essential revision questions mathswatch higher

GCSE Mathematics

ESSENTIAL REVISION

QUESTIONS

MathsWatch

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CONTENTS

Grades

C/D.........................................3 to 40

B.............................................41 to 54

A/A* ......................................55 to 71

©MathsWatch Ltd www.mathswatch.com [email protected]

Grade CClip 103

1T) a) 4t + 7t

b) 4t × 7t

c) 6y + 2w – 5y

d) 6y × 3t

e) 4e2 × 3e3

f) m7 ÷ m5

g)yy

5

2

h)62

4yy

1S) a) 3t + 8t

b) 2t × 9t

c) 12y + 3w – 5y

d) 4y × 2t

e) 3e5 × 2e7

f) x4 ÷ x3

g)rr

7

3

h)62

5

3rr

2T) a) Expand 5(3y – 1)

b) Expand 3x(2x + 4)

c) Expand and simplify 2(3x + 5) – 3(4x – 2)

d) Expand and simplify 5(2y – 3) + 2(y – 1)

e) (2x + 3)(x – 4)

2S) a) Expand 3(2y – 4)

b) Expand 5x(3x + 2)

c) Expand and simplify 5(2x + 1) – 2(3x – 4)

d) Expand and simplify 4(3y – 2) + 2(3y – 2)

e) (3x – 4)(2x – 1)

Grade CClip 102

85 Essential Questions at C to D(1 to 72 are non-calculator)


3T) Find the nth term of the following patterns

a) 3, 5, 7, 9, 11 . . . . .

b) 8, 13, 18, 23, 28, . . . . .

c) 9, 6, 3, 0, –3, . . . . .

3S) Find the nth term of the following patterns

a) 2, 6, 10, 14, 18 . . . . .

b) 7, 16, 25, 34, 43, . . . . .

c) 5, 2, –1, –4, –7, . . . . .

4T)

a) From the table above, find the mean number ofsmarties in a tube.

b) Find the median number of smarties in a tube.

Number ofsmarties

Frequency

29 2

30 5

31 2

32 1

4S)

a) From the table above, find the mean number ofsmarties in a tube.

b) Find the median number of smarties in a tube.

Number ofsmarties

Frequency

29 2

30 1

31 5

32 2

Grade CClip 112

Grade C Clip 133


5T) Factorise the following:

a) 2x + 6

b) 2x + 8

c) 2x + 12

d) 3x + 6

e) x2 + x

f) 2x2 – 6x

g) 9h2 + 6h

h) 8x2 – 10x

5S) Factorise the following:

a) 2t + 10

b) 3m – 12

c) 4y + 8

d) 2x2 + 6

e) t2 + t

f) 5t2 + 10t

g) 7t2 – 14t

h) 9h2 – 30h

6T) a) If a piece of wood is measured as 8cm to thenearest cm, what is the greatest possiblelength and the least possible length?

b) If a piece of wood is measured as 19.8cm to thenearest tenth of a cm, what is the greatest possiblelength and the least possible length?

6S) a) If a piece of wood is measured as 5cm to thenearest cm, what is the greatest possiblelength and the least possible length?

b) If a piece of wood is measured as 6.7cm to thenearest tenth of a cm, what is the greatest possiblelength and the least possible length?

Grade CClip 104

Grade CClip 125


7T) a) If a = 3 and t = –2 find the value of

(i) 3a

(ii) a2

(iii) 5a2

(iv) 4a – 2t

(v) 2(3a + t)

(vi) 47

a t−

b) Colin said “when x = 3, then the value of 4x2 is 144”

Sue said “when x = 3, then the value of 4x2 is 36”

Who was right? Explain why.

7S) a) If a = 4 and t = –5 find the value of

(i) 3a

(ii) a2

(iii) 5a2

(iv) 4a – 2t

(v) 2(3a + t)

(vi) 47

a t−

b) Colin said “when x = 5, then the value of 4x2 is 400”

Sue said “when x = 5, then the value of 4x2 is 100”

Who was right? Explain why

8T) Using the information that 726 × 34 = 24684

Write down the value of:

a) 7.26 × 3.4 =

b) 726 × 340 =

c) 246.84 ÷ 7.26 =

8S) Using the information that 38 × 362 = 13756

Write down the value of:

a) 38 × 3.62 =

b) 0.38 × 3620 =

c) 13.756 ÷ 3.8 =

Grade DClip 66

Grade C Clip 97


9T) Write the following numbers as the product of theirprime factors

a) 48

b) 60

c) Find the Highest Common Factor of 48 and 60

d) Find the Lowest Common Multiple of 48 and 60

9S) Write the following numbers as the product of theirprime factors

a) 90

b) 120

c) Find the Highest Common Factor of 90 and 120

d) Find the Lowest Common Multiple of 90 and 120

Grade CClips 95 & 96

10T) a) Draw an angle of 70 degrees and then use rulerand compasses to bisect it.

b) Draw a line of length 9cm and then bisect itusing compasses.

c) Use compasses to draw a triangle ABC with ABequal to 9cm, AC 7cm and BC 4cm

10S) a) Draw an angle of 60 degrees and then use rulerand compasses to bisect it.

b) Draw a line of length 11cm and then bisect itusing compasses.

c) Use compasses to draw an isosceles triangle withthe base equal to 8cm and the other two sides oflength 12cm

11T) What is 2 × 5 + 7 × 3?

11S) Work out the answer to 38 – 3 × 4

12T) What is 2.3 × 0.15?

12S) What is 2.7 × 0.13?

13T) –3 < x < 4

x is an integer. Write down all the possible values.

13S) –2 < x < 3

x is an integer. Write down all the possible values.

Grade C Clip 127

Grade C Clip 129

Grade DClip 59

Grade D Clip 80

Grade DClip 60

Grade C Clip 108


14T) Here are the front elevation, side elevation and theplan of a 3-D shape.

Draw a sketch of the 3-D shape.

Front elevation Side elevation

Plan

14S) Here are the front elevation, side elevation and theplan of a 3-D shape.

Draw a sketch of the 3-D shape.

Front elevation Side elevation

Plan

15T) a) Work out

b) Work out

c) Work out

of 600310

of 80058

× 4257

15S) a) Work out

b) Work out

c) Work out

of 400710

of 90029

× 5638

Grade DClip 81

Grade DClip 55


16T) If you share out £240 between Alice and Bill in theratio 5 : 3, how much more does Alice get comparedwith Bill?

16S) If you share out £60 between Alice and Bill in theratio 2 : 3, how much does each of them get?

17T) Sara and Fred share tips from their job in the ratio2 : 5. If Fred receives £35 how much does Sara get?

17S) Sara and Fred share tips from their job in the ratio3 : 4. If Sara receives £18 how much does Fred get?

18T) Some plant heights are measured as shown in thetable, below.

a) Find an estimate for the mean height of a plant.

b) In which interval does the median height lie?

Height in cm Frequency 0 < h < 20 420 < h < 40 340 < h < 60 260 < h < 80 1

18S) Some plant heights are measured as shown in thetable, below.

a) Find an estimate for the mean height of a plant.

b) In which interval does the median height lie?

Height in cm Frequency 0 < h < 20 120 < h < 40 240 < h < 60 460 < h < 80 3

Grade C Clip 94

Grade C Clip 94

Grade CClip 133


19T) a) Reflect the shaded shape in the y axis and label it T

b) Rotate T 90º anticlockwise using (0, 0) as thecentre of rotation and label the new shape U

c) Decribe fully the single transformation that willmove U back on to the shaded shape.

19S) a) Reflect the shaded shape in the x axis and label it T

b) Rotate T 90º clockwise using (0, 0) as thecentre of rotation and label the new shape U

c) Decribe fully the single transformation that willmove U back on to the shaded shape.

Grade D Clips 74, 75, 77


20T) a) Enlarge triangle A scale factor 3 using (2, 4) ascentre of enlargement

b) Enlarge triangle A scale factor ½ using (4, 0) ascentre of enlargement

20S) a) Enlarge triangle A scale factor 2 using (4, 5) ascentre of enlargement

b) Enlarge triangle A scale factor ½ using (-2, 2) ascentre of enlargement

Grade D Clip 76


21T) Find the exterior angle of this regular octagon

21S) Find the exterior angle of this regular hexagon

22T) a) In the triangle below, find an expression, in termsof x, for the perimeter of the triangle.

Simplify your expression.

b) If the perimeter of the triangleis 44 cm, find the value of x.

2x 2x

8

22S) a) In the rectangle below, find an expression, in termsof x, for the perimeter of the rectangle.

Simplify your expression.

b) If the perimeter of the rectangleis 46 cm, find the value of x.

3x + 5

x – 2

Grade DClip 70

Grade CClip 106


23T) Find the size of angle n, giving reasons

23S) Find the size of angles x and y, giving reasons

A

B C

24T) Find the size of angle x, giving reasons

24S) Find the size of angles x and y, giving reasons

Grade DClips 68, 69

Grade DClip 67

A

B C

°

°


Grade C Clip 124

25T) Solve the following equations

a) 2x = 7

b) x – 8 = 4

c) 2x + 3 = 11

d) x3

+ 5 = 7

e) 2(5x – 2) = 26

f) 25x – 3 = –1

g) 3x + 4 = 5x – 3

25S) Solve the following equations

a) 3x = 12

b) x – 9 = 3

c) 3x + 2 = 14

d) x3

+ 6 = 4

e) 2(3x + 2) = 46

f) 25x – 6 = –3

g) 4x + 3 = 2x – 3

26T) Draw a stem and leaf diagram to show the followinginformation.

The heights of 12 plants in cm are:

3.6, 5.2, 4.1, 3.4, 5.8, 6.2, 4.7, 5.2,4.7, 6.4, 5.1, 4.9

26S) Draw a stem and leaf diagram to show the followinginformation.

The weights of 10 people in kg are:

59, 52, 81, 67, 75, 62, 50, 64, 68, 71

27T) a) Change 7 m2 to cm2

b) Change 3 cm2 to mm2

c) Change 9 m3 to cm3

27S) a) Change 4 cm2 to mm2

b) Change 2 m2 to cm2

c) Change 3 cm3 to mm3

Grade CClip 105

Grade D Clip 89


30T) Draw a pie chart to show the following information

30S) Draw a pie chart to show the following information

28T) a) Anne buys 46 litres of diesel at £1.32 per litre.

How much does she spend altogether on diesel?

b) James spends £65.72 on 53 litres of petrol.

How much was each litre of petrol?

28S) a) Sara buys 34 litres of diesel at £1.43 per litre.

How much does she spend altogether on diesel?

b) Sid spends £57.12 on 42 litres of petrol.

How much was each litre of petrol?

29T) a)

b)

c)

d)

23 + 3

8

29S) a)

b)

c)

d)

35 – 1

4

34 × 8

9

23 ÷ 1

6

34 + 2

3

57 – 2

5

310 × 6

8

45 ÷ 3

10

Grade DClips 56and 57

Grade D Clip 60

Grade DClip 86

Crisp flavour FrequencyCheese 8Plain 19Beef 6

Prawn 3

Crisp flavour FrequencyCheese 8Plain 6Beef 1

Prawn 3

& Grade C Clip 100


31T) Find the areas of the following shapes

7m

3m

5cm

4cm

18cm

11cm

12cm4cm

31S) Find the areas of the following shapes

9m

6m

12cm

7cm

24cm

14cm

13cm4cm

a) b)

c)

a) b)

c)

Grade DClip 73


33T) Make the letter in the bracket the subject of theformula.

a) v = u + at (a)

b) xa

– t = bc (x)

33S) Make the letter in the bracket the subject of theformula.

a) v2 = u2 + 2as (a)

b) xa

+ y = c (x)

34T) Find the following:

a) 10% of £700

b) 15% of £80

c) 35% of £600

d) 17.5% of £48

34S) Find the following:

a) 40% of £260

b) 15% of £900

c) 85% of £800

d) 17.5% of £240

8cm

2cm

3cm

32T) Find the surface area of this cuboid.

10cm

3cm

5cm

32S) Find the surface area of this cuboid.

Grade CClip 120

Grade CClip 107

Grade DClip 52


35T) Sally’s mother lives 80km from Sally. This is thejourney to her mother’s house.

a) Sally has a rest at 8.30. What speed had shebeen travelling at until 8.30?

b) How long did she rest for?

c) What speed did she travel at for the last part ofthe journey to her mother’s house?

d) For the return journey, Sally travelled at 60km/hwithout a break. Complete the travel graph toshow this.

35S) Sally’s mother lives 90km from Sally. This is thejourney to her mother’s house.

a) What speed did Sally travel at until her firstrest?

b) What speed did she travel at for the last part ofthe journey to her mother’s house?

c) For the return journey, Sally travelled at 80km/hwithout a break. Complete the travel graph toshow this.

0800 0900 1000 1100 1200

20

40

60

80

100D

ista

nc

e in

km

fro

m h

om

e

Time

0800 0900 1000 1100 1200

20

40

60

80

100

Dis

tan

ce

in k

m f

rom

ho

me

Time

Grade C Clip 117


a) Complete the table for the equation

y = 2x2 – 3x

b) Draw the graph of y = 2x2 – 3x on theaxes at the bottom of the page

c) Use your graph to find the value of ywhen x = 2.3

d) Use your graph to find the value of ywhen x = –1.5

e) Use your graph to solve 2x2 – 3x = 5

f) Use your graph to solve 2x2 – 3x = 8

36T)

-2 -1 O 1 2 3

-2

-1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

x

y

Grade CClip 116

x –2 –1 0 1 2 3

y 14


a) Complete the table for the equation

y = 3x2 – x

b) Draw the graph of y = 3x2 – x on theaxes at the bottom of the page

c) Use your graph to find the value of ywhen x = 1.5

d) Use your graph to find the value of ywhen x = –1.5

e) Use your graph to solve 3x2 – x = 10

x –2 –1 0 1 2

y 14

x

y

-2 -1 O 1 2 3

-2

-1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

36S)

Grade CClip 116


37T) Draw a set of axes going from –5 to +5

a) Draw the graph of y = 2x – 3

b) What is the gradient?

37S) Draw a set of axes going from –5 to +5

a) Draw the graph of y = 3x + 1

b) What is the gradient?

38T) The table below shows the probability of an oddlyshaped 4-sided dice landing on 1, 2, 3, or 4.

a) Work out the value of x

b) If the dice is rolled 1000 times how many 2swould you expect to get?

1 2 3 40.15 0.37 0.24 x

38S) The table below shows the probability of an oddlyshaped 4-sided dice landing on 1, 2, 3, or 4.

a) Work out the value of x

b) If the dice is rolled 1000 times how many 3swould you expect to get?

1 2 3 40.29 0.34 0.14 x

39T) Draw a plane of symmetry on this shape

39S) Draw a plane of symmetry on this shape

Grade CClip 113

Grade CClip 132

Grade DClip 83


40T) Height Frequency

0 to 10 1

10 to 20 4

20 to 30 3

30 to 40 2

a) On the first set of axes,draw a frequency diagram

b) On the second set of axes,draw a frequency polygon

0 10 20 30 40 500

1

2

3

4

5

6

7

Height

Frequency

0 10 20 30 40 500

1

2

3

4

5

6

7

Height

Frequency

40S) Height Frequency

0 to 10 3

10 to 20 7

20 to 30 2

30 to 40 1

a) On the first set of axes,draw a frequency diagram

b) On the second set of axes,draw a frequency polygon

0 10 20 30 40 500

1

2

3

4

5

6

7

Height

Frequency

0 10 20 30 40 500

1

2

3

4

5

6

7

Height

Frequency

Grade DClip 88


41T) a) In a room there are 7 boys and 3 girls.

What percentage of the people are boys?

b) In a room there are 13 boys and 7 girls.

What percentage of the people are girls?

c) Sally scores 24 marks out of 40 in a Science test.

What was her percentage score?

41S) a) In a room there are 11 boys and 9 girls.

What percentage of the people are boys?

b) In a room there are 13 boys and 12 girls.

What percentage of the people are girls?

c) Emma scores 54 marks out of 60 in a Science test.

What was her percentage score?

42T) A point, P, moves so that the locus of P is always 2 cmfrom the line AB.

Draw the locus of P.

42S) A point, P, moves so that the locus of P is alwaysequidistant from lines AB and AC.

Draw the locus of P.

A

B

C

A

B

Grade D Clip 54

Grade C Clip 130


43T) a) Sketch a scatter diagram with positivecorrelation

‘hair length’, ‘hair colour’, ‘intelligence,’‘circumference of wrist’, ‘height’, ‘ice creamsales’, ‘weight’, ‘outside temperature’‘sale of extra-warm jackets’, ‘eye colour’

b) From the list above select two sets of data whichwould have

(i) a positive correlation

(ii) no correlation

43S) a) Sketch a scatter diagram with negativecorrelation

‘hair length’, ‘hair colour’, ‘intelligence,’‘circumference of wrist’, ‘height’, ‘ice creamsales’, ‘weight’, ‘outside temperature’‘sale of extra-warm jackets’, ‘eye colour’

b) From the list above select two sets of data whichwould have

(i) a negative correlation

(ii) no correlation

Grade D Clip 87

44T) a) What are the first four multiples of 7?

b) Write down all the factors of 30.

c) What are the first six prime numbers?

44S) a) What are the first four multiples of 5?

b) Write down all the factors of 40.

c) Which two prime numbers come next, after 13?

Grade D Clip 44

45T) Solve the inequality 2x + 3 < 11

45S) Solve the inequality 5x – 7 > 43

Grade C Clip 109

46T) Evaluate 53

46S) Evaluate 24Grade D Clip 45


47T) Find the volume of this triangular prism.

Grade D Clip 85

7cm4cm

6cm

47S) Find the volume of this triangular prism.

10cm

8cm

4cm

Grade CClip 122

48T) a) Write as a power of 7

73 × 75

b) Write as a power of 2

28 ÷ 22

48S) a) Write as a power of 5

52 × 54 × 5

b) Write as a power of 3

39 ÷ 34

Grade CClip 111

Oxtail Tomato Chicken TotalMale 25 42

Female 18 11Total 16 100

49T) Complete the two-way table which shows the favouritesoup of 100 people.

49S) 110 students studied History and Geography as shownin the two-way table.

40 males studied both subjects.

52 of the students were male.

Complete the two-way table.

History Geography Both TotalFemaleMale 8Total 15 20 110


50T) Measure this angle.

50S) Measure this angle. Grade DClip 79

Grade C Clip 93

51T) The price of a pair of shoes is £75.

How much are they after a price increase of 10%?

51S) A new car costs £8000.

If the price is reduced by 15% what is the new price?

Grade C Clip 10052T) 73.5 ÷ 0.21

52S) 18.02 ÷ 0.34

53T) What are the first 5 terms of the number sequencewith the nth term of 3n + 2?

Grade D Clip 6553S) What are the first 5 terms of the number sequence

with the nth term of 4n – 3?


54T) Translate triangle A by vector -5-3

54S) Describe fully the transformation which maps triangleA onto triangle B.

B

Grade D Clip 77

55T) Change the recurring decimal 0.27 into a fraction inits simplest form.

. .

55S) Change the recurring decimal 0.63 into a fraction inits simplest form.

. .

Grade C Clip 98


56T) What is the equation of the line?

-3 -2 -1 O 1 2 3

-3

-2

-1

1

2

3

4

5

x

y

56S) What is the equation of the line?

-3 -2 -1 O 1 2 3

-3

-2

-1

1

2

3

4

5y

Grade C Clip 114

57T) List all of the outcomes if you roll a dice andflip a coin.

57S) List all of the outcomes if you flip three coins.

Grade D Clip 90


58T) Use a protractor to work out the bearing of A from B.

A

B

N

58S) Use a protractor to work out the bearing of B from A.

A

BN

Grade C Clip 131

59T) In the list of fractions, below, which two areequivalent to ?4

5

56

89

810

1011

1620

1824

59S) In the list of fractions, below, which two areequivalent to ?2

3

812

78

612

814

1016

1421

Grade D Clip 47

60T) A map has a scale of 1:100 000.

If town A is 5cm away from town B on the map, what isthe actual distance between them in kilometres?

60S) A map has a scale of 1:500 000.

If town A is 3cm away from town B on the map, what isthe actual distance between them in kilometres?

Grade D Clip 61


61T) a) -3 × -4

b) 7 × -5

c) -12 ÷ 4

d) -8 – 6

e) 9 – -5

f) 10 + -6

g) -4 + -5

61S) a) 6 × -3

b) -10 × -2

c) 15 ÷ -3

d) 12 – 18

e) 2 – -13

f) 15 + -17

g) -6 + -8

62T) Use the graph to solve the simultaneous equationsy = 7 – x and y = 2x – 2

Grade C Clip 99

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

y = 7 – xy = 2x – 2

x

y

62S) Use the graph to solve the simultaneous equationsy = 8 – 2x and y = ½x + 3

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8y = 8 – 2x

y = ½x + 3

x

y

Grade C Clip 115


63T) Estimate the answer to 37.9 × 4171.94 × 8.03

63S) Estimate the answer to 873 × 18104

Grade C Clip 101

64T) A triangular prism has sides as shown.

Find the surface area of the prism.

64S) A triangular prism has sides as shown.

Find the surface area of the prism.

Grade CClip 121

65T) If the probability of passing a driving test is 0.42 what isthe probability of failing the test?

65S) The probability of a school football team winning afootball match is 0.34 and the probability oflosing is 0.21.

What is the probability of the team drawing the match?

Grade D Clip 91

5 cm

12 cm 13 cm

7 cm

6 m

8 m 10 m

12 m


66T) Draw the net of this right-angled triangular prism.

Grade DClip 82

3 squares 5 squares

4 squares5 squares

66S) Draw the net of this cuboid

5 squares

3 squares2 squares


67T) Write the following fractions in their simplest forms.

a)

b)

c)

Grade DClip 48

1620

915

2460

67S) Write the following fractions in their simplest forms.

a)

b)

c)

1230

721

4064

68T) Here are the ingredients needed to make salmonfishcakes for four people.

a) What weight of salmon would be needed to usethe recipe for six people?

b) For seven people, what weight of flour is needed?

450g potatoes

900g of salmon

25g butter

15g dill

50g flour

2 eggs

150g breadcrumbs

68S) Here are the ingredients needed to make shepherd's piefor five people.

a) What weight of cheese would be needed to usethe recipe for eight people?

b) For six people, how much stock is needed?

c) For nine people, what weight of lambshould be used?

500g potatoes

50g of cheese

150g butter

1 onion

2 carrots

300ml stock

1kg of lamb

Grade DClip 62


69T) Put these fractions in order of size, smallest to largest.

58

712

23

34

69S) Put these fractions in order of size, smallest to largest.

45

920

710

12

Grade D Clip 49

70T) a) What is the square of 6?

b) Find the cube of 4.

c) What is the square root of 49?

d) What is the cube root of 27?

e) Evaluate 144

70S) a) What is the square of 8?

b) Find the cube of 2.

c) What is the square root of 100?

d) What is the cube root of 125?

e) Evaluate 169

Grade DClip 46

71T) Sara wishes to find out how much pocket money peoplein her class received.

Design a suitable question she could useon a questionnaire.

You should include some tickboxes.

71S) Fred wants to know which sports are watched by pupils inhis class.

Design a suitable data collection sheet he can use to find out.

Grade D Clip 84

Grade C Clip 134

72T) Change the following fractions to decimals.

a) b)45

38

72S) Change the following fractions to decimals.

a) b)610

58

Grade D Clip 58


73T) Find the length of sides A, B and C giving your answers toone decimal place.

Grade CClip 118

7cm

12cmA

23cm

14cm

B

6.8cm

3.9cmC

73S) Find the length of sides A, B and C giving your answers toone decimal place.

9cm

A17cm

126cm

58cm

B

74T) The equation x3 + 2x = 20 has a solution between 2 and 3.Use a trial and improvement method to find this solution.Give your answer to 1 decimal place and show all workings.

9.5cm

8.5cm

C

74S) The equation x3 – 4x = 88 has a solution between 4 and 5.Use a trial and improvement method to find this solution.Give your answer to 1 decimal place and show all workings.

Grade C Clip 110

Questions 73 to 85 are all calculator questions


75T) a) 34% of £28.76 =

b) 76% of 900 =

c) Reduce £45.50 by 12.5%

Grade DClip 51

75S) a) 29% of £235.60 =

b) 43% of 2400 =

c) Reduce £260 by 30%

76T) If £1 = 1.23 Euros,

a) Change £38 to Euros.

b) Change 650 Euros to pounds (£).

76S) If £1 = 1.27 Euros,

a) Change £2000 to Euros.

b) Change 923 Euros to pounds (£).

Grade DClip 64

77T) a) Find the area of the following circles.Give both answers to 1 decimal place.

b) Find the area of this quarter circle.

7cm24cm

10cm

77S) a) Find the area of the following circles.Give both answers to 1 decimal place.

b) Find the area of this semicircle.

11cm17.6cm

19cm

Grade D Clip 71

(i) (ii)

(i) (ii)


78T) Which is the best value for money

500g of sausages for £2.75 or

650g of the same type of sausages for £3.70?

You must show all your working.

Grade DClip 50

78S) Which is the best value for money

800ml of orange juice for £0.85 or

350ml of orange juice for £0.46?

You must show all your working.

79T) a) Find the circumference of the following circles.Give both answers to 1 decimal place.

b) Find the perimeter of thisquarter circle to 1 decimal place.

7cm24cm

10cm

79S) a) Find the circumference of the following circles.Give both answers to 1 decimal place.

b) Find the perimeter of this semicircleto 1 decimal place.

11cm17.6cm

19cm

Grade D Clip 72

(i) (ii)

(i) (ii)


80T) a) Change the following to percentages.Give your answers to 1 decimal place.

(i) 17 out of 67

(ii) 134 out of 386

b) If Sue scores 82 marks out of a possible 120 marks,what was her score as a percentage?

Grade DClip 63

80S) a) Change the following to percentages.Give your answers to 1 decimal place.

(i) 44 out of 78

(ii) 12.6 out of 59

b) If Sue scores 14 marks out of a possible 75 marks,what was her score as a percentage?

81T) Find the volume of this cylinder.Give your answer to 1 decimal place.

9cm

24cm

81S) Find the volume of this cylinder.Give your answer to 1 decimal place.

20cm

47cm

Grade D Clip 53

82T) Evaluate8.23 + 2.32

(12.4 – 7.3)2

82S) Evaluate19.62 + 73 + 25

53 – 56

Grade CClip 122


83T) Find the length of the line.

Grade CClip 119

83S) Find the length of the line to 1 decimal place.

84T) a) A cyclist travels 12 miles in 2 hours.What is the cyclist's speed in mph?

b) Sue walks for 45 minutes at 14mph.How far does she travel?

c) A piece of lead has a mass of 340g and avolume of 30cm3.Work out its density in g/cm3.

84S) a) A cyclist travels at 14.3mph for 4 hours.What distance does he cover?

b) Sue drives at an average speed of 57mph and coversa distance of 256.5 miles.How long does the journey take in hoursand minutes?

c) A piece of lead has a density of 12g/cm3 and amass of 2kg.Work out its volume in cm3.

Grade CClip 126

O 1 2 3 4 5 6

1

2

3

4

5

6

y

x

y

x

O 1 2 3 4 5 6

1

2

3

4

5

6


85T) The two triangles are similar.

a) Work out the size of x.

b) Work out the size of y.

8cm

5cmy

43.2cm

x37.8cm

85S) BE is parallel to CD

Find the length of BC.

A

B

C D

E12cm

21.6cm

10cm

x

Grade CClip 123


24 Essential Questions at grade B(A calculator can be used on all questions apart from qu. 13)

2T) Mary recorded the heights, in centimetres, of the girls inher class.

She put the heights in order.

132 144 150 152 160 162 162 167167 170 172 177 181 182 182

a) Find the lower quartileb) Find the upper quartilec) On the grid, draw a boxplot for this data.

2S) Mary recorded the heights, in centimetres, of the girls inher class.

She put the heights in order.

131 142 142 150 158 161 165 169169 169 173 179 183 185 186 188

a) Find the lower quartileb) Find the upper quartilec) On the grid, draw a boxplot for this data.

Grade BClip 152

1T) Solve these two simultaneous equations

2r + 3s = 63r – 2s = 22

1S) Solve these two simultaneous equations

h + 3t = –102h – t = 8

Grade B Clip 142


3T) Work out the lengths or angles indicated by theletters a to d.

a

68°

b

13cm

8cm

c

36°

d

42cm

18cm

3S) Work out the lengths or angles indicated by theletters e to h.

e

23cm

15cm f

13cm

25cm

50cm

32°

14°

22cmg

h

19.6cm24.2cm

Grade BClip 147


4T) TR and TQ are tangents to the circle

a) Explain why angle PQR = 42º

b) Find the size of angle PRT giving reasons

4S) TR and TQ are tangents to the circle

a) Explain why angle PQR = 35º

b) Find the size of angle PRT giving reasons

5T) Find angles a and b

95°

a

105°

b

5S) Find angles a and b

63°

a125°

b

Grade BClip 150

Grade BClip 150


6T) Find the size of angle x.

o

x

124

o

y

6S) Find the size of angle y.

Grade BClip 150

84

7T) a) John places £13000 in a bank which pays 4.6%compound interest per year. How much interestdoes he earn if he leaves the money in the bankfor 3 years?

b) Sue buys a new car for £8700.Its annual rate of depreciation is 23% per year.How much is it worth after 5 years?

7S) a) Sarah buys a 5-year bond which pays compoundinterest of 5.8% per year. She buys the bond for£8000. How much can she cash the bond in for atthe end of the 5 year period?

b) Tom buys a house for £145000.It will depreciate at the rate of 2.3% per year forthe next three years. How much will it then be worth?

Grade B Clip 137


8T) The heights of 64 plants were measured and can beseen in this table.

a) Complete this cumulative frequency table.

b) Draw a cumulative frequency curve for your table.

c) Use your graph to find an estimate for theinterquartile range of the heights of the plants.

0 10 20 30 40 50 600

10

20

30

40

50

60

70

80

Height (cm)

CF

0 h < 10 3

10 h < 20 7

20 h < 30 23

30 h < 40 24

40 h < 50 5

50 h < 60 2

<

<

<

<

<

Height (cm) Frequency

<

0 h < 10 3

0 h < 20

0 h < 30

0 h < 40

0 h < 50

0 h < 60

<

<

<

<

<

<

Height (cm) Cumulative Frequency

Grade BClip 151


8S) The weights of 72 boxes of recycled metals can beseen in this table.

a) Complete this cumulative frequency table.

b) Draw a cumulative frequency curve for your table.

c) Use your graph to find an estimate for theinterquartile range of the weights of the boxes.

0 10 20 30 40 50 600

10

20

30

40

50

60

70

80

Weight (kg)

CF

0 w < 10 8

10 w < 20 12

20 w < 30 18

30 w < 40 24

40 w < 50 7

50 w < 60 3

<

<

<

<

<

Weight (kg) Frequency

<

0 w < 10 8

0 w < 20

0 w < 30

0 w < 40

0 w < 50

0 w < 60

<

<

<

<

<

<

Weight (kg) Cumulative Frequency

Grade BClip 151


9T) There are 3 green sweets and 7 red sweets in a bag.

Tom takes a sweet, at random, from the bag and eats it.

He then takes another sweet, at random, and eats it.

a) Draw a tree diagram in the space below to show

all the possibilities.

b) What is the probability that Tom ate two Green sweets?

c) What is the probability that Tom ate two

different-coloured sweets?

9S) There are 4 yellow sweets and 6 blue sweets in a bag.

Joe takes a sweet, at random, from the bag and eats it.

He then takes another sweet, at random, and eats it.

a) Draw a tree diagram in the space below to show

all the possibilities.

b) What is the probability that Joe ate two blue sweets?

c) What is the probability that Joe ate two

different-coloured sweets?

10T) a) Write 2340000 in standard form.

b) Write 0.00042 in standard form.

c) Write 7.8 × 106 as a normal number.

d) Write 4.71 × 10–5 as a normal number.

10S) a) Write 630000000 in standard form.

b) Write 0.00000715 in standard form.

c) Write 9.17 × 105 as a normal number.

d) Write 8.23 × 10–6 as a normal number.

Grade B Clip 135

Grade B Clip 154


11T) a) In a sale, all the prices have been reduced by 15%.The sale price of a shirt is £14.45What was the pre-sale price of the shirt?

b) The price of a computer is £799. This priceincludes VAT which is 17.5%.

What is the cost of the computer beforeVAT is added?

11S) a) A bank pays interest of 6.8% per year.

Emma places some money in the bank and, oneyear later, after the interest has been paid,she has £2242.80 in her account.

How much did she put in the bank?

b) After a reduction of 12.5%, Sam pays £3937.50for a car.

How much was the car before the reduction?

Grade B Clip 138

12T) In September 2007, Jim weighed 85.0kg.In September 2008, he weighed 86.7kg.

What was his percentage increase in weight?

12S) The price of a car decreases from £7600 to £5168in one year.What is the percentage depreciation in this year?

Grade B Clip 136

13T) a) b)

c) d)

2 35 + 3

4 1 16 – 2

5

4 12 × 2

33 5 13 ÷ 2

32

13S) a) b)

c) d)

1 29 + 1

2 4 23 – 5

6

2 14 × 1

35 3 47 ÷ 5

14

2 2

Grade B Clip 139

14T) Factorise and solve the following equations:

a) x2 + 6x + 8 = 0

b) x2 + 3x – 10 = 0

c) x2 – 7x + 10 = 0

d) 6x2 + 7x – 3 = 0

14S) Factorise and solve the following equations:

a) x2 + 8x + 12 = 0

b) x2 + 3x – 40 = 0

c) x2 – 4x + 3 = 0

d) 10x2 + x – 3 = 0

Grade BClip 140


15T) On the grid, draw straight lines and use shading toshow the region R that satisfies the inequalities

y <3 y 2x + 3< x + y 6<

15S) On the grid, draw straight lines and use shading toshow the region R that satisfies the inequalities

y <2 y x + 1<

Grade B Clip 144

y <3x – 6

O 1 2 3 4 5 6

1

2

3

4

5

6

x

y

O 1 2 3 4 5 6

1

2

3

4

5

6

x

y


16T) A and B are two geometrically similar solids.

The total surface area of shape A is 3200cm2

The total surface area of shape B is 16928cm2

The volume of shape A is 4760cm3

Calculate the volume of shape B.

16S) C and D are two geometrically similar solids.

The volume of shape C is 17cm3

The volume of shape D is 136cm3

The total surface area of shape C is 9.6cm2

Calculate the total surface area of shape D.

Grade B Clip 149

17T) A, B and C are all towns.A is 7.8km due east of B.B is 12km due south of C.

Calculate the bearing of A from C.Give your answer correct to 1 decimal place.

17S) A, B and C are all towns.B is due south of A.C is 18km due east of B and on a bearing of152° from A.

Calculate the distance between A and B.Give your answer correct to 1 decimal place.

Grade B Clip 147c

18S) a) Factorise (i) x2 – 36

(ii) 4y2 – 9

b) Simplify

c) Solve 16x2 – 25 = 0

4a2 – b2

8a – 4b

18T) a) Factorise (i) x2 – 64

(ii) 25y2 – 36

b) Simplify

c) Solve 9x2 = 100

4a2 – 49b2

6a + 21b

Grade B Clip 141

19T) Work out the following, giving your answer instandard form.

(7 × 106) × (9 × 104)

19S) Work out the following, giving your answer instandard form.

(8 × 108) ÷ (4 × 105)

Grade BClip 135

. .


x

y

–2

–12

–1 0 1 2

20T) a) Complete this table of values for

y = x3 + x – 2

b) On the grid, draw the graph of y = x3 + x – 2

c) Use the graph to find the value of x when y = 2

-2 -1 O 1 2

-12

-10

-8

-6

-4

-2

2

4

6

8

x

y

Grade B Clip 145


x

y

–2 –1 0 1 2

20S) a) Complete this table of values for

y = x3 – 3x

b) On the grid, draw the graph of y = x3 – 3x

c) Use the graph to find the three values of x when y = 1

x

y

-2 -1 O 1 2

-2

-1

1

2

Grade B Clip 145


22T) Sketch the graphs of

a) y = x2 b) y = x3

c) y = 2x + 4 d) y = -x3

22S) Sketch the graphs of

a) y = -x2 b) y =

c) y = 3x – 6 d) y = x2 – 4

1x

Grade B Clip 146

21T) a) A straight line is parallel to y = 3x – 1 and goesthrough (1, 7).What is its equation?

b) A straight line goes through points (1, 5) and (3, 13).What is its equation?

21S) a) A straight line is parallel to y = 5x – 3 and goesthrough (3, 17).What is its equation?

b) A straight line goes through points (1, 5) and (3, 3).What is its equation?

Grade B Clip 143


x

.P.

Q.

.

.R

S

y

z

23T)

T

.P

.

.

y23S)

T

S

x

Grade BClip 148

Point P has coordinates (7, 4, 3)

Point T is the intersection of PR and SQ.

Work out the coordinates of T.

Point P has coordinates (8, 3, 4)

a) Work out the coordinates of T.

b) Work out the coordinates of S.z

24T) Two fair six sided dice are rolled.a) Complete the tree diagram to show the outcomes.

six

notsix

Red dice Blue dice

24S) Two coins are flipped.a) Complete the tree diagram to show the outcomes.

b) What is the probability of rolling a six onone dice and 'not a six' on the other dice?

b) What is the probability of flipping a head

on one coin and a tail on the other coin?

16

Head

Tail

Coin 1 Coin 212

Grade BClip 153


26 Essential Questions at grade A/A*(A calculator can be used on all questions unless told otherwise)

1T)

The diagram shows part of the curve with equation y = f(x).The coordinates of the maximum point of this curve are (2, 1).

Write down the coordinates of the maximum point of the curvewith equation

a) y = f(x) + 3

b) y = f(x) – 1

c) y = f(x – 3)

d) y = 2f(x)

e) y = f(½x)

y

x

(2, 1)× y = f(x)

0

1S)

The diagram shows part of the curve with equation y = f(x).The coordinates of the minimum point of this curve are (1, -4).

Write down the coordinates of the minimum point of the curvewith equation

a) y = ½f(x)

b) y = f(2x)

c) y = f(x + 5)

d) y = f(x) + 4

e) y = 3f(x)

y

x

(1, -4)×

y = f(x)

0

Grade A/A*Clip 167


2T) For each triangle find the side or angle marked withthe letter x.Give your answer correct to 1 decimal place.

a) b)

c) d)

x

x

x

x

41°56°

110°

68°94 cm

66 cm

5 cm

6 cm

7 cm5 cm 9 cm

Grade A/A*Clip 173

2S) For each triangle find the side or angle marked withthe letter x.Give your answer correct to 1 decimal place.

a) b)

c) d)*

x

x

x

x

10 m

98° 95°

67°62°

12 m

14m

12 cm

5 cm

7 cm

5 cm

8 cm

3T) Solve 3x2 + 7x – 12 = 0

Give your solutions correct to 2 decimal places.

3S) Solve 2x2 – 5x + 1 = 0

Give your solutions correct to 2 decimal places.

Grade A/A* Clip 161

8 cm

*A tricky sine rule question.


5T)

The sketch shows a curve with function y = kax

where k and a are constants and a > 0.

The curve passes through points (1, 8) and (3, 200).

Calculate the value of k and the value of a.

4T) q is inversely proportional to the square of t.

When t = 5, q = 9.6

a) Find a formula for q in terms of t.

b) Calculate the value of q when t = 8.

c) When q = 2.4, calculate the value of t.

Grade A/A* Clip 159

4S) The distance d through which a body falls from rest isproportional to the square of the time taken, t.

The body falls 45m in 3 seconds.

a) Find a formula for d in terms of t.

b) How far will the body fall in 6 seconds?

c) How long will the body take to fall 20m?

x

y

(3, 200)

0

(1, 8)

x

y

(1, 3)

(4, 192)

0

5S)

The sketch shows a curve with function y = kax

where k and a are constants and a > 0.

The curve passes through points (1, 3) and (4, 192).

Calculate the value of k and the value of a.

Grade A/A*Clip 170


6T) Enlarge triangle A by scale factor -1½, centre (0, 0)

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890

A

6S) Enlarge triangle B by scale factor -2½, centre (2, 2)

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

12345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901

B

Grade A/A* Clip 171

×


7T) The maximum load a van can safely carry is 1800kg.Fred transports metal bars in the van.Each bar weighs 90kg.

Fred knows that the 1800 is rounded correct to2 significant figures and 90 is rounded correct to1 significant figure.

Calculate the greatest number of bars that Fred cansafely carry in the van. Show all workings.

7S)

All measurements are rounded correct to 1 decimal place.

a) Find the largest possible value of the shaded area.

b) Find the least possible value of the shaded area.

Grade A/A* Clip 16012345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345

10.6 m

4.8 m

6.8 m

2.6 m

8T) Calculate the area of triangle ABC.Give your answer correct to 1 decimal place.

C

8S) Calculate the area of triangle ABC.Give your answer correct to 1 decimal place.

Grade A/A* Clip 176

A

B

9 cm15 cm

104°

A

B C78°

12.6 cm

18.3 cm


9T) Simplify fully

a)

b)

c) Show that the equation

can be rearranged to give 3x2 + 12x – 16 = 0

Grade A/A* Clip 157/158

x2 + 3x – 10x2 – 6x + 8

4x + 5

3x – 2+

5x + 3

2 – 3xx – 2=

Grade A/A*Clip 163

9S) Simplify fully

a)

b)

c) Show that the equation

can be rearranged to give x2 + 3x – 31 = 0

x2 + 7x + 12x2 – 3x – 28

7x – 6

2x + 3+

4 – xx – 5

3x + 4=

10T) a) Rationalise the denominator of

b) Expand (2 + )(1 + )

Give your answer in the form a + b , wherea and b are integers.

15

5 5

10S) a) Rationalise the denominator of

b) Expand and simplify ( – )( + )

17

7 2

5

7 2

11T) Emma has 4 blue pens and 3 red pens in a pencil case.

She picks a pen at random, notes its colour and thenreplaces it. She does this two more times.

Work out the probability that when Emma takes threepens, exactly two are the same colour.

11S) A box contains toffees covered in either milk, plain orwhite chocolate. The probability of each is 0.2, 0.5and 0.3 respectively.

Tony chooses a chocolate, notes the type of chocolateand replaces it. He then chooses again.

What is the probability he chooses exactly one whitechocolate toffee?

Grade A/A* Clip 182


12S)

OPQR is a parallelogram.M is the midpoint of RQ.N is the midpoint of PQ.

OP = p OR = r

a) Find, in terms of p and/or q, the vectors

(i) MQ

(ii) MN

b) Show that RP is parallel to MN

P Q

RO

N

M

p

r

Grade A/A* Clip 180

13T) Prove that the recurring decimal 0.45 = 1533

. .

13S) Prove that the recurring decimal 0.36 = 411

Grade A/A* Clip 155

12T)

a) Find, in terms of a and b, the vectors

(i) AB,

(ii) RT,

(iii) RS

b) Explain why RST is a straight line.

The length of RS is 4 cm.

c) Find the length of RT.

O B T

A

RS

2a

b

a OAB is a triangle.B is the midpoint of OT.S is the midpoint of AB.

OR = 2a RA = a OB = b

. .


y

x360°

1

–1

0

14T) Here is the graph of y = sin x, where 0º < x < 360°

What are the equations of these three graphs?Choose from y = sin 2x

y = 2sin xy = -sin xy = sin x + 2y = sin ½xy = -2sin x

y

x360°

1

–1

0

14S) Here is the graph of y = sin x, where 0º < x < 360°

What are the equations of these three graphs?Choose from the same list as in 14T.

Grade A/A*Clip 169

x360°

1

–1

0

yc)

x360°

1

–1

0

yb)

y

x360°

1

–1

0

a)

c)

x360°

1

–1

y

0

2

a)

x360°

1

–1

y

0

2

–2

b)

x360°

1

–1

y

0

2

–2


15T) This unfinished table and histogram shows informationabout the takings per day in pounds (p) of a businesswhich sells software.

0 200 400 600 800 1000 1200 1400

Frequency

density

Takings in pounds (p)

a) Use the information in the histogram to completethe table.

b) Use the information in the table to completethe histogram.

Grade A/A* Clip 181

Takings in pounds (p) Frequency

0 < p < 400

400 < p < 600

600 < p < 800

800 < p < 1000

1000 < p < 1400

6

5

10


15S) This histogram gives information about the paintingssold in a shop one Saturday.

a) Use the histogram to complete the table.

Price (p) in pounds (£) Frequency

0 < p < 5

5 < p < 10

10 < p < 20

20 < p < 40

0 5 10 15 20 25 30 35 400

4

8

12

16

20

Price (P) in pounds (£)

This table gives information about the paintingssold in another shop on the same Saturday.

b) Draw a histogram to represent this information.

Price (p) in pounds (£) Frequency

0 < p < 5

5 < p < 10

10 < p < 20

20 < p < 40

100

40

24

96

Price (p) in pounds (£)0 5 10 15 20 25 30 35 40

0

4

8

12

16

20

Frequency

density

Frequency

density

Grade A/A* Clip 181


16T) A college has 450 students.Each student studies one of German, French,Spanish or Italian.This table shows how many students study eachof these languages.

An inspector wants to look at the work of a stratifiedsample of 80 of these students.

Find the number of students studying each language thatshould be in the sample.

Language

German

French

Spanish

Italian

Number of students

38

143

76

193

16S) The table shows the number of boys and girls in eachyear group of a secondary school.

James wants to take a stratified sample of 50 girls byyear group.

Work out the number of girls in each year group thatshould be in his sample.

Year group No. of boys

7

8

9

10

11

Total

105

148

94

63

90

500

66

112

90

48

184

500

No. of girls

Grade A/A* Clip 183

17T) Make x the subject of

4(x – 6) = y(4 – 3x)

17S) Make x the subject of the formula

mn

xx + 2t =

Grade A/A* Clip 164


18T)

OAB is a sector of a circle, centre O

a) Work out the length of the arc ABGive your answer to 1 decimal place.

b) Work out the area of sector AOB.Give your answer to 1 decimal place.

Grade A/A*Clip 178

O

A B

10 cm 10 cm60°

18S)

OAB is a sector of a circle, centre O

a) Work out the length of the arc ABGive your answer to 1 decimal place.

b) Work out the area of sector AOB.Give your answer to 1 decimal place.

O

A B

18 cm115°

18 cm

19T) By eliminating y, find the solutions to the simultaneousequations

19S) By eliminating y, find the solutions to the simultaneousequations

Grade A/A* Clip 165

x2 + y2 = 20y = x – 2

x2 + y2 = 13

y = x + 1


y

x360°

1

–1

0

20T) Here is the graph of y = sin x°, where 0 < x < 360°

Given that sin 30° = , write down the value of

(a) sin 150°

(b) sin 330°

Grade A/A*Clip 168

12

20S) Here is the graph of y = cos x°, where 0 < x < 360°

Use the graph to find estimates of the solutions,in the interval 0 < x < 360, of the equations

(a) cos x° = –0.3

(b) 4cos x° = 3

x

y

O30 60 90 120 150 180 210 240 270 300 330 360 390

-1

-0.5

0.5

1

Non calculator question



21T) Given that x2 + 8x – 2 = (x + p)2 + q for all values of x,

a) find the value of p and the value of q.

b) on the axes, draw a sketch of the graphy = x2 + 8x – 2

Grade A/A*Clip 162

x

y

O

21S) Given that x2 – 4x – 5 = (x – p)2 + q for all values of x,

a) find the value of p and the value of q.

b) on the axes, draw a sketch of the graphy = x2 – 4x – 5

x

y

O

22T) Write down the value of a) 70

b) 4–2

c) 823

22S) Write down the value of a) 120

b) 5–3

c) 8134

Grade A/A*Clip 156




23T)

The equation of the straight line through A and B is

a) Write down the equation of another straight linethat is parallel to

b) Write down the equation of another straight linethat passes through the point (0, 5).

c) Find the equation of the line perpendicular to ABpassing through B.

Grade A/A*Clip 166

x

y

×

×

B (6, 7)

A (0, 5)

0

Diagram NOTaccurately drawn

13y = x + 5

13y = x + 5

23S)

The equation of the straight line through A and B is

a) Write down the equation of another straight linethat is parallel to

b) Write down the equation of another straight linethat passes through the point (0, 4).

c) Find the equation of the line perpendicular to ABpassing through B.

x

y

×

×

B (8, 8)

A (0, 4)

0

Diagram NOTaccurately drawn

12y = x + 4

12y = x + 4


24T)

This is a cuboid, ABCDEFGH

AB = 9 cm, BC = 8 cm, AG = 16 cm

a) Calculate the length AE.Give your answer to 3 significant figures.

b) Work out the angle between CE and the horizontalplane ABCD.Give your answer to 2 significant figures.

Grade A/A* Clips 174 and 175

C

GH

FE

BA

D

9 cm

8 cm

16 cm

A B

CD

M

X24S)

The diagram shows a square-based pyramid ABCDX.

AB = BC = 9 cm.

The point M is the centre of the square base.XM = 12 cm.

a) Calculate the length of AC.Give your answer to 3 significant figures.

b) Work out the angle between the edge AX and thehorizontal plane ABCD.Give your answer to 1 decimal place.

9 cm

9 cm

12 cm


25T)

This is a sphere with radius 8 cm.

a) Find the volume of the sphere.Give your answer to 3 significant figures.

b) Find the surface area of the sphere.Give your answer to 3 significant figures.

Grade A/A* Clip 177

8 cm

25S)

This is a cone with radius 4 cm and height 13 cm.

a) Find the volume of the cone.Give your answer to 3 significant figures.

b) Find the curved surface area of the cone.Give your answer to 3 significant figures.

13 cm

4 cm

26T) Find the equation of the circle with centre (0, 0) andradius 6 cm.

26S) Find the equation of the circle with centre (0, 0) andradius 10 cm.

Grade A/A* Clip 172

IndexSymbols

3D-coordinates 543D-Pythagoras 703D-trigonometry 70

A

algebraic fractions 60alternate angles 13angles in triangle 13angles of polygons 12area of circle 36area of compound shapes 16area of rectangle 16area of sphere 71area of triangle 16areas of triangles using sine 59

B

bearings - calculation of 50bearings - finding with protractor 29best value for money 37bisect a line 7bisect an angle 7BODMAS 7bounds - difficult questions 59bounds at grade C level 5box plots 41

C

change the subject of a formula 17change the subject of formula - difficult 65circle theorems 43, 44circles - area 36circles - circumference 37circles and loci - equations 71circumference of circle 37completing the square 68compound interest/depreciation 44compound measures 39compound shapes - area 16cone - volume and surface area 71converting metric units 14coordinates - 3D 54cosine rule 56cubes, squares and roots 34cubics - drawing graphs of 51, 52cumulative frequency 45, 46curvy graphs 19, 20cylinder - volume of 38

D

density, mass, volume 39difference of two squares 50direct proportion 57directed numbers - four rules 30

E

enlargements - negative scale factor 58enlargements - positive scale factor 11equations 14equivalent fractions 29estimate for the mean 9estimation 31evaluate with calculator 38Evaluating numers with indices - simple 24Expanding brackets 3exponential functions 57

F

factorising - simple 5factorising quadratics 48factors, multiples and primes 24foreign currency conversion 36forming equations 12forming expressions 12fraction of an amount 8fractional and negative indices 68fractions - algebraic 60fractions - changing to decimal 34fractions - four rules 15fractions - four rules, difficult 48fractions - putting in order 34fractions - simplifying 33frequency diagrams 22frequency polygons 22

G

gradients of parallel and perpendicular lines 69graph of trig functions 67graphs - linear 21graphs - recognising 53graphs - transformations 55graphs of cubics 51, 52graphs of quadratics 19, 20

H

hard calculator question 38highest common factor 7histograms 63, 64

I

index notation - multiply and divide 25indices - fractional and negative 68inequalities - integers 7inequalities - shading regions 49inequalities - solving 24inverse proportion 57

L

linear graphs 21loci 23long division 26long multiplication 15lower bounds 5lowest common multiple 7

M

mean from a table 4measuring angles 26median from a table 4metric units 14moving averages 47multiples 24multiplication of decimals 7

N

negative indices 68nets 32nth term - finding from sequence 4nth term - generating a sequence from 26

O

outcomes - listing 28

P

percentage increase/decrease 48percentages - change to % with calc. 38percentages - change to % without calc. 23percentages - find % with calc. 36percentages - find % without calc. 17percentages - increase and reduction 26percentages - reverse 48perimeter involving circles 37pie charts 15place value 6planes of symmetry 21plans and elevations 8prime numbers 24probability - experimental 21probability - mutually exclusive events 31probability AND/OR questions 60product of prime factors 7proportion - direct and inverse 57Pythagoras - in 2D 35Pythagoras - in 3D 70Pythagoras - line on graph 39

Q

quadratic equations - solving with formula 56quadratics - factorisation 48questionnaires 34

R

ratio - map scales 29ratio - recipe questions 33ratio - sharing 9real-life money questions 36real-life number questions 15rearranging difficult formulae 65recipes - ratio 33recognising graphs 53recurring decimals - changing to fraction 27recurring decimals - from first principles 61reflections 10reverse percentage 48rotations 10

S

scatter diagrams 24sectors of circles 66similar 3D shapes 50similar triangles 40simplification of algebraic terms 3simultaneous equations - solving graphically 30simultaneous equations involving a quadratic 66simultaneous linear equations 41sine rule 56solve quadratic equation with formula 56solving equations 14speed, distance, time 39spheres - area and volume 71squares, cubes and roots 34standard form 47standard form - calculation 50stem and leaf diagrams 14straight lines - finding equation of 28stratified samples 65subject of a formula - simple 17substitution 6surds 60surface area of cuboids 17surface area of triangular prisms 31surface area of sphere 71symmetry - planes of 21

T

transformation of graphs 55transformation of trig functions 62transformations 10translations 27travel graph 18tree diagrams 47, 54trial and improvement 35triangles - drawing with compasses 7trig functions - graphs 67trig functions - transformations 62trigonometry - 2D 42trigonometry - 3D 70two-way tables 25

U

unit conversions 14upper bounds 5

V

value for money 37vectors 61volume of cone 71volume of cylinder 38volume of prism 25volume of sphere 71

Y

y = mx + c 53

essential revision questions mathswatch higher

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