IntermediateN2c/C Number

1 Calculate, giving your answer in standard form correct to 3 significant figures.

1.52 10 5 - 4.6 10 4 4.56 10-2

152 000 - 46 000 = 106 000106 000 0.0456 = 2.32 106

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N2c/C2 The distance of the Earth from the Sun at a particular moment is 93.5

million miles.a Write 93.5 million in standard form.

The distance of the Earth from the moon at a particular moment is 2.5 105 miles.b Write 2.5 105 as an ordinary number.

c How many times further is the Earth from the Sun than it is from the moon?Give your answer in standard form.

a) 9.35 107

b) 250 000c) 93 500 000 250 000 = 3.74 102

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N2c/C/B3 a Write down the value of

i 50

ii 4-2

b Simplify

a) i) 1ii) 1/16

b) 1/8 2=1/4

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N2c/B4 The area of the Earth covered by sea is 362 000 000 km2.

a Write 362 000 000 in standard form.

The surface area, A km2, of the Earth may be found using the formulaA = 4r2

where r km is the radius of the Earth.r = 6.38 103.b Calculate the surface area of the Earth. Give your answer in standard form, correct to 3 significant figures.

c Calculate the percentage of the Earth's surface which is covered by sea. Give your answer correct to 2 significant figures

a) 3.62 108

b) From 5.11 108 to 5.12 108

c) (a)/(b) 100 = between 70 and 71 inclusive

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N2c/B5 Express 0.327 105 in standard form. 3.27 104 2

N2c/B6 My computer can carry out 2.7 108 calculations in one hour.

Work out how many of these calculations my computer can carry out in one second.Give your answer in standard form.

2.7 108 3600 (= 75000) = 7.5 104

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N2c/B

7 A US Centillion is the number A UK Centillion is the number

a How many US Centillions are there in a UK Centillion? Give your answer in standard form.

bWrite the number 40 US Centillions in standard form.

a) 10 600 ÷ 10 303 = 10 600-

303 = 1×10 297 or 10 297

b) 40×10 303 = 4×10 304

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N2c/B8 The diameter of an atom is:

0.000 000 03 m.a Write 0.000 000 03 in standard form.

Using the most powerful microscope, the smallest objects which can be seen have diameters which are one hundredth of the diameter of an atom.b Calculate the diameter, in meters, of the smallest objects which can be seen using this microscope.Give your answer in standard form.

a) 3×10 -8

b) (a) ÷ 100 = 3×10 -104

N3b/E9 Do NOT use a calculator for this question.

You must show all your working.

Work out 453 73.

453__73 13593171033069

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N3b/N3d/E10 Mrs. Evans decides to take 863 students on a trip to Euro Disney.

They travel by coach.Each coach can hold up to 51 students.In this part of the question you MUST NOT use a calculator .You MUST show ALL your workinga Work out the smallest number of coaches Mrs. Evans should book so that all the students can go on the trip.

Each student has to pay £37 for the trip.745 students decide to go on the trip.In this part of the question you MUST NOT use a calculator.You MUST show ALL your workingb How much money is collected if all 745 students pay £37 each.

The trip actually cost £25 000c Use your calculator to work out the percentage loss that Mrs. Evans will make on the trip.

a)

= 17 coaches

b) 745 37

5215 22350 27565 = £27 565

c) [{(b)-25 000 }/25000]×100 = 10.26%

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N3c/E11 It takes 6 men 8 days to build a wall. 1 man takes 6×8 = 48

days4 men take 48÷4 = 12 days

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All the men work at the same rate.How long would it take 4 men to build a wall the same size?

N3c/E12 Jugdev pays to see the Tigers.

It normally costs £2.40 but there is 20% off the price.a Work out how much he pays.

Jugdev then pays to see the Cheetahs.

It normally costs £2.70 but there is off the price.b Work out how much he pays.

a) 20/100 × 2.40 = £1.92b) 2.70-1/3 ×2.70 2.70-0.90 = £1.80

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N3d/E13 Cedric buys 12 pencils for £3.48.

Work out the cost of 20 pencils.

1 costs 3.48 ÷ 1220 costs 3.48 ÷ 12×20 = £5.80

2

N3d/E14 Work out:

a i of £9.60ii 24% of 35 metres.

a) i) 9.60÷8×5 = £6ii) 35×24÷100 = 8.4 m

b) i) 3÷8 = 0.375ii) 3/8×100 or (I)×100

= 37.5%

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b Change into

i a decimal fraction, ii a percentage.

N3d/E15 The same type of training shoes is advertised in three different shops.

Work out the cost of the training shoes in each of the three shops.

Tom (25×17.5÷100)+25 = £29.38Pete's 48-(48÷3) = £32.00City 40-(40×25÷100) = £30.00

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N3f/E16 i Write down two numbers you could use to estimate the answer to

793 ÷ 21

ii Work out your estimate.

i) 800 ÷ 20ii) 40

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N3c/D17 Malika's father won £128.

He shared the £128 between his three children in the ratio 6:3:1.Malika was given the biggest share.a Work out how much money Malika received.

Malika saved of her share.b Work out how much Malika saved.

a) 6 + 3 + 1 = 10128/"10" = 12.86 × 12.8 = 76.8 =

£76.80b) "76.8"/3 2 = £51.20

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N3c/D18 Frances see three different advertisements for jeans.

Work out the cost of the jeans in each advertisement.i Bobsii Disco's iii Sanjay's

i) 30 - (30 × 15/100) = £25.50ii) 36 × 2/3 = £24iii) 22 + (22 × 17.5/100) = £25.85

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N3d/C19 Marcus see a motorbike advertised for £750.

This is the price after a reduction of 15%.Work out the original price of the motorbike.

750 is 85%1% = 750 ÷ 85100% = 750 × 85 ÷ 100 = £882.35

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N3e/C20 Use your calculator to evaluate:

560.3 20.3 (0.2 + 4.5)2

Write down all the figures on your calculator.

11374.09_ = 11374.09 (0.2 + 4.5)2 4.72

= 514.89769...

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N3e/C21 In this question you MUST use your calculator and you MAY write

down any stage in your calculation.

Evaluate:

__59 5.7_ = _336.3_200.3 8.05 1612.415= 0.208569 = 0.208 or 0.209

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N4a/F/E/C22 The diagram shows a metal box.

The box is a cuboid.

a Work out the volume, in m3, of the box

Shiftem deliver these boxes in the UK.They charge £28.85 for each m3 of a box's volume.b Work out Shiftem's charge for delivering one of these boxes.

The weight of a box is 0.125 tonnes.c Write 0.125 tonnes in kg.

Le Goff deliver these boxes to Paris.They charge 7.92 French francs for each kg.d Work out Le Goff's charge, in French francs, for delivering one of these boxes.

Le Goff deliver 50 of these boxes to Paris.

a) 3 × 2 × 0.5 = 3 (F)b) "3" × 25.85 = 77.55(F)c) 0.125 × 1000 = 125 (F)d) "125" × 7.92 = 990 (E)e) "990" × 50 (= 49500) "49500" ÷ 8.85 (= 5593.220...) = 5593 (C)

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£1 = 8.85 French francs.e Work out Le Goff's charge, in £, for delivering the 50 boxes. Give your answer correct to the nearest £.

N4a/E23 Michelle goes to France for her holiday.

She changes £80 into French francs.The exchange rate is £1 = 9.50FfHow many French francs should Michelle receive?

9.50 × 80 = 760Ff 2

N4a/E24 It normally takes Sylvie 20 minutes to drive to work.

One day Sylvie has to drive at half her normal speed.How long does it take her to drive to work on that day?

20 × 2 = 40 mins 2

N4a/E25 Mustapha pays Income Tax at 22%.

He is allowed to earn £3 500 before he pays any Income Tax.He earns £12 500 in one year.Work out how much Income Tax he pays in that year.

12 500 - 3 500 = 90009000 × 22 ÷ 100 = £1980

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N4a/D26 Fatima has 35 CDs and tapes.

The ratio of the number of CDs to the number of tapes is 3:4Work out how many CDs she has.

35/(3 + 4) (= 5)3 × 5 = 15 OR 3/7×35 = 15

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N4a/C27 Shreena put £484 in a new savings account.

At the end of every year, interest of 4.3% was added to the amount in her savings account at the start of that year.Calculate the total amount in Shreena's savings account at the end of 2 years.

484 × 4.3/100

484 + 20.81 (= 504.81)504.81 × 4.3/100 = 21.7069504.81 + 21.71OR484 × 1.043 = 504.81"504.81" × 1.043 = 526.52OR484 × 1.0432 = 526.52Accept £526.51 or £526.52

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N4a/C28 Astrid bought a motor car for £10 000 on the First of January 1996.

It lost 15% of its value during 1996 and then 10% during every year from the First of January 1997.Work out the value of the car on the First of January 1999.

1st Jan 1997 £85001st Jan 1998 £76501st Jan 1999 £6885

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N4d/C29 Natalie measured the distance between two points on a map.

The distance she measured was 5 cm correct to the nearest centimetre.

a Write down the i least upper bound of the measurement, ii greatest lower bound of the measurement,

a) i) 5.5 cmii) 4.5 cm

b) 0.2 km

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The scale of the map is 1 to 20 000bWork out the actual distance in real life between the upper and lower bounds. Give your answer in kilometres.

N3b/N4a/E30 John is going to Spain on holiday.

He changes £190 to Spanish pesetas.£1 = 183 pesetas.a i Work out how many pesetas John gets.

ii Write your answer to part (i) correct to 3 significant figures.

IN THIS PART OF THE QUESTION YOU MUST SHOW ALL YOUR WORKING The holiday costs £621.John has to pay the £621 in 27 equal weekly amounts.b i Without using a calculator, work out how much he must pay each week.

ii Write down an approximate calculation you could use to check your answer.

iii Work out the answer to the approximate calculation

a) i) 183 × 190 = 34770ii) 34 800

b) i)

27

ii) 600 30iii) 20

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N4d/E31 The diagram represents the surface of a lake in winter. The lake is shaded

on the grid.

a Estimate the area, in cm2, of the diagram that is shaded.

Each square on the grid represents a square with sides of length 100m.b Work out the area, in m2, represented by one square on the grid.

c Estimate the area, in m2, of the lake.

In summer the area of the lake decreases by 15%.d Work out the area ,in m2, of the lake in summer.

a) 11 cm2

b) 100 × 100 = 10000m2

c) 10000 - 11000 m2

d) (b) × 85/100; OR (b) - (b) × 15/100 = 93500 m2

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N3d/N4d/D32 Some oil is spilt. The spilt oil is in the shape of a circle.

The circle has a diameter of 12 centimetres.

a Work out the circumference, in cm, of the spilt oil. Give your answer correct to 1 decimal place.

The diameter of the spilt oil increases by 30%b Work out the new diameter, in centimetres, of the spilt oil.

a) 2 × × 6 or × 12 = 37.7 cmb) 12 × 130/100; 12 + 12 × 30/100 = 15.6 cm

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A2b/E Algebra33 Here are the first five numbers in a simple number sequence.

1, 3, 7, 13, 21, ....., .....

a Write down the next two numbers in the sequence.

b Describe, in words, the rule to continue this sequence.

a) 31, 43b) add multiples of 2 in order to the previous number

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A2b/E/D34 a Write in the missing numbers in the following sequence.

2, 5, 8, 11, 14, ....., ....., 23,

b Work out the 12th number in the sequence.

c Work out an algebraic expression for the nth term in the sequence.

a) 17, 20 (E)b) 12 × 3 - 1 = 35 (E)c) 3n - 1 (D)

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A2d/E/D35 a Complete this table of values for y = 3x - 1.

x -2 -1 0 1 2 3y -1 8

b Draw the graph of y = 3x - 1 on the grid below.

a) -7, -4, 2, 5(E)b) pts plotted, line drawn (D)c) y = 3.5 x = 1.5

x = -1.5 y = -5.5(D)

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c Use your graph to findi the value of x when y = 3.5ii the value of y when x = -1.5

A2d/D36 a Complete the table of values for the graph of y = 2x + 3

x -3 -2 -1 0 1 2 3y = 2x + 3 -3 1 5

b Use the values to draw the graph on the grid below.

x -3, -2, -1, 0, 1, 2, 3y , -1, , 3, , 7, 9

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A2b/C37 Work out an algebraic expression for the nth term of this sequence of

numbers.

2, 8, 18, 32, 50,.......

2n × n, 2(n × n) = 2n2 2

A2b/C38 The expression n ( n +1) 5n(n + 1) 2

2

is the nth term of the sequence of triangular numbers

1, 3, 6, 10, ...

Write down an expression, in terms of n, for the nth term of the sequence

10, 30, 60, 100, ...

A2b/C39 Here are the first terms of a number sequence.

5, 8, 11, 14, 17,

Write down an expression for the nth term of the sequence.

3n + 2 3

A2b/C40 The numbers of lines joining points form a number sequence.

Complete the table to find the number of lines joiningi 6 pointsii 10 pointsiii n points

Points Lines2 13 34 65 10610n

i) 6 15ii) 10 45iii) n n ( n -1)

2

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A2d/C41 a Make a table of values for y = 6 - 2x

xy

b Draw the graph of y = 6 - 2x on the grid below.

a) -2, -1, 0, 1, 2, 3, 410, 8, 6, 4, 2, 0, -2Ignore outside -2 to 4

b) graph drawnc) i) x = -1.5, y = 9

ii) y = 3.4, x = 1.3

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c Use your graph to findi the value of y when x = -1.5ii the value of x when y = 3.4

A2c/B42 The diagram shows part of a distance/time graph for a bus after if had left

a bus stop.

a Use the graph to find the distance the bus travelled in the first 20 seconds after it had left the bus stop.

b Describe fully the journey of the bus represented by the parts AB,BC and CD of the graph.

a) 88 mb) AB constant speed BC gradually slowing down CD stationary.

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A2d/B43 i On the grid below draw the graph of

y = x2 - 3x - 5 for values of x between -2 and +5.x -2 -1 0 1 2 3 4 5

y

ii Use your graph to solve the equation

i) x -2, -1, 0, 1, 2, 3, 4, 5

y 5, -1, -5, -7, -7, -5, -1, 5ii) x = -1.2

x = 4.2

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x2 - 3x - 5 = 0

A3a/b/c/F/D44 The diagram shows two straight lines AB and CD.

Each line is cut into sections.The length, in centimetres, of each section is shown in the diagram.a Write down, in terms of d,

i the length of AB,ii the length of CD

The length of AB is equal to length of CDb i Write down an equation in d.

ii Solve your equation to find the value of d.

a) i) 2d + 3 + 2d = 4d + 3

ii) d + 5 + d + 5 = 2d + 10 (F)b) i) 2d + 3 + 2d = d +5 + d + 5 4d + 3 = 2d + 10

ii) 4d - 2d = 10 -3 2d = 7 so d = 3.5 (D)

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A3b/E45 a Write, in symbols, the rule "To find y, multiply k by 3 and then

subtract 1"

b Work out the value of k when y = 14.

a) y = 3k -1b) 3k - 1 = 14 3k = 14 + 1 = 15 so k = 5

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A3c/E46 Simplify:

i 2x + 3xii h × h × h × h × hiii 2m × 3niv 2(x + 3) + 5(x - 3)

i) 5xii) h5

iii) 6 mniv) 7x - 9

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A3d/E/D/C47 Solve the equations:

a 3y + 7 = 28

b 2(3p + 2) = 19

c 3t - 4 = 5t - 10

a) 3y = 21 so y = 7 (E)b) 6p = 15 so p = 2.5 (D)c) 6 = 2t or -6 = -2t so t = 3 (C)

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A3b/D48 Bhavna uses this formula to work out her Electricity bill.

Cost of Electricity = Number of units used × Cost for each unit + Meter hire

Bhavna uses 350 unitsThe cost for each unit is 7.5pThe Meter hire is £15.50.

Work out the cost of Bhavna's Electricity bill.

350 × 7.5 + 15.50 = £41.75

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A3c/D49 a Write down and simplify an algebraic expression for the perimeter of

this triangle.

b Write down and simplify an algebraic expression for the perimeter of this rectangle.

a) a + 1 + a + 2 + a + 3 = 3a + 6b) 2(2b + 3) + 2(3b - 1) = 10b + 4

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A3d/D50 Solve the following equations:

i 3p + 5 = 29ii 5(q - 3) = 25iii 6r - 5 = 7 - 2r

i) 3p = 29 - 5 3p = 24, p = 8ii) 5q - 15 = 25; q = 8iii) 8r = 12; r = 1.5

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A3d/D51 The perimeter of this triangle is 31 cm.

Work out the value of c.

2c - 3 + 2c + 3 + 4c - 5 = 318c - 5 = 318c = 36; c = 4.5

4

A3d/D52 a Solve 3x = 24

b Solve 18 + 3y = 6 - y.

a) x = 8b) 3y + y = 6 - 18 4y = - 12; y = -3

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A3d/D53 Solve the following equations.

a 4x - 7 = 20

b 3(y + 5) = 42

a) 4x - 7 = 20 4x = 20 + 7 4x = 27 x = 27 ÷ 4 = 6.75b) 3(y + 5) = 42 3y + 15 = 42 3y = 42 - 15 3y = 27 y = 27 ÷ 3 = 9Alternative: y + 5 = 42 ÷ 3

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y + 5 + 14 y = 14 - 5 y = 9

A3c/C54 x is an integer, such that -3 < x 2.

List all the possible values of x.-2, -1, 0, 1, 2 2

A3c/C55 x is an integer.

Write down the greatest value of x for which 2x < 7.3 1

A3d/C56 Use the method of trial and improvement to find the positive solution of

x3 + x = 37Give your answer correct to 1 decimal place.

3.2 4

A3d/C57 Use a trial and improvement method to solve the equation

x3 - x = 15

Complete the working below and find a solution correct to one decimal place.

x x3 - xx = 2 23 - 2 = 6 Too smallx = 3 33 - 3 = 24 Too big

2.53 - 2.5 = 13.1252.63 - 2.6 = 14.9762.73 - 2.7 = 16.983so x = 2.6

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A3b/B/C58 The velocity of a particle is given by the formula:

v 2 = u 2 + 2as

a Calculate the value of the velocity v when u = -5, a = and s = 5.67.

b Rearrange the formula to make u the subject.

a) 25 + 2 2/3 5.6732.56

b) u2 = v2 -2asu = (v 2 - 2as)(B)

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A3b/B59 y = ab + c

Calculate the value of y when

a = , b = and c =

Give your answer in the form where p and q are integers.

(21 - 16)/32 = 5/32 3

A3b/B60 The volume, V, of the barrel is given by the formula ( 60)/3000 (2 252 3

= 3.14, H = 60, R = 25 and r = 20.

Calculate the value of V.Give your answer correct to 3 significant figures.

+ 202) = ( 60)/3000 1650 = 103.67...3.14 103.623.142 103.68..22/7 103.71..so V = 104

A3b/c/B61 In the diagram, each side of the square ABCD is (3 + x) cm.

a Write down an expression in terms of x for the area, in cm2, of the square ABCD.

The actual area of the square ABCD is 10cm2.b Show that x 2 + 6x = 1

a) (3 + x)(3 + x) or (3 + x)2 = (x + 3)2

b) (3 + x)(3 + x) = 10 9 + 3x + 3x + x2 = 10 x2 + 6x + 9 = 10 and x2 + 6x = 1

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A3b/A3c/B62 a Calculate the value of v when u = -6, a = 5 and s = 0.8 using the

formula: v 2 = u 2 + 2as

Give your answer to one significant figure.

b Make u the subject of the formula v 2 = u 2 + 2as.

a) (-6)2 + 2 5 0.8 = 7or -62 + 2 5 0.8 =

7b) u 2 = v 2 -2as u = (v 2 - 2as)

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A3c/B63 a Factorise completely

i 4st + 8tu - 2tvii 15x + 3x2

a) i) 2t(2s + 4u - v) ii) 3x(5 + x)b) 8a - 2a2

c) 2c2 - 8c + 3c - 12 =

7

b Expand 2a(4 - a)

c Expand and simplify (2c + 3)(c - 4)

2c2 - 5c - 12

A3c/B64 a Simplify

i 12 x 5 3 y 3 9x2y

ii (4p2q3)2

b Factorise completelyi 9a2b3 + 15a3b2

ii x2 + 7x - 60

c On the number line below show the solution to these inequalities.-7 2x - 3 < 3

a) i) 4x3y2

ii) 16p4q6

b) i) 3a2b2(3b + 5a)ii) (x + 12)(x - 5)

c)

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A3c/B65 Solve the inequality

7y > 2y - 37y - 2y > - 3 5y > - 3; y > -3/5

2

A3d/B66 Solve the simultaneous equations

3x + 2y = 11 x - y = 7

3x + 2y = 112x - 2y = 14Adding gives5x = 25 so x = 5Substituting gives15 + 2y = 11so 2y = -4therefore y = -2

3

A3d/B67 Solve the simultaneous equations

3p + 2q = 62p + 5q = -7

6p + 4q = 126p + 15q = -21Subtracting gives11q = -33 q = -3; p = 4

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A2b/A3b/F/D/C68 Rods can be fixed together using bolts.

The diagrams show rods fixed together to form a pattern of hexagons in a row.

a) Draw 3 more hexagons(F)

b) 18, 22, 26, 30 in a table (D)c) 4 15 + 2 = 62

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a Complete the diagram below to show how rods can be fixed together to form a pattern of 4 hexagons in a row.

b Complete the table

Number of hexagons 1 2 3 4 5 6 7Number of bolts 6 10 14

c Work out the number of bolts needed to form a pattern of 15 hexagons in a row.

A2d/A3b/E69 The width of the rectangle is x cm.

The length of the rectangle is 4 cm more than the width.

a Write down an expression in terms of x for the length of the rectangle.

The perimeter of the rectangle is P cm.b Write down a formula for P in terms of x.

The table gives the value of P when x = 6.

c Complete the table for x = 2, 4 and 8.

d On the grid below draw the graph of P against x for values of x from 2 to 8.

a) x + 4b) p = x + 4 + x + 4 + x + x = 4x + 8c) p = 16 24 (32) 40d) graph plotted

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A2d/A3c/C/B70 a Make y the subject of the equation x + 2y = 6

b On the grid, draw the line with equation x + 2y = 6

a) 2y = 6 - x or x/2 + y = 3;

or

(B)

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c On the grid, shade the region for which x + 2y 6, 0 x 4 and y 0.

b) e.g.(0,3 ), (6, 0), (2, 2), (4, 1) (C)c)

(B)

A2d/A3d/C71 a On the grid below, draw the graphs of:

i x + y = 4ii y = x + 2

b Use the graphs to solve the simultaneous equations: x + y = 4 y = x + 2

a) i) graph of x + y = 4 or y = -x + 4 ii) graph of y = x + 2b) x = 1, y = 3

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A2c/B72 A car travels between two sets of traffic lights. The diagram represents

the velocity/time graph of the car.

The car leaves the first set of traffic lights.

a Use the graph to find the velocity of the car after 15 seconds.

b Describe fully the journey of the car between the two sets of traffic lights.

The car leaves the first set of traffic lights.c Calculate an estimate for the acceleration of the car, in m/s-2, after 10 seconds.

a) Velocity = 11.4 m/s. Do not accept responses which merely read off values without adding interpretationb) The car accelerates (the speed increases). Then it travels at a constant speed (or velocity), then there is a constant deceleration (or the car brake steadily).c) Draw tangent at t = 10. Calculate the gradient as 0.57 - 0.73.

Alternative: allow a chord about the required point e.g (11.4 - 5)/10 = 0.64

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S2c/E Shape73 Draw in one plane of symmetry on this shape. One of: 2

S2b/D74 Karl's and Eleanor's school is near a busy main road.

They decide to carry out a survey of the different types of vehicles that travel on the main road.Design a suitable data sheet so that they can collect their data easily.

Vehicle type more than 1TallyFrequency

3

S2d/D75 a The diagram shows a quadrilateral

Work out the size of the angle marked aº.

b The diagram shows a regular hexagon.

Work out the size of the angle marked bº.

c The diagram shows a regular octagon.

a) 360 - (120 + 85 + 93)360 -298 = 62

b) 360 ÷ 6 = 60c) 90 + 45, 180 - 45 or 3 × 45 or 2 × 67.5 = 135

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Work out the size of the angle marked cº.

S2e/C76 Calculate the length of AB.

Give your answer correct to 1 decimal place.

(182 - 122) = 13.4 3

S2e/f/C77 The diagram is part of a map showing the positions of three Nigerian

towns.

Kaduna is due North of Aba.a Calculate the direct distance between Lagos and Kaduna.Give your answer to the nearest kilometre.

b Calculate the distance between Kaduna and Aba.Give your answer to the nearest kilometre.

a) ( )440 4402 2 = 622 kmb) Tan 20º = x/440

x = 440 Tan 20º = 160Distance = 440 + 160

= 600 km

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S2e/f/C78 Sidney places the foot of his ladder on horizontal ground and the top

against a vertical wall.The ladder is 16 feet long.

a) ( )16 42 2 = 15.5b) cos angle = 4/16; angle

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The foot of the ladder is 4 feet from the base of the wall.

a Work out how high up the wall the ladder reaches.Give your answer to 3 significant figures.

b Work out the angle the base of the ladder makes with the ground.Give your answer to 3 significant figures.

= 75.5º

S2e/f/C/B79 Here is a side view of a swimming pool.

ABCD is a horizontal straight line. AH, BG, CF and DE are vertical lines.

a Calculate the length of the line FG. Give your answer correct to 3 significant figures.

b Calculate the angle that the line GF makes with the horizontal. Give your answer correct to 1 decimal place.

a) 5.32 + "0.9"2 = 5.38(C)b) tan angle = "0.9"/5.3; angle = 9.6º (B)

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S2f/C80 In the diagram AB = 17.9 m,

BD = 8.2 m, angle CBD = 37º and angle BDC = 90º.

a) DC/8.2 = tan 37ºDC = 8.2 × tan 37º =

6.179...b) sin DAB = 8.2/17.9 = 0.4581... so DAB = 27.26... º = 27.3º

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ADC is a straight line.a Calculate the length of DC.Give your answer, in metres, correct to 3 significant figures.

b Calculate the size of angle DAB. Give your answer correct to 1 decimal place.

S2f/C81 The diagram shows a house and a garage on level ground.

A ladder is placed with one end at the bottom of the house wall.The top of the ladder touches the top of the garage wall.The distance between the garage wall and the house is 1.4 m.The angle the ladder makes with the ground is 62º.a Calculate the height of the garage wall. Give your answer correct to 3 significant figures.

A ladder of length 3.5 m is then placed against the house wall.The bottom of this ladder rests against the bottom of the garage wall.b Calculate the angle that this ladder makes with the ground.Give your answer correct to 1 decimal place.

a) x/1.4 = tan 62ºx = 1.4 × tan 62º (=

1.4 × 1.8807...) = 2.63(30..)b) cos x = 1.4 / 3.5 x = 66.4218… x = 66.4º

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S2e/B82 Calculate the length of a diagonal of this rectangle.

Give your answer in centimetres correct to one decimal place.(152 + 122) = 19.2 cm 3

S3a/E83 San Fernando is on a bearing of 157º from Pasadena.

Draw this bearing accurately on the diagram above.

Bearing of 157 degrees drawn.

2

S3c/E84 The shape shown can be used to tessellate the inside of the rectangle

shown.

Show, on the grid below, how this shape tessellates.

Tessellation ignore axes 2

S3d/E

85 Rashmi uses a map with a scale of 1 to 50 000.She measures the distance between two points on the map.The distance that Rashmi measures on the map is 8.2 cm.Work out the actual distance between the two pointsGive your answer in kilometres.

8.2 × 50 000 ÷ 100 000 = 4.1 km

3

S2b/D86 The scale drawing below shows the positions of an airport tower, T, and a

radio mast, M.

1 cm on the diagram represents 20 km.

a i Measure, in centimetres, the distance TM.ii Work out the distance in km of the airport tower from the radio

mast.

b i Measure and write down the bearing of the airport tower from the radio mast.

ii Write down the bearing of the radio mast from the airport tower.

A plane is 80 km from the radio mast on a bearing of 220º.

c Plot the position of the plane, using a scale of 1 cm to 20 km on the scale diagram.

a) i) 5 cm ii) "5" × 20 = 100 km

(E)b) i) 060º

ii) 180º + "60º" = 240º(D)

c) plane plotted 4 cm from mast bearing of 220º

(E)

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S3d/C87 The Fast Foto company uses two letter F's as part of their logo.

The letter F's are similar in shape.The lengths of the large F and the lengths of the small F are in the ratio 3:2.

a) 0.9 ÷ 3 × 2 = 0.6 mb) 28 ÷ 2 × 3 = 42 cm

4

The height of the large F is 0.9m.a Work out the height of the small F.

The width of the small F is 28 cm.b Work out the width of the large F.

S3d/C88 Seamus and Mick set off on a journey from a point A They travelled 30

km on a bearing of 060º to a point B. From B they travelled 48 km on a bearing of 210º to a point C.a Using a scale of 1 cm to represent 4 km draw a scale drawing of their journey.

b i Work out how far C is from A.ii Write down the bearing of A

from C.

a) accurate journey drawnb) i) 6.7 km ii) 356º

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S3d/C89 Shape A is shown in the diagram.

Shape A is enlarged to obtain the shape B.

a Write down the scale factor of the enlargement.b Complete the drawing of shape B on the diagram.

a) 1/3b)

3

S3e/C90 P and Q are two points marked on the grid. Perpendicular bisector of

PQ constructed.2

Construct accurately the locus of all points which are equidistant from P and Q.

S3b/C/B91 a Reflect shape S in the line x = 0. Label the new shape T.

b Rotate the new shape T through an angle of 90º anticlockwise using (0, 0) as the centre of rotation. Label the new shape U.

c Describe fully the single transformation that will move shape U back onto shape S.

a) and b)

(C)c) Reflection in the line y = -x (B)

6

S3d/B92 Triangle ABC is similar to triangle PQR. i) 3 × 5/4 = 3.75 cm

ii) 6.5 ÷ (5/4) or 6.5 × (4/5) = 5.2 cm

5

Angle ABC = angle PQR.Angle ACB = angle PRQ.

Calculate the length of:i PQii AC

S3d/B93 Here is a diagram of a company logo.

The diagram is enlarged so that the length BC becomes 7.5 cm.a Work out the length of the enlarged side AD.

The enlarged side AB is 6 cm.b Work out the length AB on the original diagram.

c What is the size of angle A in the enlarged diagram?

a) 9 × 1.5 = 13.5 cmb) 6 ÷ 1.5 = 4 cmc) 60º

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S4d/E94 In this question you must write down the units of your answer.

a Work out the area of the base of the solid shape.

b i Work out the volume of the solid shape.ii Write this volume in litres

a) 20 × 10 = 200 cm2

b) i) 20 × 10 × 15 = 3000 cm2

ii) 3000 ÷ 1000 = 3 litres

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S4d/D95 The diagram shows a circle of diameter 70 cm inside a square of side 70

cm.

A = r2 = × 35 × 35 = 3846.5 (3.14), 3850 (22/7), 3848.9 (3.14), 3848.4 () 70 × 70 = (4900) "4900" - "3850"A = 1050 cm2

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Work out the area of the shaded part of the diagram.Give your answer correct to 3 significant figures.

S4d/D96 Here is a side view of a swimming pool.

ABCD is a horizontal straight line.

AH, BG, CF and DE are vertical lines.

a Write down the mathematical name for the quadrilateral BCFG.

b Work out the area of quadrilateral BCFG.

a) trapeziumb) 5.3 1.2 + ½ 0.9 5.3

OR ½ (1.2 + 2.1) 5.3 area = 8.745 m2

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S4d/D97 Mary has a circular dining table with a radius of 0.65 m.

a Work out the area of the top of the table. Give your answer to 3 significant figures.

The perimeter of the circular tablecloth is 5m.b Work out the diameter of the tablecloth.

a) × 0.65 × 0.65 = 1.33 m2

b) D = 5 ÷ = 1.59 m

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S4a/C98 There are 12 inches in 1 foot.

There are 3 feet in 1 yard.There are 2.54 centimetres in 1 inch.

100 cm = 100 ÷ 2.54 = 39.3700 ÷ 36 = 1.0936

3

Express 1 metre in yards. Give your answer correct to 3 decimal places. = 1.094

S4a/C99 There are 2.54 centimetres in 1 inch.

There are 12 inches in 1 foot.There are 3 feet in 1 yard.

i Calculate the number of yards in 10 metres.

ii Calculate the number of metres in 10 yards.

i) 1000/(2.54 3 12) = 10.9(36..) ydsii) 100/"10.9" = 9.1743... = 9.1 - 9.2 m

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S4a/C100 There are 14 pounds in a stone.

There are 2.2 pounds in a kilogram.A man weighs 13 stone 6 pounds.Work out his weight in kilograms.Give your answer to the nearest kilogram.

(1314) + 6 = 1881882.2 = 85 kg

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S4d/C101 The diagram shows a triangular prism.

BC = 4 cm, CF = 12 cm and angle ABC = 90º.The volume of the triangular prism is 84 cm3.Work out the length of the side AB of the prism.

Area of base × 12 = 84½ × 4 × h = 7h = 3.5

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S4d/C102 The shape below is the cross section of a prism 10 cm long.

Calculate the volume of the prism.

(2 + 4)/2 × 2 × 10 = 60 cm2

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S4d/C103 The diagram shows a cylinder. 3.14 × 4.3 × 4.3 × 26.3 = 3

The height of the cylinder is 26.3 cm.The diameter of the base of the cylinder is 8.6 cm.

Calculate the volume of the cylinder.Give your answer correct to 3 significant figures.

1526.9 ( 1527.7) 3.142 1527.9 = 1530

S4a/C/B104 There are 6 groats in a florin and 5 florins in 10 shillings.

Work out how manyi groats there are in 5 florins,ii florins there are in 24 shillings,iii groats there are in 8 shillings.

i) 5 × 6 = 30 groats(C)ii) 10 shillings = 5 florins

1 shilling = 0.5 florins24 shillings = 24 × 0.5

= 12 florins (C)iii)1 shilling = 0.5 florins

3 groats = 1 shilling 8 shillings = 24 groats

(B)

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S4d/B105 The expressions shown below can be used to calculate lengths, areas or

volumes of various shapes.The letters r and h represent lengths. , 2, 3, 4, 5 and 10 are numbers which have no dimensions.

r( ) 2 4 2rh r(r + 4h)

rh4

45

3r

10 3r ( )r h 2 3 3rh

r h r2 ( )

Draw a circle around each of the expressions which can be used to calculate an area.

circle around: r(r + 4h), rh4

, 3 3rh

3

S4d/B106 The diagram represents a solid shape.

From the expressions below, choose the one that represents the volume of the solid shape.

and 13

are numbers which have no dimensions.

13h(b2 + ab + a2) 1

a, b and h are lengths.

13(b2 - ab + a2),

13h(b2 + ab + a2),

13h2(b2 - a2),

13(a2 + b2),

13h2(b2 - ab + a2).

Write down the correct expression.

S3e/S4b/C107 The scale diagram shows the position of a radio mast, M.

1 cm on the diagram represents 20 km.

M

Signals from the radio mast can be received up to a distance of 100 km.a Shade the region on the scale diagram in which signals from the radio mast can be received.

The distance of a helicopter from the radio mast is 70 km correct to the nearest kilometre.b Write down

i the maximum distance the helicopter could be from the radio mast,

ii the minimum distance the helicopter could be from the radio mast.

a) circle drawn at 5 cm radius circle shadedb) i) 70.5

ii) 69.5

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D2a/D Handling Data108 In a town 1800 cars were stolen in a year. The table shows information

about the times of day when they were stolen.Time Number of cars

Midnight to 6 am 7006 am to midday 80Midday to 6 pm 2806 pm to midnight 470Time unknown 270

This information can be shown in a pie chart.a Work out the angle of each sector of the pie chart.

Time Angle of sectorMidnight to 6 am6 am to middayMidday to 6 pm6 pm to midnightTime unknownTotal of angles 360º

a) 140º, 16º, 56º, 94º, 54º or answers that round to.b) Sectors drawn, ft from (a). If it fits overlay than (a) & (b) gets 3 + 3 or 3 + 2 dep. on labels and non-contradicting table.c) 289/1800 =7/45

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b Construct the pie chart in the circle below.

c What fraction of the number of cars was stolen between Midday and 6pm? Write your fraction in its simplest form.

D2f/D109 Fred is conducting a survey into television viewing habits.

One of the questions in his survey is"How much television do you watch?"His friend Sheila tells him that it is not a very good question.Write down two ways in which Fred could improve his question.

Specify a period of time, e.g. “How much television do you watch in a day?”Include some options such as 0-5 hours, 6-10 hours etc.

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D2f/D110 50 pupils are going on an educational visit. The pupils have to choose to

go to one of the theatre or the art gallery or the science museum.23 of the pupils are boys.11 of the girls choose to visit the theatre.9 of the girls choose to visit the art gallery.13 of the boys choose to visit the science museum.

Theatre Art gallery Science museum TotalsGirls 11 9Boys 13 23Totals 19 20 50

a Complete the table.

b How many of the girls choose to visit the science museum?

a)Theatre Art gallery Science museum Totals

Girls 7 27Boys 8 2Totals 11

b) 7

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D2f/D111 Information about oil was recorded each year for 12 years.

The table shows the amount of oil produced (in billions of barrels) and the average price of oil (in £ per barrel).

a) graphb) negative

4

Amount of oilproduced (billions

of barrels)

Averageprice of oil (£

per barrel)7.0 3411.4 1310.8 1911.3 129.6 238.2 37.7 3010.9 12.58.0 28.59.9 13.59.2 26.59.4 15.5

a Draw a scatter graph to show the information in the table.

b Describe the correlation between the average price of oil and the amount of oil produced.

D2c/f/D112 The table lists the weights of twelve books and the number of pages in

each one.

Number of pages Weight (g)80 160155 330100 200125 260145 32090 180140 290160 330135 260100 180115 230165 350

a Draw a scatter graph to show the information in the table.

a) points plottedb) High positive, good accept description of relationship

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b Describe the correlation between the number of pages in these books and their weights.

D2c/f/D113 Joe has twelve cars for sale.

The scatter diagram shows the ages and prices of the twelve cars.

Joe buys five more cars to sell.The table lists the ages and prices of these cars.

Age in years 3 4 1 5 4Price in £ 3000 2500 3750 1500 2250

a Plot this information on the scatter graph.

b Describe the correlation between the ages of these seventeen cars and their prices.

a) points correctly plottedb) negative

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D2d/C114 Andrew did a survey at the seaside for his science coursework.

He measured the lengths of 55 pieces of seaweed.The results of the survey are shown in the table.

a) 2 × 10 + 22 × 30 + 13 × 50 + 10 × 70 + 5 × 90 + 2 × 110 + 1 × 130 = 20 + 660 + 650 + 700 + 450 + 220 + 130 = 2830 (= 51.4545...) = 51.5b) 40 < L 60

6

Length of seaweed(L cm)

Frequency

0 < L 20 220 < L 40 2240 < L 60 1360 < L 80 10

80 < L 100 5100 < L 120 2120 < L 140 1

Andrew needs to calculate an estimate for the mean length of the pieces of seaweed.a Work out an estimate for the mean length of the piece of seaweed. Give your answer correct to 1 decimal place.

b Write down the interval which contains the median length of a piece of seaweed.

D2d/C115 A survey was carried out to find how much time was needed by a group

of pupils to complete homework set on a particular Monday evening.The results are shown in the table below.

Time, thours,spent onhomework

Numberof pupils

0 30 < t 1 141 < t 2 172 < t 3 53 < t 4 1

Calculate an estimate for the mean time spent on homework by the pupils in the group.

(3 × 0) + (14 × 0.5) + (17 × 1.5) + (5 × 2.5) + (1 × 3.5)= 48.548.5 ÷ 40 = 1.21

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D2d/C116 Bronwen owns a pet shop.

The table gives information about the weights of hamsters in Bronwen's shop.

Weight w ofhamsters in g

Number ofhamsters

28 < w 30 930 < w 32 532 < w 34 434 < w 36 2

Calculate an estimate for the mean weight of the hamsters in Bronwen's shop.

29 × 9 = 26131 × 5 = 15533 × 4 = 13235 × 2 = 70

618618 ÷ 20 = 30.9

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D2c/f/C117 Information about oil was recorded each year for 12 years.

The scatter graph shows the amount of oil produced (in billions of a) Line of best fitb) Draw line "amount =

4

barrels) and the average price of oil (in £ per barrel).

a Draw a line of best fit on the scatter graph.

In another year the amount of oil produced was 10.4 billion barrels.

b Use your line of best fit to estimate the average price of oil per barrel in that year.

10.4" on graph or state use of amount = 10.4; price about £16.50

D2c/f/C118 The table list the weights of twelve books and the number of pages in

each one.

Number of pages Weight (g)80 160155 330100 200125 260145 32090 180140 290160 330135 260100 180115 230165 350

This information is presented below as a scatter graph.

a Draw a line of best fit on your scatter graph.

b Use your line of best fit to estimatei the number of pages in a book of weight 280 g,ii the weight, in grams, of a book with 110 pages.

a) Line of best fit (only str. line)b) i) accept 136 - 140 pages

ii) accept 216 - 220 g

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D2b/B119 Martin, the local Youth Centre leader, wishes to know why attendance at

the Youth Centre is less than at the same time last year.He thinks that it could be due to a number of changes that occurred during the course of the year.These changes were:

the opening hours changeda new sports centre opened nearbysome of the older members started bullying the younger members.

Design a suitable question, that is easily answered, to find out why people do not attend the Youth Centre.

Look for a question that links to the original problem via the perceived causes and a way of completing the questionnaire easily e.g. boxes

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D2c/B120 Pippa collected data for the heights (h) of the students in her class.

Here is the grouped frequency table of her results.Height (h) incm

Frequency

160 h < 165 7165 h < 170 6170 h < 175 2175 h < 180 10180 h < 185 5

a Use the table to calculate an estimate of the mean for her results.

b Complete the cumulative frequency table for Pippa's data and hence draw a cumulative frequency graph for the data.

Group Frequency Cumulativefrequency

160 h < 165 7 7160 h < 170 6160 h < 175 2160 h < 180 10160 h < 185 5

c Use the cumulative frequency graph to calculate an estimate ofi median of the dataii interquartile range of the data

a) Mid point Total162.5 1137.5167.5 1005172.5 345177.5 1775182.5 912.5Total 5175Mean = 5175 ÷ 30 =

172.5 cmb) 7, 13, 15, 25, 30c) Median = 175 Interquartile range = 17

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D2c/B121 A survey is made of all 120 houses on an estate. a) plot points, joined with 6

The floor are, in m2, of each house is recorded.The results are shown in the cumulative frequency table.

Floor area (x) in m2 CumulativeFrequency

0 < x 100 40 < x 150 200 < x 200 490 < x 250 970 < x 300 1140 < x 350 1180 < x 400 120

a On the grid draw a cumulative frequency graph for the table.

b Use your cumulative frequency graph to estimate the interquartile range of the floor areas of the houses.

The houses on the estate with the greatest floor areas are called luxury houses.10% of the houses are luxury houses.c Use your graph to estimate the minimum floor area for a luxury house.

smooth curve/lineb) segments 240 - 170 = 70c) 10% is 12 houses. Read off where cf = 120 - 12 = 108; floor area = 275 m2

D2c/d/B122 150 year 11 pupils took a mathematics examination.

The table shows information about their marks.

Marks (x) Frequency 0 x < 20 620 x < 30 1730 x < 40 2240 x < 50 4550 x < 60 2660 x < 70 1970 x < 80 980 x < 100 6

a Complete the cumulative frequency table below.

a) 6, 23, 45, 90, 116, 135, 144, 150b) cum freq diag drawn: ignore line between first point and the originc) 60% of 150 = 90

150 - 90 = 60 pass mark about 42 - 45 marks

7

Marks (x) CumulativeFrequency

0 x < 200 x < 300 x < 400 x < 500 x < 600 x < 700 x < 800 x < 100

b On the grid below, draw a cumulative frequency diagram to show these marks.

60% of the pupils passed the examination.c Use your diagram to find an estimate for the pass mark for the examination.

D3a/E123 A game in an amusement arcade can show the following pictures.

The fraction under each picture shows the probability of the picture being shown at the first window.

Calculate the probability of the game not showing a Bar at the first window.

1 - 1/12 = 11/12accept 4/12 + 2/12 + 3/12 + 2/12 = 11/12

2

D3d/E124 22 coloured balls are used to play a game of snooker.

15 of them are red and the rest have different colours.One of the balls is chosen at random.Write down the probability that the ball chosen will bei red,ii not red.

i) 15/22ii) 7/22

3

D3e/E125 A fair coin is tossed and a fair dice is thrown.

One possible outcome is (Heads, 4).List all the possible outcomes.

H1, H2, H3, H4, H5, H6T1, T2, T3, T4, T5, T6

2

D3/a/c/f/E/D/C126 A fair dice is to be thrown.

a Write down the probability of the dice landing oni a sixii an even number

A second dice is to be thrown.The probability that this dice will land on each of the numbers 1 to 6 is given in the table.

number 1 2 3 4 5 6probability x 0.2 0.1 0.3 0.1 0.2

The dice is to be thrown once.b Calculate the value of x.

c Calculate the probability that the dice will land on a number higher than 3.

The dice is thrown 1000 times.d Estimate the number of times the dice is likely to land on a six.

a) i) 1/6ii) 3/6 (E)

b) 1 - (0.2 + 0.1 + 0.3 + 0.1 + 0.2) = 0.1 (E)c) 0.3 + 0.1 + 0.2 = 0.6

(D)d) 0.2 × 1000 = 200

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D3a/D127 Alison, Brenda, Claire and Donna are the only runners in a race.

The probabilities of Alison, Brenda and Claire winning the race are shown below.

Alison Brenda Claire Donna0.31 0.28 0.24

Work out the probability that Donna will win the race.

1 - (0.31 + 0.28 + 0.24) = 0.17

2

D3c/e/D128 A packet contains only yellow counters and green counters.

There are 8 yellow counters and 5 green counters.A counter is to be taken from the packet at random.a Write down the probability that

i a yellow counter will be taken,ii a yellow counter will not be taken.

A second counter is to be taken from the packet.

a) i) 8/13 or 0.62... ii) 1 - "8"/13 = 5/13 (or 0.38..)b) (y, y) (y, g) (g, y) (g, g)

4

b Write down all the possible outcomes of taking two counters from the packet.

D3b/C129 A dice has six faces numbered 1, 2, 3, 4, 5 and 6.

The dice, which is biased, is thrown 200 times and the number on the upper face is recorded.The frequencies of the numbers obtained are shown in the table.

Numbershown on dice

1 2 3 4 5 6

Frequency 38 22 46 25 53 16

Estimate the probability that the next time the dice is thrown it will show the number 3.

46/200 or 23/100 or 0.23 or 23%

2

D3a/B/C130 The probability of a machine being able to manufacture a component

within a tolerance of one tenth of a millimetre is 0.995.a Work out the probability of the machine not being able to manufacture a component to within a tolerance of one tenth of a millimetre.

Ten thousand components are manufactured in one day.b Work out an estimate of how many components will be outside the tolerance of one tenth of a millimetre.

a) 1 - 0.995 = 0.005 (C)

b) 10 000 × (a) - 50(B)

4

D3e/B131 Two dice with faces numbered 1 to 6 are rolled and the sum of the scores

on upward facing faces noted.

The score on these dice is 1 + 4 = 5

a Complete the table of probabilities for the chance of scoring all the totals available.

Score Possibilities Probability2 1 + 13 1 + 2, 2 + 14 1 + 3, 3 + 1, 2 + 25 1 + 4, 4 + 1, 2 + 3, 3 + 26789101112

a) 1/36, 2/36, 3/36 etcb) i) 10/36 ii) 10/36 iii) 15/36

6

b Work out the probability that the score will bei more than 9,ii less than 5,iii more than 6 and less than 10.

D3e/B132 The probability of a car chosen at random having defective

tyres is 0.065brakes is 0.032steering is 0.044Work out the probability that a vehicle chosen at random will havei defective tyres, brakes and steering,ii has defective tyres but no other defects,iii has no defects.

i) 0.0625 × 0.032 × 0.044 = 0.0000915ii) 0.065 × 0.968 × 0.954 = 0.06iii) 0.935 × 0.968 × 0.954 = 0.863

7

D3f/B133 Nikki and Ramana both try to score a goal in netball.

The probability that Nikki will score a goal on her first try is 0.65.The probability that Ramana will score a goal on her first try is 0.8.

i Work out the probability that Nikki and Ramana will both score a goal on their first tries.

ii Work out the probability that neither Nikki nor Ramana will score a goal on their first tries.

i) 0.65 × 0.8 = 0.52ii) 1 - 0.65 (= 0.35)

1 - 0.8 (= 0.2)0.35 × 0.2 = 0.07

5

D3c/e/B/C134 Peter and Asif are both taking their driving test for a motor cycle for the

first time.The table below gives the probabilities that they will pass the test at the first attempt or, if they fail the first time, the probability that they will pass at the next attempt.

Probabilityof passing atfirst attempt

Probability ofpassing at nextattempt if they failthe first attempt

Peter 0.6 0.8Asif 0.7 0.7

On a particular day 1000 people will take the test for the first time.For each person the probability that they will pass the test at the first attempt is the same as the probability that Asif will pass the test at the first attempt.a Work out an estimate for how many of these 1000 people are likely to pass the test at the first attempt.

b Calculate the probability that both Peter and Asif will pass the test at the first attempt.

c Calculate the probability that Peter will pass the test at the first attempt and Asif will fail the test at the first attempt.

a) 1000 0.7 = 700 (C)b) 0.6 0.7 = 0.42

(B)c) 0.6 0.3 = 0.18 (B)

6

S2c/D3d/D Integrated questions135 Here is a frequency table of the animals on Mr. McDonald's farm a) Animal Angle

Hens 4510

Animal FrequencyHens 30Sheep 80Cows 104Pigs 20Geese 6

a Draw a fully labelled pie chart to show this data

An animal is chosen at random from Mr. McDonald's farm.b What is the probability that the animal

i is a pig,ii is a horse,iii has four legs?

Sheep 120Cows 156Pigs 30Geese 9

b) i) 1/12ii) 0iii) (80 + 104 +

20)/240 = 17/20

N4d/S4b/C136 Jomo is going to design a circular roundabout. The roundabout will have

a circumference of 7 metres.Jomo is given three estimates for the length of the diameter of the roundabout.The estimates are:2.2278803 metres2 metres2.23 metresa Give a reason why 2.23 metres is the most reasonable estimate to use.

b Explain why 2.2278803 metres and 2 metres are not appropriate to use.

a) e.g. 2.23 m can be measured: normally give to 2 d.p.b) 2nd not accurate; not near enough to 7m; 1st too accurate: cannot be measured

3

S4d/N4d/C137 This container is made from a cylinder and a cube. a) r2h = 82 20 =

4021.. cm3

b) 16 16 16 = 4096 cm3 (a) + "4096" = 8117 cm3

c) i) 7.5 cm ii) 8.5 cm

7

The cylinder has a height of 20 cm. It has a base radius of 8 cm.The cube has sides of edges 16 cm.a Calculate the total volume, in cm3, of the cylinder. Give your answer to the nearest cm3.

b Calculate the total volume, in cm3, of the container. Give your answer to the nearest cm3.

When the radius of 8 cm was measured, this measurement was rounded to the nearest centimetre.c i Write down the minimum length, in cm, it could be.

ii Write down the maximum length, in cm, it could be.

A3b/N4c/B138 Matthew uses this formula to calculate the value of D.

a Calculate the value of D when a = 19.9 and c = 4.05. Write down all the figures on your calculator display.

Matthew estimates the value of D without using a calculator.b i Write down an approximate value for each of a and c that Matthew could use to estimate the value of D. ii Work out the estimate that these approximations give for the value of D. Show all your working.

a)

b) i) a = 20, c = 4

ii) = = 2

6