

= 200 x = 14.14 ………. (1)

Perimeter = (4 × 14.14) + (4 × 50) = 256.56 cm ……….(1) [ 5 marks RA ]

13. Electro- city Deposit = 10% of £750 = £75 ………. (1) Payments = 12 × £58 = £696 ………. (1) Total = £75 + £696 = £771 ………. (1) TownTV Deposit = £50 Payments = 18 × £40 = £720 ………. (1) Total = £50 + £720 = £770 ………. (1) TownTV cheaper by £1 ………. (2) [ 7 marks KU ]

10

10 x

14. tan 39o = h10

………. (1)

h = 10 tan 39o ……….(1)

= 8.1 ………. (1) 10

39o h

Yes it can be cut safely, since 8.1 < 10 ………. (1) [ 4 marks RA ]

15. (a) For C ∝ s2 or C = ks2 ………. (1) 35 = 2500k ………. (1) k = 0.014 ………. (1) C = 0.014 s2 ………. (1) [ 4 marks KU ]

(b) C = 0.014 s2 = 0.014 × 900 ………. (1) = £12.60 ………. (1) [ 2 marks KU ]

C 2 3 4 5 6 7 N 2 4 6 8 10 12

……….(2)

(b) N = 2C − 2 ……….(2)

(c) N = (2 × 12) − 2 ……….(1) = 22 ……….(1)

(d) 36 = 2C − 2 ……….(1) 38 = 2C ……….(1) C = 19 ……….(1)

(e) 10m = 1000 cm ………. (1)

No of patterns = = 25 ………. (1)

No of crosses = 25 × 2 ………. (1) = 50 ………. (1) [ 13 marks RA ]

17. Time from 9.15 – 1200 = 2h 45 m ………. (1)

S = D ………. (2) T= =

2002 75

72 7.

⋅

No. He will break the limit ………. (1) [ 4 marks RA ] (pupils may work out journey time for 70mph etc.)

16. (a)

1000

40

KU RA40 40

Totals

General Mathematics - Practice Exam A Marking Scheme

1. For 10x − 4 < 16 . ......... (1) 10x < 20 ......... (1)

x < 2 ……. (1) [ 3 marks KU ]

2. 1.08 × 108 ……. (1) for number ……. (1) for power of 10 [2marks KU ]

3.

cutlery pots toaster towels lamp mugs glasses radio √ √ √ √ √ √

√ √ √ √ √ √

√ √ √ or any other acceptable possibility [ 5 marks RA ]

4. For a = 90o (angle in a semi-circle) …… (1) For b = [180 − (47 + 90)]o …… (1) = 43o …… (1) [ 3 marks KU ]

5. (a) i) C = 50 + (25 × 40) + (20 × 8) ……. (1) = 1210 .......... (1) [ 2 marks KU ]

ii) mean cost = peopleofnumberttotal cos ……. (1)

= 40

1210£ ……. (1)

= £30.25 ……. (1) [3 marks KU]

(b) 3200 = 50 + (25 × 110) + 20b ……. (1) 3200 = 2800 + 20b 400 = 20b ……. (1) b = 20 Twenty bottles of champagne can be ordered. ... (1) [ 3 marks RA ]

6. (a) Number of books =

535

1545

2060 ×× ……. (1)

= 3 × 3 × 7 ……. (1) = 63 ……. (1) [ 3 marks KU ] (pupils may find an arrangement which is not the max. marks3

2 ) (b) weight of books = 63 × 800g = 50400g ……. (1) weight of box + books = 50400 + 300 = 50700g ……. (1) = 5.07 kg ……. (1) [ 3 marks RA ]

(1) each

7. (a) (b) (1) for axes (2) for lines

[ 3 marks KU ] (c) Hasty Hires ……. (1) (d) VG Van Hire ……. (1) [ 2 marks RA ]

VG Van Hire Number of miles 10 20 30 40 50 60

Cost (£) 60 70 80 90 100 110 Hasty Hires Number of miles 10 20 30 40 50 60

Cost (£) 45 60 75 90 105 120 [ 4 marks KU ]

8. (a) 12x − 4y = 4 (3x − y) .......... (1) for common factor 4 .......... (1) for remaining bracket [ 2 marks KU ]

9. (a) Saveway : 3 for 2 ⇒ 6 for 4 ……. (1) 4 × £1.24 = £4.96 ……. (1)

Winterfield : 3 bottles costs £2.51 6 bottles cost 2 × £2.51

= £5.02 ……. (1) Freshco : Buy 3 get 3 at ½ price ……. (1) 3 × £1.24 = £3.72 3 × £0.62 = £1.86 ……. (1) total = £5.58 ……. (1) Best value for money − Saveway ……. (1) [ 7 marks RA ] (b) 6 × £1.24 = £7.44 Saving = £7.44 − £4.96 ……. (1)

= £2.48 ……. (1) [ 2 marks KU ]

10 20 30 40 50 60

80

20

60

40

100

120

VG Van Hire

Hasty Hires

11. Area of radiator A = 9000 cm2 ......... (1) U ∝ A U = kA ......... (1) 3 = 9000 × k

k = 1/3000 ......... (1)

U = 3000

1 A ......... (1)

Area of radiator B = 3600 cm2 ......... (1)

U =3000

1 × 3600

= 1.2 kW ......... (1) [ 6 marks KU ]

12. T = SD =

90498 .......... (1)

= 5.53 h = 5 h 32 min .......... (1)

Arrival (UK time) = 7.15 am + 5 h 32 min =12.47 pm .......... (1)

Arrival (French time) = 12.47 pm + 1 h = 1.47 pm .......... (1) [ 4 marks RA ]

13. (a) For OA = 50 cm .......... (1) [1 mark KU] OA2 = OC2 + AC2 .......... (1) or knowing to use Pythagoras OC2 = 502 − 352

= 1275 .......... (1) OC = 35.7 .......... (1) = 36 cm to the nearest cm ….. (1) [ 4 marks RA ]

10. (a) For £94.66 × 48 .......... (1) = £4543.68 .......... (1)

(b) £4543.68 − £3000 = £1543.68 .......... (1)

(c) 1003000

68.1543 × .......... (1)

= 51% .......... (1) [ 5 marks KU ]

14. (1) for reflection A (1) for reflection B (2) for reflection C

[ 4 marks RA ] 15. (a) [3 marks KU] (b) B = 3F − 3 ……. (2)

(c) B = (3 × 20) − 3 ……. (1) = 57 ……. (1)

(d) 30 = 3F − 3 ……. (1) 33 = 3F ……. (1) F = 11 ……. (1) [7 marks RA] 16. (a) For isosceles ……. (1) [1 mark KU]

(b) For knowing to split isosceles triangle into rt ∠ ’d triangles ……. (1) ……. (1)

sin 3o = 23200

x ……. (1)

x = 1214.2 ……. (1)

distance AB = 2 × 1214.2 = 2428.4 ……. (1) = 2428 mls to the nearest mile. ……. (1) [6 marks RA] 17. (a) (i) 6 ……. (1) (ii) 36 ……. (2) [3 marks KU] (b) 6 2 = 36 (or 6×6) ……. (1) [1 mark RA] (c) (i) 10 ……. (1) (ii) 100 ……. (2) [3 marks KU] (d) 102 = 100 ……. (1) [1 mark RA]

Totals

K U R A

49 47

(2) for 4,8,10 (1) for 18

3o

23200 x

number of fish (F) 2 3 4 5 6 10

number of birds (B) 3 6 9 12 15 27

A

B C

General Mathematics - Practice Exam C Marking Scheme

1. 1.2 × .......... (1) for number 310−

.......... (1) for power of 10 [ 2 marks KU ] 2. (a) For 4 – (-1) = 5°C .......... (1) (b) For -1 + 9 = 8°C .......... (1) [ 2 marks KU ] 3. (a) For 0.07 × £12600 .......... (1) = £882 .......... (1)

£882 + £12600 = £13482 .......... (1) [ 3 marks KU ]

(b) £1062 × 12 .......... (1) for multiplying by 12 = £12744 .......... (1) (or £13482 12÷ etc.)

No. Maggie has been underpaid by £738 per year. .......... (1) [ 3 marks RA ] (or £61.50 per month) 4. (a) For plotting points .......... (1) For joining points .......... (1)

(b) For PR = 5 + 5 .......... (1) 2 2 2

= 50 .......... (1) PR = 7.1 .......... (1) (any rounding ok) [ 5 marks KU ] 5. For 3x – 4 = 20 .......... (1) 3x = 24 .......... (1) x = 8 .......... (1) [ 3 marks KU ]

6. (a) For 2601122

××1 .......... (2) (or equivalent)

= 14560 cm 2 .......... (1) [ 3 marks KU ] (b) A rec = 160 × 260 = 41600 cm .......... (1) 2

A Plain = 41600 – 14560 = 27040 cm 2 .......... (1) [ 2 marks RA ]

(c) 10041600

×27040 .......... (2)

= 65% .......... (1) [ 3 marks RA ]

7. (a) For 4 .......... (1) 20630 −−+ aa 10 a2− .......... (1) For -2a .......... (1) For 10

(b) For 3b 2 - 6b .......... (1) For 3b 2

.......... (1) For – 6b [ 5 marks KU ] 8.

.......... (3) (1 mark for each correct quadrant)

[ 3 marks KU ] 9. For ∠ OBA = 50° .......... (1) ∠ BOC = 50° .......... (1) x = 40° .......... (1) [ 3 marks KU ] 10. For knowing to change 160 cm into 1.6m .......... (1)

scale factor = 43 ⋅

102 = 30 .......... (2) (pupils may use equal fractions)

Hotel = 30 × 1.6 = 48 metres .......... (1) [ 4 marks KU ]

11. For total parts = 7 .......... (1)

Red = 74 of 42 .......... (1) Award mark for

74

= 6 × 4 = 24 .......... (1) For ans 24 [ 3 marks RA ]

12. (a) 40 miles .......... (1) [ 1 mark KU ]

(b) 1 hr + 1.5 hr + 45 mins .......... (1) = 3 hrs 15 mins or 3.25 hrs .......... (1) [ 2 marks RA ]

(c) S = TD =

25.3160 .......... (1) For formula

.......... (1) For working = 49.2 mph .......... (1) [ 3 marks KU ]

13. (a) C = π = × 50 .......... (1) d π C = 157 cm .......... (1)

Perimeter = 80 + 80 + 157 = 317 cm .......... (1) [ 3 marks RA ] (b) r = 25 cm = 0.25 m .......... (1) A circle = π r = × 0.25 .......... (1) 2 π 2

= 0.2 m 2 (0.196) .......... (1) A glerec = 0.8 × 0.5 = 0.4 .......... (1) tan

A total = 0.4 + 0.2 ≈ 0.6 m 2 .......... (1) [ 5 marks RA ]

(c) For using 3.17 metres .......... (1) For 3 × .......... (1) 85

04.2£90.017 =⋅

For 60 .2£40.3 =× .......... (1) ⋅For final answer .... £4.89 .......... (1) [ 4 marks RA ]

14. (a) ...... (2) for 16, 21, 26

hB

(b) B

(c) 1 5 h 15. S S V

S 16. For

t

Y

1 2 3 4 5 10 6 11 16 21 26 51
..... (1) for 51 [ 3 marks KU ]
= 5h + 1 .......... (2) [ 2 marks RA ]

20 = 5h + 1 .......... (1) h = 119 .......... (1) = 23.8 no it is not possible. .......... (1) [ 3 marks RA ]

pecs R Us : £120 + £12 = £132 .......... (1)

pec Express : £130 .......... (1) ision Direct : 20% of £110

= £22 .......... (1) frames = £88 .......... (1) 88 + 26 + 12

= £126 .......... (1) o Vision Direct is the cheapest .......... (1) [ 6 marks RA ]

knowing to use tan .......... (1)

an x = 157 470 ⋅≈ .......... (1)

x = 25.2° .......... (1) es the ramp can be used. .......... (1) [ 4 marks RA ]

TOTAL KU = 40 TOTAL RA = 40

General Mathematics Practice Exam D Marking Scheme - Paper 2 1. (c) ans: 3.9 ( 0 2⋅ ) 3 KU ± (a) • interperet scattergraph 1 (b) • 1 draw line of best fit (c) • 1 use line of best fit to estimate

value 2. ans: 123, 423, 143, 243 3 RE 1 interpret code • 2 take a systematic approach • take a systematic approach 3• 3. ans: 2.9 m 4 RE 1 strategy • 2 carry out strategy • evaluate length of hypotenuse 3• 4 round answer • 4. (a) ans: graph 1 KU 1 plot coordinate points •

(b) ans: 53 2 KU

1• know how to find gradient 2 find gradient • 5. (a) ans: 5.84 2 KU 1 know how to calculate mean • 2 calculate mean • (b) ans: 4 1 KU 1 calculate range • 6. ans: 249.73 m² 4 RE 1 know how to calculate radius • 2 know how to calculate area of a circle • know how to calculate area of rectangle 3• 4 carry out subtraction •

1••

1•± ⋅

•

•3•

••

3••

1•

1••

1••

1•

1••

3••

mark X at (4.3,4.6)

1 reasonable attempt to draw line value consistent with line of best

fit ( 0 2 ) 1 all combinations have 2 or 4 as 2nd

digit 2 all combinations end in a 3 four correct codes 1 Pythagoras theorem 2 diameter² = 2² + 2² diameter = 2.83 4 diameter = 2.9 (must round up)

3 points correctly plotted

any valid method

2 correct answer

(a) 146 ÷ 25 2 5.84 (b) 4 years

4 m 2 A = π × 16 = 50.27 A = 25 × 12 = 300 4 249.73 m²


7. (a) ans: scale drawing 3 KU 1 interpret bearing and draw angle correctly • 2 interpret compass point and draw •

angle correctly use scale 3• (b) ans: 2 KU

1• identify appropriate angle 2• measure angle correctly

8. ans: 22.9 cm 5 KU 1 half width of kite • 2 identify valid trogonometric ratio • set up ratio 3• 4 evaluate trigonometric function • process statement and calculate x 5• 9. ans: 533 3 KU 1 know how to use angle at centre • 2 carry out calculation • round to nearest whole number 3• 10. ans: diagram 3 RE 1 rotate through 90° about X • 2 rotate through 90° about X • rotate shape through 90° 3• 11. ans: 1808.64 cm² 4 RE 1 identify radius • 2 square radius • calculation 3• 4 correct answer •


1• ±• ±

3•

1•2• ±

•2•

3•16x

4•

5•

1•360120

•3•

1•

•3•

••

3••

55° ( 2°) 2 135° ( 2°) both lines drawn correctly

284° ( 2°)

1 16 cm

tan

tan 55° =

1.428m (may be implicit in next mark)

x = 16 × tan 55° = 22.9 cm

2 533.3333 533

one part rotated (correct position and length)

2 . Further part rotated complete shape rotated 1 r = 12 2 A = 4 × π × 12² A = 4 × π × 144 4 A = 1808.64 cm² (1809.56 cm²)

12. (a) ans: 47.12 cm 3 KU 1 knowing to use circumference formula • 1• C= πd 2 calculation • 2• C = π × 15 correct answer 3• 3• C = 47.12 cm (b) ans: No – rope too short 5 RE 1 changing metres to cm • 1• 3.8 m = 380 cm 2 multiplying circumference • 2• 7 × 47.1 = 329.7 cm adding bucket height 3• 3• 329.7 + 45 = 374.7cm 4 subtraction • 4• 380 – 374.7 = 5.3cm correct answer and reason 5• 5• No ..... the rope is 5.3cm short. ≈

TOTAL 48

KU - 25 RE - 23


General Mathematics Practice Exam E Marking Scheme - Paper 2

Give 1 mark for each • Illustrations for awarding each mark 1.

• knows how to rotate through 180o • knows how to rotate through 45o • completed diagram

• see completed diagram at end of marking scheme no marks to be given for reflecting diagram

3 marks RE2(a)

2(b)

• knows how to find 24%

• finding percentage correctly • know to subtract £3312 from £6233 • know to divide by 46% to find remainder of taxable income • dividing correctly • know to add •1 and •3 onto tax free allowance • adding correctly

• 8001310024 ×

• £3312 2 marks KU

• 6233 – 3312 = £2921 • 2921 ÷ 0⋅46 (or equivalent) • £6350 • £3500 + £13800 + £6350 • £23650

5 marks RE3(a) 3(b) 3(c) 3(d)

• know to calculate total no. of pupils • calculates probability • know to calculate total no. who wear glasses • calculates probability

• calculates probability • calculates probability

• 16 + 13 = 29 • 29

16 2 marks KU

• 4 + 3 = 7 • 29

7 2 marks KU

• 294

1 mark KU

• 133

1 mark KU

4.

• know to change 1⋅5 metres into cm • finding area of rectangle • knows how to find area of semi-circle • findind area correctly • adding two areas together

• 1⋅5 m = 150 cm • Area = 150 × 80 = 12 000 cm2 • 0⋅5 × 240×π• 2512cm2 (if 143 ⋅=π ) • 14512 cm2

5 marks KU5(a)

5(b)

• know to use Pythagoras’ Theorem • square and add numbers correctly • show that AC = 17 by taking square root. • know to use trigonometry • use trig. ratio correctly • finds correct angle

• AC2 = 152 + 82 • = 225 + 64 = 289 • AC = 17 m

3 marks KU• tan = .......... • tan ACB = 15

8 • ACB = 28o

3 marks KU

Pegasys 2005


Give 1 mark for each • Illustrations for awarding each mark 5(c) 5(d)

• correct angle stated • know to half angle of 28o as triangle is isosceles and create 2 congruent right-angled triangles • and • uses trigonometry correctly • calculates x i.e. half of DC • finds length of DC

• angle DAC = 28o (alternate angles) 1 mark KU

• 28 ÷ 2 = 14o • and • sin 14o = 17

x • x = 4⋅11 m • DC = 8⋅22 m

5 marks RE6.

• knows to divide by exchange rate • converts prices to £ correctly • draws correct conclusion

• 9000 ÷ 3100 and 78 ÷ 21 • £2⋅90 and £3⋅71 • It is cheaper for Anna to pay in Lire, by 81p.

3 marks RE7(a) 7(b) 7(c)

• two coordinates correct • another two coordinates correct • straight line with correct x-intercept • straight line with correct y-intercept • know that ground level is when y = 0 • correct coordinates

• • (20, 1200), (40, 1000), (60, 800) (80, 600)

2 marks KU• straight line cutting x-axis at 140 • straight line cutting y-axis at 1400

2 marks KU• writes down coordinate where y = 0 • (140, 0) or alternative depending on pupil’s own line.

2 marks RE8(a) 8(b) 8(c) 8(d)

• two correct entries in table • third entry correct • and • correct formula • put formula = 2000 • solve equation • correct conclusion • know to put n = 28 in formula • correct height

• and • (4, 1856), (5, 1868), (10, 1928)

2 marks RE• and • h = 12n + 1808 or equivalent

2 marks RE• 12n + 1808 = 2000 • n = 16 • yes, she was correct as answer is a whole number.

3 marks RE• h = (12 × 28) + 1808 • h = 2144 m

2 marks RE9(a)

• knows how to calculate volume • substitutes correct value for r • correct calculations (ignore rounding – only for guidance)

• V hr2π=• = 5160 2 ⋅×⋅×π• = 1 70⋅ m3

3 marks KU

Pegasys 2005

Give 1 mark for each • Illustrations for awarding each mark 9(b) 9(c)

• knows to find surface area • calculates curved surface area correctly • calcuates area of 2 circular ends (i.e. top and bottom) • adds areas together

• knows volume of cuboid = 1 m70⋅ 3 • knows to divide volume by (length × breadth) • calculates height correctly

• attempts working • 5121 ⋅×⋅×π = 5 m65⋅ 2 • = 2 m260 2 ×⋅×π 26⋅ 2 • Surface area = m917 ⋅ 2

4 marks RE• 1 70⋅ = l × b × h

• 9051

701⋅×⋅

⋅=h

• 1 26⋅ m 3 marks RE

10.

• 2 or 3 correct combinations • 4 or 5 correct combinations • all 6 correct combinations

• 4 2 3 5 4 2 5 3 4 3 2 5 4 3 5 2 4 5 2 3 4 5 3 2

3 marks RE Total for Papers I and II : KU 49 RE 48 Diagram for Question 1 X

Pegasys 2005

General Mathematics Practice Exam F Marking Scheme - Paper 2


1(b)

• know to divide 360o by 8 • answer • calculate no. of segments • rotates clockwise • rotates anti-clockwise

• 360 ÷ 8 • 45o

2 marks KU• 135 ÷ 45 = 3 parts • triangle EOF • triangle HOG

3 marks KU2.

• calculates no. of pages • calculates area of business cards • calculates area of page • calculates waste paper for whole batch

• 1000 ÷ 10 = 100 pages • 8⋅7 × 5⋅1 ( ×10) = 443⋅7 cm2 • 21⋅1 × 29⋅7 = 626⋅67 cm2 • Waste = (626⋅67 – 443⋅7) × 100 = 18297 cm2

4 marks RE3.

• uses correct trigonometric ratio • calculates opposite side correctly • calculates height of tree correctly • conclusion

• tan 32o = 30h

• h = 18⋅75 m • height = 18⋅75 + 1⋅5 = 20⋅25 m • Alan’s dad is correct

4 marks RE 4(a) 4(b)

• calculates length • calculates breadth • calculates height • calculates volume of box • calculates volume of cylinder • multiplies volume of cylinder by 2 • calculates space left in box

• 4 × 9 = 36 cm • 2 × 9 = 18 cm • 20 cm

3 marks KU• 36 × 18 × 20 = 12960 cm3 • cm38508920922 ⋅=××= ππ hr 3 • 5089⋅38 × 2 = 10178⋅8 cm3 • Space = 12960 – 10178⋅8 = 2781⋅2 cm3


• finds distances from mileage chart • adds distances correctly • calculates total mileage allowed • calculates extra miles travelled • calculates cost • uses correct formula • answer

• Key West to Miami = 160 miles Miami to Orlando = 232 miles Orlando to Key West = 390 miles • Total = 782 miles

2 marks KU• 7 × 75 = 525 miles • 782 – 525 = 257 miles • 257 × 0⋅20 = $51⋅40

3 marks RE

• 7515

782⋅

==TDS

• 49⋅7 mph 2 marks KU

Pegasys 2005

Marking Instructions for General Level - Paper II (cont.)

Give 1 mark for each • Illustrations for awarding each mark 6

• finding no. of squares on grid • knowing how to find probability • simplifying answer

• 20 × 10 = 200 • 200

12 • 50

3 or 0⋅06 3 marks RE

7(a) 7(b)

• knows how to work out area of triangle • calculates area correctly • calculates amount of waste • knows to divide by area of square • calculates %

• Area = 21 × 30 × 20

• 300 cm2 2 marks KU

• 900 – 300 = 600 cm2

• 900600

• 3266 %


• entries 6 and 12 in table • entry 39 in table • and • correct formula • making equation • solving equation

• see table below • see table below

2 marks RE• and • e = 3p – 3

2 marks RE• 3p – 3 = 117 • 3p = 120 p = 40 i.e. 40 paving stones used

2 marks RE9.

• common factor • bracket

• 9 • (2a – 3)

2 marks KU10(a) 10(b)

• knowing to work out one quarter • answer • calculate missing angle in pie chart • calculate fraction of pie chart • calculate no. of people

• 41 of 60

• 15 people 2 marks KU

• 360 – (90 + 120) = 150o

• 125

360150 or × 60 = 25 people

• 25 – 15 = 10 people more go to Spain 3 marks KU

No. of paving stones (p) 2 3 4 5 14 No. of edges joined (e) 3 6 9 12 39

Question 8: Total marks: KU 21 RE 27

Pegasys 2005

General Mathematics Practice Exam G Marking Scheme - Paper 2

Give 1 mark for each • Illustrations for awarding each mark 1. • knows how to find radius

• finds radius correctly • knows how to calculate area • calculates area correctly

• 30 = 2 π r ; r = 30 ÷ 2π • 4⋅77 m • A = π r2 = π × 4⋅772 • 71⋅48 m2

4 marks RE2(a) 2(b)

• knows to add number of males and females • knows to divide no. of males by total • finds % correctly • knows to calculate 30% of 360o or 3/10 of 360o • calculates angle correctly

• 15 + 35 = 50 • 15 ÷ 50 • 30%

3 marks KU• 0⋅3 × 360 etc. • 108o

2 marks KU3(a) 3(b)

• knows to calculate no. of litres in 3000 gallons • calculates correctly • attempts to convert litres to cubic metres • converts correctly • finds volume of tank • correct conclusion (consistent with answer to (a))

• 3000 × 4⋅546 • 13638 litres • ÷ 1000 or converts to ml first • 13⋅638 m3

4 marks RE• 3⋅5 × 2⋅5 × 1⋅5 = 13⋅125 m3 • 3000 gallons will not fit in tank

2 marks RE4.

• knows how to find time • finds time correctly • converts correctly to hours and minutes

• T = D ÷ S • T = 240 ÷ 50 = 4⋅8 hours • 4 hours 48 minutes

3 marks KU5(a) 5(b)

• multiplies correctly out of the brackets • gathers like terms correctly • finds x • knows to put into brackets • finds common factor • finds correct terms inside bracket

• 6x – 14 = 2x + 10 • 6x – 2x = 10 + 14; 4x = 24 • x = 6

3 marks KU• • 9a • 9a(3a + 2b)

3 marks KU6. • knows how to find curved surface area

• substitutes correctly for r and h • correct answer

• 2 π rh • 2 × π × 10⋅5 × 91 • 6003⋅58 cm2

3 marks KU7(a) 7(b) 7(c)

• any one correct entry • all three correct entries • points plotted correctly • line drawn through points • finds correct co-ordinates • plots points correctly • draws line through points

• • –1 → 9; 3 → 1; 5 → -3

2 marks KU• (-1, 9) , (3, 1) , (5, -3) • graph

2 marks KU• any suitable co-ordinates (minimum 2) • •

3 marks KU

© Pegasys 2005

Give 1 mark for each • Illustrations for awarding each mark 7(d) • states point of intersection of two lines

(consistent with candidate’s graph) • (2, 3) or otherwise

1 mark RE8. • finds number between 1 and 10

• rounds number to 3 decimal places • finds correct power

• 2⋅652528….. • 2⋅653 • 2⋅653 × 1032

3 marks KU9. • finds basis wage

• subtracts basic wage from gross salary • finds rate of pay for overtime • finds no. of hours of overtime worked

• 39 × 5⋅80 = £226⋅20 • 287⋅10 - 226⋅20 = £60⋅90 • 5⋅80 × 1⋅5 = £8⋅70 • 60⋅90 ÷ 8⋅70 = 7 hrs overtime

4 marks RE10. • calculates adjacent side in triangle

• identifies correct trig ratio • uses ratio correctly • finds height of tent

• 4⋅6 ÷ 2 = 2⋅3 m • tangent ratio • tan 42o = h/2⋅3 • h = 2⋅3 tan 42o = 2⋅07 m

4 marks RE11(a) 11(b)

• Makes attempt at listing square numbers • Lists all three digit square numbers (may be implied) • Identifies numbers which have two digits equal • identifies correct three digits • identifies correct telephone number

• 100, 121, 144, etc • • 100, 121, 144, 225, 400, 441, 484, 676, 900

3 marks RE• 484 • 086 484 6404

2 marks RE12. • subtracts to find extra amount in grms

• knows to divide difference by 900 (i.e. constructs a fraction) • multiplies by 100 to convert to %

• 1035 - 900 = 135g • 900

135

• %15100900135 =×

3 marks RE Total Marks for Paper II : KU 27 RE 27 Total marks for Papers I and II KU 43 RE 41 © Pegasys 2005

General Mathematics Practice Exam H Marking Scheme - Paper 2

• 4200£%44 ×⋅

•

• 80184£128

⋅×

•

0 1

1

•

•

•

• ×

1

2 £184⋅80 3

4 £123⋅20

4 marks KU

x -3 -1 0 1 3

y -8 -2 1 4 10

2 marks KU

2 marks KU

1 2 litres = 2000 millilitres

2 total shares = 10

3 multiplying factor = 200

4 200 2 = 400millilitres 4 marks RE

Illustrations for awarding mark Give one mark for each ●

1 1 identify correct rate of interest • 2 correctly calculate yearly interest • 3 strategy for calculating monthly interest • 4 answer • 2(a) 1 substitute x values into formula • 2 correctly evaluates formula • 2(b) 1 points plotted correctly • 2 line drawn through points • 3. 1 change litres to millilitres • 2 & 3 correct strategy • • 4 correct final answer •

Pegasys 2005

Pegasys 2005

•

•

•

•

• •2

3331+

• •

•

•

•

•

•

•

•

•

Give one mark for each ● Illustrations for awarding mark

4(a) 1 stem correct 1 8 9 2 2 7 7 7 8 8

2 leafs correct 3 0 1 3 4 4 4 5 7 7 4 3 4 5

3 leafs re-ordered 1 8 = 18

4 key stated n = 20 4 marks KU

4(b) 1 correct strategy 1

2 answer 2 32 2 marks KU 5(a) 1 finds total of 5 times 2 knows to divide by 5 3 answer 5(b) 1 makes valid comparison 6. 1 identifies right angled triangle 2 knows to use Pythagoras Theorem 3 calculates sloping edge 4 calculates perimeter

•

•

•

•

•

• 222 4750 +⋅=BC

•

•

1 192⋅65 secs

2 192⋅65 ÷ 5

3 38⋅53 secs 3 marks KU

1 faster time/less than the mean etc. 1 mark KU

B1

4cm

C0⋅75cm

2

3 BC = 4⋅1cm

4 Perimeter = 2(4⋅1) + 3⋅5 + 5 = 16⋅7cm

4 marks RE

7(a) 1 correct strategy • • 1 2

90360 −

2 calculates angle • • 2 135o 2 marks KU

7(b) 1 calculate fraction of pie chart • • 1 83

360135

=

2 calculate number of people • • 2 84083

× = 315 students

2 marks KU

8 (a) 1 uses correct trigonometric ratio • • 1 123tan =x

2 calculates angle correctly • • 2 x = 14⋅04o 3 conclusion • • 3 The stop is effective as 10 <14⋅03 <15 3 marks RE

8(b) 1 calculates C.S.A. • • 1 C.S.A. = 21831221 cm=××

2 calculates volume • • 2 Volume = 18 ×5 = 90cm3 3 calculates weight correctly • • 3 Weight = 90× 0⋅67 = 60⋅3g 4 rounds correctly • • 4 60g 4 marks RE 9(a) 1 correct common factor • • 1 4 2 bracket • • 2 3x – 2y 2 marks KU 9(b) 1 collects like terms • • 1 4a > 16 2 solves correctly • • 2 a > 4 2 marks KU

Illustrations for awarding markGive one mark for each ●

Pegasys 2005

10(a) 1 correct strategy • • 1 Perimeter = 2l + 2b 2 states equation • • 2 ( ) ( ) 36032322 =++− xx 2 marks RE 10(b) 1 correctly solves equation • • 1 603606 =⇒= xx 2 finds breadth • • 2 b = 63m 2 marks RE

11. 1 calculates swimming time for A • • 1 min2075

1500==AT

2 calculates swimming time for B • • 2 1880

1500)( ==swimBT min 45sec

3 correctly calculates resting time for B • • 3 9 rests = 90 sec 4 calculates time for B • • 4 T = 18 m 45sec + 90 sec = 20min 15sec B

5 conclusion • • 5 A finished 15 sec earlier than B 5 marks RE

Illustrations for awarding markGive one mark for each ●

Total marks: KU 26 RE 24 Overall totals: KU: 40 RU: 40

Pegasys 2005

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