Write your name here

Surname Other names

Centre Number Candidate Number

Pearson EdexcelLevel 1/Level2 GCSE (9-t1

You must have: Ruler graduated in centimetres and millimetres,protractor, pair of compasses, pe h, HB pencil, eraser, calculator.Tracing paper may be used.

Mathematics N,,\Y

ANSYr€R-SPaper 3 (Calculator)

Hiqher TierWednesday 8 November 2017 - MorningTime: t hour 3O minutes

Paper Reference

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lnstructionso Use black ink or ball-point pen.o fill in the boxes at the top of this page with your name,

centre number and candidate number.o Answer all questions.o Answer the questions in the spaces provided

- there may be more space than you need.

o You must show all your working.o Diagrams are IIOT accurately drawn, unless otherwise indicated.o Calculators may be used.o lf your calculator does not have a n button,.take the value of n to be

3.142 unless the question instructs otherwise.

lnformationo The total mark for this paper is 80o 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.o Keep an eye on the time.o fry to answer every question.o Check your answers if you have time at the end.

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Answer ALL questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

The table shows information about the heights of 80 children.

Height (h cm) Frequency

130<ft<140 4

140<ft<150 l1

150<&<160 z4

160<h<t70 22

170</?<180 t9

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(a) Find the class interval that contains the median.

(b) Draw a frequency polygon for the information in the table.

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Frequency

tsO 160 170 I 80

Height (fr cm)

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In London, I litre of petrol costs 108.9p

In New York, I US gallon of petrol costs $2.83

I US gallon : 3.785 litresf I : $1.46

In which city is petrol better value for money, London or New York?

You must show your working.

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3 A gold bar has a qrqqs of 12.5 kg.

The density of gold is l9.3glq!d * O' : I 1,,1 3work out the volume of the gold bar. FL3{O^

Give your answer correct to 3 significant figures.

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estion3is3marks

There are only blue pens, green pens and red pens in a box.

The ratio of the number of blue pens to the number of gle_e,npens is 2 : 5The ratio of the number of greelr.nens to the number of redpens is 4 : I

There are less than I00 pens in the box.

What is the greatest possible number of red pens in the box?

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5 (a) Find the value of the reciprocal of 1.6

Give your answer as a decimal.

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Jess rounds a number, r, to one decimal place.

The result is 9.8

(b) Write down the error interval for x.

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6 Here is a rectangle.

The length of the rectangle is 7cm longer than the width of the rectangle.

4 of these rectangles are used to make this 8-s-ided tnuP."L* -,

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The perimeter of the 8-sided shape is 70 cm.

Work out the area of the 8-sided shape.

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8-.. 2 28)t = 3'S

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7 Work out (13.8 ,. 10t) x (5.4 x 10-12)

Give your answer as an ordinary number.

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(Total for Question 7 is 2 marks)

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When a drawing pin is dropped it can land point down or point up.

Lucy, Mel and Tom each dropped the drawing pin a number of times.

The table shows the number of times the drawing pin landed point down and the number

of times the drawing pin landed point up for each person.

Lucy Mel Tom

point down 3l 53 16

point up t4 27 9

ap$ 8*Rachael is going to drop the drawing pin once.

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(a) Whose results will give the best estimate for the probability that the drawing pin willland point up?

Give a reason for your answer.

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Stuart is going to drop the drawing pin twice.

(b) Use all the results in the table to work out an estimate for the probability that the

drawing pin will land pgilt1g.the firsttime and p911:loy!,_!!e-second time.

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Jack bought a new boat for f.12500

The value, f,V, of Jack's boat at the end of nyears is given by the formula

v: t2500 x (0.85r

(a) At the end of how many years was the value of Jack's boat first less than 50% of thevalue of the boat when it was new?

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A savings account pays interest at a rate of RYo per year.

Jack invests f5500 in the account for one year.

At the end of the year, Jack pays tax on the interest at a rate of 40%;o.

After paying tax, he gets f79.20

(b) Work out the value of R.

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(Total for Question 9 is 5 marks)

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10 There are only blue counters, yellow counters, green counters and red counters in a bag.

A counter is taken at random from the bag.

The table shows the probabilities of getting a blue counter or a yellow counter or a green counter.

Colour blue yellow green red

Probabilifv 0.2 0.35 0.4 .(}-s*

(a) Work out the probability of getting a red counter.

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(b) What is the least possible number of counters in the bag?

You must give a reason for your answer.

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11 The cumulative frequency graph shows information about the weights of 60 potatoes.

Cumulativefrequency

30 40 50 60

Weight (g)

(a) Use the graph to find an estimate for the median weight.

s*1\*.!

Jamil says,

'080 - 40 : 40 so the range of the weights is 40 g."

(b) Is Jamil comect?You must give a reason for your answer'

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(c) Show that less than25Yo of the potatoes have a weight greater than 65 g.

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12 Alan has two spinners, spinner A and spinner B.

Each spinner can land on only red or white.

The probability that spinner A will land on red is 0.25

The probability that spinner B will land on red is 0.6

The probability tree diagram shows this information.

Spinner A Spinner B

red L*-lrs

white

red

oa

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L_- cr

white

Alan spins spinner A once and he spins spinner B once.

He does this a number of times.

The number of times hoth spinners land on red is 24 _Work out an estimate for the number of times both spinners land on white.

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13 Write x2 + 6x - 7 in the form (x + a)2 + b where a and b are integers.

(x. r 3)'* 1*a(-. *- :slt- I 6'

/ r2-(=+3) -\6(Total for Question 13 is 2 marks)

14 Cone A and cone B are mathematically similar.The ratio of the volume of cone A to the volume of cone B is 27 : 8

The surface arca of cone A is 297 cm2

Show that the surface area of cone B is 132 cm2

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(Total for Question 14 is 3 marks) _

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15 (a) Showthattheequation x3 +7x - 5 - 0 hasasolutionbetweenx:0andx: I

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As bLere is ^ <-ho^3<- -+ s\tf\--{J^*f-* u'-S o\ Sol.*l'o""- t*J=t^'€-s^

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(b) Show that the equation x3 + 7x- 5 : 0 can be aruanged to give t: ]13A:(--+ -l:-- - 5' a O

tt\

3.x- f {3'

f<-1.^i{-qd

qaJ

5(c) Starting with xo : 1, use the iteration formula xn+t: .: . ? three times to find

an estimate for the solution of f + 7x - 5 : 0

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(d) By substituting your answer to part (c) into x3 + 7x - 5,

comment on the accuracy of your estimate for the solution to

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x3 + 7x - 5 :0

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(Total for Question 15 is 9 marks)

16 The petrol consumption of a car, in litres per I00 kilometres, is given by the formula

Petrol consumptio" :

Nathan's car travelled 148 kilometres, correct to 3 significant figures.The car used 11.8 litres of petrol, correct to 3 significant figures.

Nathan says,

"My car used less than 8 litres of petrol per 100 kilometres."

Could Nathan be wrong?You must show how you get your answer.

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17 ABC and ADC are triangles.

The area of triangle ADC is 56m2

Work out the length of AB.Give your answer correct to I decimal place.

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17 is 5 marks

16

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18 Here is a speed-time graph for a train.

Speed (m/s)

Time (s)

(a) Work out an estimate for the distance the train travelled in the first 20 seconds.

Use 4 strips of equal width.

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(b) Is your answer to (a) an underestimate or an overestimate of the actual distance the

train travelled?Give a reason for your answer.

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19 Prove algebraically that the straight line with equation x - 2y =circle with equation x' -r y' : rO

@

o10 is a tangent to the

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(=S*l c:)t * '.3' = La.2-+A'- +* +O3* loc -t f- 2a

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19 is 5 marks

18

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20

A, B and C are points on the circumference of a circle, cenfte O.AOB is a diameter of the circle.

Prove that angle ACB is 90"You must not use any circle theorems in your proof.

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'= CIA

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uestion 20 is 4 marks

19

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OAN, OMB and APB are straight lines.AN:2O4.M is the midpoint of OB.

m:u oE:nZF : kIE where fr is a scalar quantity.

Given that MPN is a straight line, find the value of fr.

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