1 hour 45 minutes 1MA0 / 2MB01...2014/04/03 · 1MA0 1H – Practice Paper (Set G) QWC Question Working Answer Mark Notes *1 comparative figure(s) Maths with correct 2 M1 for correct

Instructions

Use black ink or ball-point pen.

Fill in the boxes at the top of this page with your name,

centre number and candidate number.

Answer all questions.

Answer the questions in the spaces provided – there may be more space than you need.

Calculators must not be used.

Information

There are 26 questions on this paper; the total mark is 101

The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.

All questions are labelled with an asterisk (*) and are ones where the quality of your written communication will be assessed.

Advice

Read each question carefully before you start to answer it.

Keep an eye on the time.

Try to answer every question.

Check your answers if you have time at the end.

Higher Tier – QWC Practice Papers Set G

1MA0 / 2MB01 1 hour 45 minutes

2

GCSE Mathematics (Linear) 1MA0

Formulae: Higher Tier

You must not write on this formulae page.

Anything you write on this formulae page will gain NO credit.

Volume of prism = area of cross section × length Area of trapezium = 21 (a + b)h

Volume of sphere 34 πr3 Volume of cone

31 πr2h

Surface area of sphere = 4πr2 Curved surface area of cone = πrl

In any triangle ABC The Quadratic Equation

The solutions of ax2+ bx + c = 0

where a ≠ 0, are given by

x = a

acbb

2

)4( 2

Sine Rule C

c

B

b

A

a

sinsinsin

Cosine Rule a2 = b2+ c2– 2bc cos A

Area of triangle = 21 ab sin C

3

Answer ALL TWENTY SIX questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

You must NOT use a calculator.

*1. Karen got 32 out of 80 in a maths test.

She got 38% in an English test.

Karen wants to know if she got a higher percentage in maths or in English.

Did Karen get a higher percentage in maths or in English?

(Total for Question 1 is 2 marks)

___________________________________________________________________________

4

*2. Here is part of Gary’s electricity bill.

Electricity bill

New reading 7155 units

Old reading 7095 units

Price per unit 15p

Work out how much Gary has to pay for the units of electricity he used.


___________________________________________________________________________

5

*3. Bill uses his van to deliver parcels.

For each parcel Bill delivers there is a fixed charge plus £1.00 for each mile.

You can use the graph to find the total cost of having a parcel delivered by Bill.

(a) How much is the fixed charge?

£ ..............................................

(1)

Ed uses a van to deliver parcels.

For each parcel Ed delivers it costs £1.50 for each mile.

There is no fixed charge.

(b) Compare the cost of having a parcel delivered by Bill with the cost of having a parcel

delivered by Ed.

(3)


___________________________________________________________________________

6

*4. Steve wants to put a hedge along one side of his garden.

He needs to buy 27 plants for the hedge.

Each plant costs £5.54.

Steve has £150 to spend on plants for the hedge.

Does Steve have enough money to buy all the plants he needs?


___________________________________________________________________________

7

*5. The diagram shows the floor of a small field.

Kevin is going to keep some pigs in the field.

Each pig needs an area of 36 square metres.

Work out the greatest number of pigs Kevin can keep in the field.


___________________________________________________________________________

8

*6.

ABC is parallel to EFGH.

GB = GF

Angle ABF = 65°

Work out the size of the angle marked x.

Give reasons for your answer.


___________________________________________________________________________

9

*7. Railtickets and Cheaptrains are two websites selling train tickets.

Each of the websites adds a credit card charge and a booking fee to the ticket price.

Railtickets

Credit card charge: 2.25% of ticket price

Booking fee: 80 pence

Cheaptrains

Credit card charge: 1.5% of ticket price

Booking fee: £1.90

Nadia wants to buy a train ticket.

The ticket price is £60 on each website.

Nadia will pay by credit card.

Will it be cheaper for Nadia to buy the train ticket from Railtickets or from Cheaptrains?


___________________________________________________________________________

10

*8.

CDEF is a straight line.

AB is parallel to CF.

DE = AE.

Work out the size of the angle marked x.

You must give reasons for your answer.


___________________________________________________________________________

11

*9. Milk is sold in two sizes of bottle.

A 4 pint bottle of milk costs £1.18.

A 6 pint bottle of milk costs £1.74.

Which bottle of milk is the best value for money?

You must show all your working.


___________________________________________________________________________

12

*10. The diagram shows the floor of a village hall.

The caretaker needs to polish the floor.

One tin of polish normally costs £19.

One tin of polish covers 12 m2 of floor.

There is a discount of 30% off the cost of the polish.

The caretaker has £130.

Has the caretaker got enough money to buy the polish for the floor?

You must show all your working.


___________________________________________________________________________

13

*11. Debbie drove from Junction 12 to Junction 13 on a motorway.

The travel graph shows Debbie’s journey.

Ian also drove from Junction 12 to Junction 13 on the same motorway.

He drove at an average speed of 66 km/hour.

Who had the faster average speed, Debbie or Ian?

You must explain your answer.


___________________________________________________________________________

14

*12. You can change temperatures from °F to °C by using the formula

5 32

9

FC

F is the temperature in °F.

C is the temperature in °C.

The minimum temperature in an elderly person’s home should be 20°C.

Mrs Smith is an elderly person.

The temperature in Mrs Smith’s home is 77°F.

Decide whether or not the temperature in Mrs Smith’s home is lower than the minimum

temperature should be.


___________________________________________________________________________

15

*13. Talil is going to make some concrete mix.

He needs to mix cement, sand and gravel in the ratio 1 : 3 : 5 by weight.

Talil wants to make 180 kg of concrete mix.

Talil has

15 kg of cement

85 kg of sand

100 kg of gravel

Does Talil have enough cement, sand and gravel to make the concrete mix?


___________________________________________________________________________

16

*14. Here is a map.

The position of a ship, S, is marked on the map.

Scale 1 cm represents 100 m

Point C is on the coast.

Ships must not sail closer than 500 m to point C.

The ship sails on a bearing of 037°

Will the ship sail closer than 500 m to point C?



___________________________________________________________________________

17

*15.

Competition

a prize every 2014 seconds

In a competition, a prize is won every 2014 seconds.

Work out an estimate for the number of prizes won in 24 hours.

You must show your working.


___________________________________________________________________________

18

16. The students in a class kept a record of the amount of time, in minutes, they spent doing

homework last week.

The table shows information about the amount of time the girls spent doing homework

last week.

Minutes

Least amount of time 60

Range 230

Median 170

Lower quartile 100

Upper quartile 220

(a) On the grid, draw a box plot for the information in the table.

(2)

The box plot below shows information about the amount of time the boys spent doing

homework last week.

*(b) Compare the amount of time the girls spent doing homework with the amount of time

the boys spent doing homework.

......................................................................................................................................................

......................................................................................................................................................

......................................................................................................................................................

......................................................................................................................................................

(2)


___________________________________________________________________________

19

*17. One sheet of paper is 9 × 10–3 cm thick.

Mark wants to put 500 sheets of paper into the paper tray of his printer.

The paper tray is 4 cm deep.

Is the paper tray deep enough for 500 sheets of paper?



___________________________________________________________________________

20

*18. The cumulative frequency graph shows information about the times 80 swimmers take to

swim 50 metres.

A swimmer has to swim 50 metres in 60 seconds or less to qualify for the swimming team.

The team captain says,

“More than 25% of swimmers have qualified for the swimming team.”

Is the team captain right?

You must show how you got your answer.

21


___________________________________________________________________________

22

*19.

B, C and D are points on the circumference of a circle, centre O.

AB and AD are tangents to the circle.

Angle DAB = 50°

Work out the size of angle BCD.

Give a reason for each stage in your working.


___________________________________________________________________________

23

*20. Prove algebraically that the difference between the squares of any two consecutive integers is

equal to the sum of these two integers.


___________________________________________________________________________

24

*21.

A, B, C and D are points on the circumference of a circle, centre O.

Angle AOC = y.

Find the size of angle ABC in terms of y.

Give a reason for each stage of your working.


___________________________________________________________________________

25

22. OACB is a parallelogram.

OA = a and OB = b.

D is the point such that AC = CD .

The point N divides AB in the ratio 2 : 1.

(a) Write an expression for ON in terms of a and b.

..............................................

(3)

*(b) Prove that OND is a straight line.

(3)


___________________________________________________________________________

26

*23.

OAB is a triangle.

M is the midpoint of OA.

N is the midpoint of OB.

OM = m

ON = n

Show that AB is parallel to MN.


___________________________________________________________________________

27

*24. A is the point with coordinates (1, 3).

B is the point with coordinates (4, –1).

The straight line L goes through both A and B.

Is the line with equation 2y = 3x − 4 perpendicular to line L?

You must show how you got your answer.


___________________________________________________________________________

28

25.

OAYB is a quadrilateral.

OA = 3a

OB = 6b

(a) Express AB in terms of a and b.

....................................................................

(1)

X is the point on AB such that AX : XB = 1 : 2

and BY = 5a – b

*(b) Prove that OX = 5

2 OY

(4)


___________________________________________________________________________

29

26.

APB is a triangle.

N is a point on AP.

AB = a AN = 2b NP = b

(a) Find the vector PB , in terms of a and b.

.....................................................

(1)

B is the midpoint of AC.

M is the midpoint of PB.

*(b) Show that NMC is a straight line.

(4)


TOTAL FOR PAPER IS 101 MARKS

30

BLANK PAGE

1MA0 1H – Practice Paper (Set G) QWC

Question Working Answer Mark Notes *1

Maths with correct

comparative figure(s)

2 M1 for correct method to find figure(s) to compare,

eg 32

10080

(=40) oe or 0.38×80 oe (=30.4)

C1 for maths with 40% or 30.4 or and oe

*2 9 4 M1 for 7155 – 7095 or 60 seen or 7155×15 (or .15) or 7095×15 (or

.15) or 107325 or 106425 or 1073.25 or 1064.25

M1 for ‘60’ ×15 or 7155 ×15 – 7095 × 15 [or .15 instead of 15]

A1 for 9 or 9.00 or 900

C1 (ft ) for answer with correct units (money notation) identified as

the answer.

32


Question Working Answer Mark Notes *3 (a)

(b)

Miles 0 10 20 30 40 50

Ed 0 15 30 45 60 75

Bill 10 20 30 40 50 60

10

Ed is cheaper up to 20

miles, Bill is cheaper

for more than 20 miles

1

3

B1 cao

M1 for correct line for Ed intersecting at (20,30) ±1 sq tolerance or

10 + x = 1.5x oe

C2 (dep on M1) for a correct full statement ft from graph

eg. Ed cheaper up to 20 miles and Bill cheaper for more than 20 miles

(C1 (dep on M1) for a correct conclusion ft from graph

eg. cheaper at 10 miles with Ed ; eg. cheaper at 50 miles with Bill

eg. same cost at 20 miles; eg for £5 go further with Bill OR

A general statement covering short and long distances eg. Ed is

cheaper for shorter distances and Bill is cheaper for long distances)

OR M1 for correct method to work out Ed's delivery cost for at least 2

values of n miles where 0 < n ≤ 50 OR

for correct method to work out Ed and Bill's delivery cost for n miles

where 0 < n ≤ 50

C2 (dep on M1) for 20 miles linked with £30 for Ed and Bill with

correct full statement


(C1 (dep on M1) for a correct conclusion

eg. cheaper at 10 miles with Ed; eg. cheaper at 50 miles with Bill

eg. same cost at 20 miles; eg for £5 go further with Bill OR

A general statement covering short and long distances eg. Ed is

cheaper for shorter distances and Bill is cheaper for long distances)

SC : B1 for correct full statement seen with no working


QWC: Decision and justification should be clear with working clearly

presented and attributable

10

20

30

40

5 10 15 20 25 30 0 x

y

33


Question Working Answer Mark Notes *4 554

×27

3878

11080

14958

500 50 4 ×

10

000

1000 80 2

0

3500 350 28 7

10000

1000

3500

350

80

28

14958

Yes with correct

working

4 M1 for a complete method with relative place value correct. Condone

1 multiplication error, addition not necessary.

M1 (dep) for addition of all the appropriate elements of the

calculation.

A1 for £149.58 or 42p (spare)

C1 ft (dep on M1) for correct decision for their total cost

OR M1 for a complete grid with not more than 1 multiplication error,

addition not necessary

M1 (dep) for addition of all the appropriate elements of the calculation



PTO

OR

M1 for sight of a complete partitioning method, condone 1

multiplication error, addition not necessary.

M1 (dep) for addition of all the appropriate elements of the

calculation.



OR

M1 for 150.0... ÷ 27 at least 5 seen and 15 carried or 50

9

M1 (dep) for full correct process to divide 150 by 27 or 5

59

A1 for £5.55 or £5.56 or £5.55...

C1 ft (dep on M1) for correct decision for their plant cost

OR M1 for 150.0…÷ 5.54 at least 2 seen and 392 carried

M1 (dep) for full correct process to divide 150 by 5.54

A1 for 27 (.07…)

C1 ft (dep on M1) for correct decision for their number of plants

1 0 1 0 0 8

3 5 3 5 2 8

1 4 9 5 8

34


Question Working Answer Mark Notes *5 3 4 M1 for a method to calculate at least one area eg 10 × 7 (=70) or 16 ×

10 (=160)

M1 for a method to find the total area (=124)

M1 (dep on M1) for “124” ÷ 36

C1 (dep on M3) for 3 (pigs) clearly identified and supported by correct

calculations

Or

M1 for an area of 36m² drawn with dimensions shown

M1 for 3 areas of 36m² drawn with dimensions shown

M1 (dep on M1) for method to find the area left (=16)

C1 (dep on M3) for 3 (pigs) clearly identified and supported by correct

calculations

*6 x = 130 + correct

reasons

4 M1 for angle BFG = 65 may be seen on diagram

M1 (dep) for correct method to calculate x, eg (x=) 65 + 65 (=130) or

(x=) 180 − (180 – 2 × 65) (=130)

C2 for x = 130 and full appropriate reasons related to method shown

(C1 (dep on M1) for any one appropriate reason related to method

shown)

eg alternate angles;

base angles in an isosceles triangle are equal;

angles in a triangle add up to 180o;

angles on a straight line add up to 180o;

exterior angle of triangle = sum of two interior opposite angles;

co-interior angles add up to 180o (allied angles)

NB Any reasons stated must be used

35


Question Working Answer Mark Notes *7 2.25 × 60 ÷ 100 = 1.35

1.35 + 0.80 = 2.15

1.5 × 60 ÷ 100 = 0.90

0.90 + 1.90 = 2.80

OR

2.25 – 1.5 = 0.75

0.075 × 60 ÷ 100 = 0.45

0.80 + 0.45 = 1.25

1.25 < 1.90

Railtickets with correct

calculations

4 NB. All work may be done in pence throughout

M1 for correct method to find credit card charge for one company

eg. 0.0225 × 60(=1.35) oe or 0.015 × 60 (=0.9) oe

M1 (dep) for correct method to find total additional charge or total

price for one company

eg. 0.0225×60 + 0.80 or 0.015×60 + 1.90 or

2.15 or 2.8(0) or 62.15 or 62.8(0)

A1 for 2.15 and 2.8(0) or 62.15 and 62.8(0)

C1 (dep on M1) for a statement deducing the cheapest company, but

figures used for the comparison must also be stated somewhere, and a

clear association with the name of each company

OR M1 for correct method to find percentage of (60+booking fee)

eg. 0.0225 × 60.8(=1.368) oe or 0.015 × 61.9(=0.9285)

M1 (dep) for correct method to find total cost or total additional cost

eg. '1.368' + 60.8(=62.168) or '1.368' + 0.8 (=2.168) or

'0.9285' + 61.9 (=62.8285) or '0.9285' +1.9 (=2.8285)

A1 for 62.168 or 62.17 AND 62.8285 or 62.83 OR

2.168 or 2.17 AND 2.8285 or 2.83




OR M1 for correct method to find difference in cost of credit card charge

eg. (2.25 – 1.5) × 60 ÷ 100 oe or 0.45 seen

M1 (dep) for using difference with booking fee or finding difference

between booking fees

eg. 0.80 + “0.45”(=1.25) or

1.90 – “0.45” (=1.45) or 1.90 – 0.8 (=1.1(0))

A1 1.25 and 1.9(0) or 0.45 and 1.1(0)




QWC: Decision and justification should be clear with working clearly

presented and attributable

36


Question Working Answer Mark Notes *8 Angle AED = 38 alternate

angles are equal

Angle ADE =

(180 – 38) ÷ 2 = 71

x = 180 – 71

base angles of an isosceles

triangle are equal

angles in a triangle add up

to 180

angles on a straight line

sum to 180

x = 109 4 B1 for angle AED = 38 or AEF = 142

M1 for a complete method to find one of the base angles of the

isosceles triangle

C2 (dep M1) for x = 109 with complete reasons

(C1 (dep M1) for one reason correctly used and stated)

*9 1.18 ÷ 4 = 0.295

(118 ÷ 4 = 29.5)

1.74 ÷ 6 = 0.29

(174 ÷ 6 = 29)

1.18 ÷ 2 = 0.59

1.74 ÷ 3 = 0.58

1.74 × 4 = 6.96

1.18 × 6 = 7.08

1.74 × 2 = 3.48

1.18 × 3 = 3.54

1.18÷2×3=1.77

1.74÷3×2=1.16

4÷1.18=3.3(…)

6÷1.74=3.4(…)

6 pints

3

M1 for division of price by quantity for both bottles or division of

quantity by price for both bottles or complete method to find price of

same quantity of milk

A1 for two correct values that could be used for a comparison

C1 ft (dep on M1) for comparison of their values with a correct

conclusion.

37


Question Working Answer Mark Notes *10 Not enough,

needs £133

5 M1 for splitting the shape (or showing recognition of the “absent”

rectangle) and using a correct method to find the area of one shape

M1 for a complete and correct method to find the total area

M1 for a complete method to find 70% of 19 (= 13.3) or 70% of their

total cost or 70% of their area

A1 114(m2) and (£)133 or 114(m2) and (£)13.3(0) and 108(m2)

C1 (dep on M2) for a conclusion supported by their calculations

OR

M1 for a complete method for the number of tins required for one

section of the area of the floor

M1 for a complete method to find the number of tins for the whole

floor

M1 for a complete method to find 70% of their total number of tins

and multiply by 19

A1 (£)133

C1 (dep on M2) for a conclusion supported by their calculations

38



× 60 = 75

Debbie + explanation 4 M1 for reading 24 (mins) and 30 (km) or a pair of other values for

Debbie

M1 for correct method to calculate speed

eg. 30 ÷ 24 oe

A1 for 74 – 76 or for 1.2 – 1.3 and 1.1

C1 (dep on M2) for correct conclusion, eg Debbie is fastest from

comparison of “74 – 76” with 66 (kph) or “1.2 – 1.3” and 1.1 (km per

minute)

OR

M1 for using an appropriate pair of values for Ian’s speed eg 66 and

60, 33 and 30, 11 and 10

M1 for pair of values plotted on graph

A1 for correct line drawn

C1 (dep on M2) for Debbie is fastest from comparison of gradients.

OR

M1 for reading 24 (mins) and 30 (km) or a pair other values for

Debbie

M1 for Ian’s time for same distance or Ian’s distance for same time.

A1 for a pair of comparable values.

C1 (dep on M2) for Debbie is fastest from comparison of comparable

values.

*12

No, temp is 25°C

3

M1 for substitution of 77 into the RHS of the formula

A1 for 25 cao or for 225/9 and 180/9 cao

C1 (dep on M1) for conclusion (ft) following from working shown

OR

M1 for substitution of 20 into LHS of formula and correct process to

find F

A1 for 68 cao

C1 (dep on M1) for conclusion (ft) following from working shown

39


Question Working Answer Mark Notes

*13

180÷9×1:180÷9×3:180÷9

×5

=20:60:100

Not enough cement

(but enough sand and

enough gravel)

OR

1×15:3×15:5×15

=15:45:75

15+45+75=135 (<180)

Not enough cement (to

make 180kg of concrete)

No + reason 4 M1 for 180 ÷ (1+3+5) ( = 20) or 3 multiples of 1: 3: 5

M1 for 1×”20” or 3×”20” or 5×”20” or 20 seen or 60 seen or 100

seen

A1 for (Cement =) 20, (Sand =) 60, (Gravel) = 100

C1 ft (provided both Ms awarded) for not enough cement oe

OR M1 for (1×15 and) 3×15 and 5×15 or 9×15 or sight of the numbers

15, 45, 75 together.

M1 for ‘15’ + ‘45’ + ‘75’

A1 for 135 (<180)

C1 ft (provided both Ms awarded) for not enough cement oe

*14 Yes with explanation 3 M1 for bearing ± 2 within overlay

M1 for use of scale to show arc within overlay or line drawn from C to

ship’s course with measurement

C1(dep M1) for comparison leading to a suitable conclusion from a

correct method

*15 Answer in range

35 – 50

4 M1 for a method to either find the exact or approximate number of

seconds in one day, e.g. 24 × 60 × 60 (=86400) or the number of

minutes in 2014 seconds, e.g. 2014 ÷ 60 or 2000 ÷ 60 (≈30)

M1 for a correct method to find the number of prizes; eg. ‘24 × 60 ×

60’ ÷ 2014 oe or 60 ÷ “30” × 24 oe

B1 for rounding at least one appropriate value in the working to 1 sf,

e.g. 24 rounded to 20 or 2014 rounded to 2000 or 86400 rounded to

90000

C1 (dep on M2) for answer in 35 – 50 clearly identified

*16 girls boys

Med 170 190

Range 230 210

IQR 120 100

2 comparisons 2 C1 for a correct comparison of a measure of spread (using either range

or IQR) or ft their box plot

C1 for a correct comparison of medians (accept averages)

For the award of both marks at least one of these comparisons must be

in the context of the question.

40


Question Working Answer Mark Notes

*17 No + explanation 3 M1 for 500 × 9 × 10-3 oe

A1 for 4.5

C1 (dep M1) for correct decision based on comparison of their paper

height with 4

OR

M1 for 4 ÷ 500 oe

A1 for 0.008

C1 (dep M1) for correct decision based on comparison of their paper

thickness with 0.009

OR

M1 for 4 ÷ (9 × 10-3) oe

A1 for 444(.4...)

C1 (dep M1) for correct decision based on comparison of their number

of sheets of paper with 500

*18 Yes

as 28 > 20

or 35% > 25%

or 53 < 60

3 M1 for reading a value from graph at time = 60 (=28, accept 27 to 28)

M1 for ‘28’ ÷ 80 × 100 (= 35) or 25 ÷ 100 × 80 (= 20)

C1 (dep on M2) for correct decision based on their figures

OR

M1 for 25 ÷ 100 × 80 (= 20)

M1 for reading a value from graph at cf = 20 (=53, accept 52 to 54)

C1 (dep on M2) for correct decision based on their figures

41


Question Working Answer Mark Notes *19 ABO = ADO = 90°

(Angle between tangent

and radius is 90°)

DOB = 360 – 90 – 90 – 50

(Angles in a quadrilateral

add up to 360°)

BCD = 130 ÷ 2

(Angle at centre is twice

angle at circumference)

OR

ABD = (180 – 50) ÷ 2

(Base angles of an

isosceles triangle)

BCD = 65

(Alternate segment

theorem)

65o 4 B1 for ABO = 90 or ADO = 90 (may be on diagram)

B1 for BCD = 65 (may be on diagram)

C2 for BCD = 65o stated or DCB = 65o stated or angle C = 65o stated

with all reasons:

angle between tangent and radius is 90o;

angles in a quadrilateral sum to 360o;

angle at centre is twice angle at circumference

(accept angle at circumference is half (or 1

2 ) the angle at the centre)

(C1 for one correct and appropriate circle theorem reason)

QWC: Working clearly laid out and reasons given using correct

language

OR

B1 for ABD = 65 or ADB = 65 (may be on diagram)

B1 for BCD = 65 (may be on diagram)

C2 for BCD = 65o stated or DCB = 65o stated or angle C = 65o stated

with all reasons:

base angles of an isosceles triangle are equal;

angles in a triangle sum to 180o;

tangents from an external point are equal;

alternate segment theorem

(C1 for one correct and appropriate circle theorem reason)

QWC: Working clearly laid out and reasons given using correct

language

42


Question Working Answer Mark Notes *20 (n + 1)2 – n2

= n2 + 2n + 1 – n2 = 2n

+ 1

(n + 1) + n = 2n + 1

OR

(n + 1)2 – n2

= (n + 1 + n)(n + 1 – n)

= (2n + 1)(1) = 2n + 1

(n + 1) + n = 2n + 1

OR

n2 – (n + 1)2 = n2 – (n2 +

2n + 1) =

–2n – 1 = – (2n + 1)

Difference is 2n + 1 (n + 1) + n = 2n + 1

proof 4 M1 for any two consecutive integers expressed algebraically

eg n and n +1

M1(dep on M1) for the difference between the squares of ‘two

consecutive integers’ expressed algebraically eg (n + 1)2 – n2

A1 for correct expansion and simplification of difference of

squares, eg 2n + 1

C1 (dep on M2A1) for showing statement is correct,

eg n + n + 1 = 2n + 1 and (n + 1)2 – n2 = 2n + 1 from correct

supporting algebra

*21 360 y 180

2

y

4 M1 ADC =

2

y

A1 180 2

y

C2 (dep on M1) for both reasons

Angle at centre is twice the angle at the circumference

Opposite angles in cyclic quadrilateral add to 180˚

(C1 (dep on M1) for one appropriate circle theorem reason)

OR

M1 reflex AOC = 360 y

A1 2

360 y oe

C2 (dep on M1) for both reasons Angles around a point add up to 360˚

Angle at centre is twice the angle at the circumference

(C1 (dep on M1) for one appropriate circle theorem reason)

43



= + +

= a + b + b

= a + 2b

OD = 3(3

1a+

3

2b )

OD = 3ON

Proof

3

M1 for a correct vector statement for OD or ND in terms of a and b,

e.g. = a + b + b oe or ND = 3

2(b + a) + b + b oe

A1 for correct and fully simplified vectors for ON (may be seen in

(a)) and for OD (= a + 2b) or ND (=2

3a +

4

3b)

C1 (dep on A1) for statement that or ND is a multiple of (+

common point)

*23 Proof 3 M1 for (= n – m)

or (= m – n)

or (= 2n – 2m) or (= 2m – 2n)

M1 for = n – m and = 2n – 2m oe

C1 (dep on M1, M1) for fully correct proof, with = 2 or AB is

a multiple of [SC M1 for = 0.5n – 0.5m

and = n – m

C1 (dep on M1) for fully correct proof, with = 2 or AB is a

multiple of of ]

*24 2y = 3x − 4

y = 3

2x − 2; m =

3

2

3 1

1 4

=

4

3

3

2×

4

3 = −2

No with reason 4 M1 for

3

2oe or oe

M1 for method to find gradient of AB, eg 3 1

1 4

or

1 3

4 1

or

4

3 oe

A1 for identifying gradients as 3

2oe and oe

C1 (dep on M1) for a conclusion with a correct reason, eg No as

product of 3

2 and

4

3 is not −1, ft from their two gradients

44



(b)

6b – 3a

1

4

B1 for 6b – 3a oe

M1 for AX = 1

3AB or

1

3’(6b – 3a)’ or ft to 2b – a

M1 for OY = OB + BY = 6b + 5a – b (= 5b + 5a ) oe

M1 for OX = 3a + ‘2b – a’ = 2a + 2b oe

Or

OX = 6b – ‘(6b – 3a)’ (= 2a + 2b) oe

C1 for 5

2 OY =5

2 ×5(a + b) = 2(a + b) = OX

45



*(b)

a – 3b 1

4

B1 for a – 3b oe

M1 for (NC =) 2 2a b oe

M1 for (NM =) 1

" 3 "2

b a b

A1 for 1

2a b oe and 2 2a b oe

C1 for NC is a multiple of NM (+ common point)

OR

M1 for (NC =) 2 2a b oe

M1 for (MC =) 1

" 3 "2

a b a

A1 for 3

2a b oe and 2 2a b oe

C1 for NC is a multiple of MC (+ common point)

OR

M1 for (NM =) 1

" 3 "2

b a b

M1 for (MC =) 1

" 3 "2

a b a

A1 for 1

2a b oe and

3

2a b oe

C1 for NM is a multiple to MC (+ common point)

46

Results Plus data for these questions:

New Question

Original Question

Original Paper Skill tested

Mean score

Maximum score

Mean Percent

1 2 1H 1411 Express a given number as a percentage of another number 0.74 2 37

2 3 1H 1211 Add, subtract, multiply and divide any number 1.85 4 46

3a 3a 1H 1206 Discuss, plot and interpret graphs modelling real situations 0.71 1 71

3b 3b 1H 1206 Discuss, plot and interpret graphs modelling real situations 0.97 3 32

4 6 1H 1411 Add, subtract, multiply and divide whole numbers, integers, fractions, decimals and numbers in index form 2.46 4 62

5 7 1H 1406 Calculate areas of shapes made from triangles and rectangles 3.13 4 78

6 8 1H 1411 Understand and use the angle properties of parallel lines 0.95 4 24

7 10 1H 1206 Use percentages in real life situations 2.19 4 55

8 10 1H 1303 Understand and use the angle properties of parallel lines 1.08 4 27

9 10 1H 1406 Add, subtract, multiply and divide whole numbers, integers, fractions, decimals and numbers in index form 2.05 3 68

10 10 1H 1311 Calculate areas of shapes made from triangles and rectangles 3.21 5 64

11 11 1H 1306 Interpret distance-time graphs 1.87 4 47

12 12a 1H 1406 Substitute numbers into a formula 1.99 3 66

13 13 1H 1211 Divide a quantity in a given ratio 1.76 4 44

14 13 1H 1306 Measure or draw a bearing between the points on a map or scaled plan 1.40 3 47

15 13 1H 1406 Estimate answers to calculations, including use of rounding 1.75 4 44

16(a) 15(a) 1H 1411 Produce box plots from raw data and when given quartiles, median 0.88 2 44

16(b) 15(b) 1H 1411 Compare the mean and range of two distributions, or median and interquartile range, as appropriate 0.45 2 23

17 15 1H 1306 Calculate with standard form 1.49 3 50

18 18b 1H 1311 Interpret cumulative frequency diagrams 1.64 3 55

19 21 1H 1206 Find missing angles on diagrams 0.89 4 22

20 21 1H 1303 Algebraic proof 0.11 4 3

21 22 1H 1311 Prove and use the facts that: the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference 0.65 4 16

22(a) 24(a) 1H 1311 Calculate the resultant of two vectors 0.48 3 16

22(b) 24(b) 1H 1311 Apply vector methods for simple geometrical proofs 0.26 3 9

23 24 1H 1406 Apply vector methods for simple geometrical proofs 0.59 3 20

24 24 1H 1411 Explore the gradients of parallel lines and lines perpendicular to each other 0.10 4 3

25a 26a 1H 1303 Understand and use vector notation 0.32 1 32

25b 26b 1H 1303 Apply vector methods for simple geometrical proofs 0.29 4 7

26a 28a 1H 1211 Understand and use vector notation 0.19 1 19

26b 28b 1H 1211 Solve geometrical problems in 2-D using vector methods 0.14 4 4

TOTAL 36.59 101 36

Documents

1 hour 45 minutes 1MA0 / 2MB01...2014/04/03 · 1MA0 1H – Practice Paper (Set G) QWC Question Working Answer Mark Notes *1 comparative figure(s) Maths with correct 2 M1 for correct