daveprakdotcom.files.wordpress.com€¦ · Web viewInstructions. Use . black. ink or ball-point pen. Fill in the boxes. at the top of this page with your name, centre number and

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. Without sufficient working, correct answers may be awarded no marks. Answer the questions in the spaces provided

– there may be more space than you need. Calculators may be used. You must NOT write anything on the formulae page.

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

Information The total mark for this paper is 100. The marks for each question are shown in brackets

– use this as a guide as to how much time to spend on each question.

Advice Read each question carefully before you start to answer it. Check your answers if you have time at the end.

Answer ALL TWENTY questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1 Here is a hexagon ABCDEF.

CD is parallel to AF.

Work out the area of hexagon ABCDEF.

....................................................... cm2

(Total for Question 1 is 4 marks)____________________________________________________________________________

2 The table gives information about the times, in hours, some students spent doing sportone week.

Time (T hours) Frequency

0 < T ⩽ 2 5

2 < T ⩽ 4 9

4 < T ⩽ 6 24

6 < T ⩽ 8 40

8 < T ⩽ 10 7

Calculate an estimate for the mean time these students spent doing sport.Give your answer in hours, correct to 1 decimal place.

....................................................... hours


3 Behnaz makes candles.She has 6.3 kilograms of wax and uses it all to make candles.Each candle Behnaz makes uses 210 grams of wax.

Behnaz sells of the candles for $13 each.

She then reduces this price by 20% and sells the rest of the candles.

Work out the total amount of money Behnaz gets by selling all the candles she made.

$......................................................


4 (a) Expand and simplify 3(c – 7) + 2(3c + 4)

.......................................................(2)

(b) Expand and simplify (x + 7)(x – 2)

.......................................................(2)

(c) Factorise fully 28y2 – 21y

.......................................................(2)

(d) Solve = 3x + 1

Show clear algebraic working.

x =.......................................................(3)


5 Here is an empty pool in the shape of a cuboid.

The width of the pool is 3 m.The length of the pool is 12 m.The top of the pool is 2.5 m above the base of the pool.

Jeb is going to put water in the pool.The level of the surface of the water will be 60 cm below the top of the pool.

Water flows into the pool at 400 litres per minute.1 m3 = 1000 litres

How long will it take to fill the pool to 60 cm below the top of the pool?Give your answer in hours and minutes.

............................ hours ............................ minutes


6 From point A, Stanley walks 200 m due east to point B.From B, he then walks 160 m due south to point C.

Work out the length of AC.Give your answer correct to 3 significant figures.

......................................................metres

(Total for Question 6 is 3 marks)

____________________________________________________________________________

7 ABCD is a trapezium.

Work out the size of angle x.Give your answer correct to 1 decimal place.

......................................................°


8 The table shows information about the amount of money spent on holiday by each of 120families.

Money spent (£m) Frequency

0 < m ⩽ 100 10

100 < m ⩽ 200 36

200 < m ⩽ 300 34

300 < m ⩽ 400 20

400 < m ⩽ 500 15

500 < m ⩽ 600 5

(a) Write down the modal class.

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

(b) Complete the cumulative frequency table for the information in the table.

Money spent (£m) Cumulative frequency

0 < m ⩽ 100

0 < m ⩽ 200

0 < m ⩽ 300

0 < m ⩽ 400

0 < m ⩽ 500

0 < m ⩽ 600

(1)

(c) On the grid, draw a cumulative frequency graph for your table.(2)

(d) Use your graph to find an estimate for the interquartile range.

£.......................................................(2)

(e) Use your graph to find an estimate for the number of families that spent more than£450 on holiday.

.......................................................(2)


9 A company makes cars.

In 2016, the company made 350 cars.

In the first 6 months of 2017, the company made 25 cars each month.In the last 6 months of 2017, the company made 45 cars each month.

(a) Work out the percentage increase in the number of cars the company made from2016 to 2017.

....................................................... %(4)

The company’s income in 2017 was $500 000 more than the company’s income in 2016.

The company’s income in 2017 was 8% more than the company’s income in 2016.

(b) Work out the company’s income in 2016.

$.......................................................(3)


10 (a) Simplify (2e2 f 3)3

.......................................................(2)

(b) Expand and simplify (3x − 4y)(x + 3y)

.......................................................(2)

can be written in the form a k

(c) Find the value of k.

k = .......................................................(2)

(d) Simplify

.......................................................(2)


11 The diagram shows two straight lines drawn on a grid.

(a) Write down the solution of the simultaneous equations

3y = 2x + 64x + 3y = 24

x = .......................................................

y = .......................................................(1)

(b) Show, by shading on the grid, the region defined by all five of the inequalities

x ⩾ 0 y ⩾ 0 x + y ⩾ 4 3y ⩽ 2x + 6 4x + 3y ⩽ 24

Label the region R.

(3)


12 The straight line L1 has equation y = 6 – 2xThe straight line L2 is perpendicular to L1 and passes through the point (4, 7)

Find the coordinates of the point where the line L2 crosses the x-axis.

(............................ , ............................)


13 There are 8 counters in a bag.There is a number on each counter.

Fiona takes at random three of the counters.She adds the numbers on the three counters to get her total.

Work out the probability that her total is an odd number.

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


14 T is directly proportional to the square root of r

T = 18 when r = 4

(a) Find a formula for T in terms of r

.......................................................(3)

(b) Work out the value of T when r = 36

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


15 Solve the simultaneous equations

2x2 + 3y2 = 14

x = 2y – 3

Show clear algebraic working.

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


16 Here is a quadrilateral PQRS.

Angle SRQ is acute.

Work out the size of angle SQR.Give your answer correct to 1 decimal place.

....................................................... °


17 Show that can be written in the form n + , where n is an integer.

Show your working clearly.

(Total for Question 17 is 3 marks)__________________________________________________________________________

18 Express as a single fraction in its simplest form.

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


19 A 3-D shape consists of a hollow sphere made of metal.

The diagram shows a cross section drawn through the centre, O, of the sphere.

The internal radius of the sphere is 1.2 m.The thickness of the metal is t cm.

The density of the metal is 2700 kg per m3

The mass of the 3-D shape is 1980 kg.

Work out the value of t.Give your answer correct to 2 significant figures.

t = .......................................................


20 (a) Express 7 – 4x – x2 in the form p – (x + q)2 where p and q are constants.

.......................................................(2)

(b) Use your answer to part (a) to solve the equation 7 – 4(y + 3) – (y + 3)2 = 0

Give your solutions in the form e where e and f are integers.

.......................................................(3)

The curve C has equation y = 3 – 5(x + 1)2

The point A is the maximum point on C.

(c) Write down the coordinates of A.

(............................ , ............................)(1)

(Total for Question 20 is 6 marks)

TOTAL FOR PAPER IS 100 MARKS

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daveprakdotcom.files.wordpress.com€¦ · Web viewInstructions. Use . black. ink or ball-point pen. Fill in the boxes. at the top of this page with your name, centre number and