Name: _______________________________________________

U4 Block Test 1 Revision Pack

2024

Page
Section 1: Algebra 2
Section 2: Geometry & Data 10
Section 3: Past Paper Questions
Quadratics 24
Proportion 28
Volume & Surface Area 32

Answers: 34

Utilise the following clinic slots if you have questions or would like additional support:
Tuesday p7 - Miss Morris in MA6 (or Mr. Stephens in En3)
Tuesday p8 - Mr. Lam in MA6
Wednesday p7 – Mr. Mackay in MA4
Wednesday p8 – Mrs Buzzacott in MA2
Thursday p7 – Mr. Watson in MA8
Thursday p8 – Mr. Watson in MA8 (or Mr. Stephens in En3)
Friday p8 – Mr. Chiba in MA6 (or Mr. Stephens in En3)
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Algebra
Question 1

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

…………………………

Question 2

Write 𝑥2 − 4𝑥 + 5 in the form (𝑥 + 𝑎)2 + 𝑏 where 𝑎 and 𝑏 are integers.

…………………………

Question 3

Write 𝑥2 + 6𝑥 + 10 in the form (𝑥 + 𝑎)2 + 𝑏 where 𝑎 and 𝑏 are integers.

…………………………

Question 4

Write 𝑥2 − 6𝑥 + 16 in the form (𝑥 + 𝑎)2 + 𝑏 where 𝑎 and 𝑏 are integers.

…………………………
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Question 5

Write 𝑥2 + 𝑥 − 1 in the form (𝑥 + 𝑎)2 + 𝑏 where 𝑎 and 𝑏 are constants to be found.

…………………………

Question 6

Write 𝑥2 + 3𝑥 − 5 in the form (𝑥 + 𝑎)2 + 𝑏 where 𝑎 and 𝑏 are constants to be found.

…………………………

Question 7

Express 𝑦2 + 8𝑘𝑦 + 4 in the form (𝑦 + 𝑎)2 + 𝑏, where 𝑎 and 𝑏 are in terms of 𝑘.

…………………

Question 8
Factorise: 3𝑥2 + 7𝑥 + 4

…………………………
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Question 9
Factorise: 6𝑥2 + 13𝑥 + 6

…………………………

Question 10
Factorise: 4𝑥2 − 25𝑥 + 6

…………………………

Question 11

Factorise: 3𝑦2 − 22𝑦 + 7

…………………………

Question 12
Factorise the following: 16𝑥2 − 8𝑥 − 3

…………………………
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Question 13
Solve by factorising: 𝑥2 + 2𝑥 − 35 = 0

𝑥 = ...........
or 𝑥 = . . . . . . . . . . .

Question 14
Solve by factorising: 2𝑥2 + 13𝑥 + 6 = 0

𝑥 = ...........
or 𝑥 = . . . . . . . . . . .

Question 15
Solve by factorising: 2𝑥2 − 11𝑥 + 14 = 0

𝑥 = ...........
or 𝑥 = . . . . . . . . . . .

Question 16
Solve by factorising: 3𝑥2 − 20𝑥 − 7 = 0

𝑥 = ...........
or 𝑥 = . . . . . . . . . . .
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Question 17
Solve the following quadratic equation, giving your answer accurate to 2 decimal places:

3𝑥2 − 13𝑥 + 5 = 0

𝑥 = ...........
or 𝑥 = . . . . . . . . . . .

Question 18
Solve the following quadratic equation, giving your answer accurate to 2 decimal places:

𝑥2 − 4𝑥 + 3 = 0

𝑥 = ...........
or 𝑥 = . . . . . . . . . . .

Question 19
Solve the following quadratic equation, giving your answer accurate to 2 decimal places:

𝑥2 − 6 = 0

𝑥 = ...........
or 𝑥 = . . . . . . . . . . .

Question 20
Expand and simplify

5𝑥2 (3𝑥3 − 2)

…………………………
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Question 21
Expand and simplify 3𝑦3 (5𝑦2 − 2𝑝 − 2)

…………………………

Question 22
Expand and simplify (𝑥 + 1)(𝑥 + 5)

…………………………

Question 23
Expand and simplify (2𝑥 + 7)(𝑥 + 1)

…………………………

Question 24
𝑞 is directly proportional to 𝑥2 .

When 𝑞 = 4, 𝑥 = 4

Find a formula connecting 𝑞 and 𝑥.

𝑞 = …………………………
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Question 25
𝑝 is inversely proportional to 𝑦.

When 𝑝 = 4, 𝑦 = 3

Find a formula connecting 𝑝 and 𝑦.

𝑝 = …………………………

Question 26

𝑥 is directly proportional to 3√𝑦

𝑦 is inversely proportional to 3√𝑧

Given that 𝑥 = 2 and 𝑧 = 64 when 𝑦 = 8 find a formula for 𝑥 in terms of 𝑧

𝑥 = …………………………

Question 27

𝑎 is inversely proportional to 𝑏2
𝑏 is directly proportional to 𝑐2

Given that 𝑎 = 7 and 𝑐 = 8 when 𝑏 = 6 find a formula for 𝑎 in terms of 𝑐

𝑎 = …………………………
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Question 28
𝑥 is inversely proportional to 𝑞2

𝑞 is decreased by 50%

Work out the percentage increase in 𝑥.

………………………… %

Question 29

𝑧 is inversely proportional to 3√𝑦

𝑦 is decreased by 87.5%

Work out the percentage increase in 𝑧.

………………………… %

Question 30
𝑦 is inversely proportional to 𝑥2 .

When 𝑦 = 1, 𝑥 = 5

Find a formula connecting 𝑦 and 𝑥.

𝑦 = …………………………
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Geometry & Data

Question 1
Here are the number of times a group of eleven pupils have been late to school this term.

5 2 5 8 7
5 6 7 6 8
8
Work out the median number of times.

………………………… times

Question 2
A group of 15 pupils practise their times tables, and the time spent by each pupil is recorded
below.

2 2 3 4 4 8djsfs10dn10

14 14 15 17 17 18sdf20

Find the interquartile range.

IQR = ………………………… minutes

Question 3
11 pupils have recorded the number of pens that they own.

1 3 5 5 6 10 12 12 15 16 16

Find the interquartile range.

IQR = ………………………… pens

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Question 4
A group of 19 pupils practise their times tables, and the time spent by each pupil is recorded
below.

1 1 1 1 3 8 8 8 9 10 10 11 11 13 14 15 19 19 20

Find the interquartile range.

IQR = ………………………… minutes

Question 5
Find the perimeter of the sector.

Give your answer correct to 1 decimal place.

………………………… mm
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Question 6
Find the perimeter of the sector.

Give your answer correct to 1 decimal place.

………………………… cm

Question 7
Given that the arc length of sector below is 9 cm, work out its angle, marked 𝑦 on the
diagram.

Give your answer correct to 1 decimal place.

𝑦 = ………………………… °

Question 8
Given that the arc length of sector below is 13 cm, work out its radius, marked 𝑥 on the
diagram.

Give your answer correct to 1 decimal place. 𝑥 = …………… cm

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Question 9
Calculate the area of the sector.

Give your answer correct to 1 decimal place.

………………………… cm 2

Question 10
Calculate the area of the sector.

Give your answer correct to 1 decimal place.

………………………… mm 2
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Question 11
𝐴𝑂𝐵 is a sector of a circle, centre 𝑂 and radius 19 cm.

The perimeter of the sector is 59 cm.

Work out the area of the sector.

………………………… cm 2

Question 12
𝐴𝑂𝐵 is a sector of a circle, centre 𝑂 and radius 14 cm.

The area of the sector is 79 cm 2 .

Work out the perimeter of the sector.

Give your answer correct to 2 decimal places.

………………………… cm
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Question 13
The volume of the cuboid is 560 cm 3 .

Find the value of 𝑝.

𝑝 = ………………………… cm

Question 14
Work out the volume of the triangular prism.

………………………… cm 3
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Question 15
Work out the volume of the trapezoidal prism.

………………………… cm 3

Question 16
The diagram shows a cube with a surface area of 2166 m 2 .

Find the volume of the cube.

………………………… m 3
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Question 17

Said has a container in the shape of a cuboid which he is going to fill with match sticks. The
container has a base which measures 40 cm by 30 cm and can hold a maximum volume of
42 litres.

1 litre= 1000 cm 3

Calculate the depth of the container.

………………………… cm

Question 18
Work out the surface area of the prism.

………………………… cm 2
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Question 19
Find the volume of the cylinder with a diameter of 25.4 cm and height of 6.5 cm, as shown
on the diagram below.

Give your answer correct to 1 decimal place.

………………………… cm 3

Question 20
Find the volume of the cylinder with a diameter of 7.8 cm and height of 4.1 cm, as shown on
the diagram below.

Give your answer correct to 1 decimal place.

………………………… cm 3
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Question 21
A cylinder has a radius of 4 cm and height of 10 cm, as shown on the diagram below.

Work out the surface area of the cylinder.

Give your answer correct to 1 decimal place.

………………………… cm 2

Question 22
A cylinder has a radius of 6 cm and height of 8 cm, as shown on the diagram below.

Work out the surface area of the cylinder.

Give your answer correct to 1 decimal place.

………………………… cm 2
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Question 23
The diagram below shows a small scale model of a building in the shape of a prism.

Find the volume of the model.

………………………… cm 3

Question 24
The diagram below shows a small scale model of a building in the shape of a prism.

Calculate the volume of the model.

………………………… cm 3
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Question 25
The volume of a cylinder with radius 14.2 cm is 7095 cm 3 .

Find the height of the cylinder.

Give your answer correct to 1 decimal place.

ℎ = ………………………… cm

Question 26
The diagram shows a rectangle with area 60 m 2 .
All measurements are in m.

Show that 3𝑥2 + 𝑏𝑥 + 𝑐 = 0 where 𝑏 and 𝑐 are constants to be found.

𝑏 = …………………………
𝑐 = …………………………
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Question 27

The area of the trapezium is 105 m2.

All measurements are in m.

Show that 4𝑥2 + 𝑏𝑥 + 𝑐 = 0, where 𝑏 and 𝑐 are integers to be determined.

𝑏 = …………………………
𝑐 = …………………………

Question 28

The area of the trapezium is 135 cm2.

All measurements are in cm.

Show that 15𝑦2 + 𝑏𝑦 + 𝑐 = 0, where 𝑏 and 𝑐 are integers to be determined.

𝑏 = …………………………
𝑐 = …………………………
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Question 29
The surface area of the cylinder is 1823 cm 2 .

Find the value of 𝑥.

Give your answer correct to 1 decimal place.

𝑥 = ………………………… cm

Question 30
A right-angled triangle has sides (𝑥 + 1) cm, (𝑥 + 2) cm and 6 cm.

Find the value of 𝑥.

Give your answer correct to 2 decimal places.

𝑥 = ………………………… cm
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Recent Past Paper Questions

Quadratics

Q1. Jan 21R Paper 2, Question 9, [3 marks]

Q2. Jan 20R Paper 1, Question 6, [3 marks]

Q3. SAM 3H, Question 6, [5 marks]

(a) Factorise fully 18e3f + 45e2f 4

(b) Solve x2 – 4x – 12 = 0
Show clear algebraic working.

Q4. June 18 Paper 1, Question 3, [9 marks]

Q5. June 22R Paper 1, Question 5, [5 marks]

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Q6. Jan 21 Paper 1, Question 9, [5 marks]

Q7. January 2023 Paper 1HR, Question 8 [ a) 2 marks, bi) 2 marks bii) 1 mark]

Q8. June (Nov) 20, Paper 1, Question 7, [8 marks]

Q9. Jan 20 Paper 2, Question 7, [5 marks]

Q10. May 18 Paper 1, Question 11, [6 marks]

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Q11. SAM 3H, Question 15, [7 marks]

A rectangular lawn has a length of 3x metres and a width of 2x metres.
The lawn has a path of width 1 metre on three of its sides as shown in the diagram.

The total area of the lawn and the path is 100 m2

(a) Show that 6x2 + 7x – 98 = 0

(b) Calculate the area of the lawn.

Show clear algebraic working.

Q12. Jan 19 Paper 2, Question 15, [6 marks]

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Q13. Specimen Paper 1H, Question 21, [6 marks]

 28

Proportion

1. January 2019 Paper 1H, Question 14 a) 3 marks b) 1 mark

2. June 2020 Paper 1H, Question 14 3 marks

3. June 2020 Paper 2HR, Question 20 a) 3 marks b) 1 mark

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4. Specimen Paper 1H, Question 15 a) 3 marks b) 2 marks

5. SAMs Paper 4H, Question 16 a) 3 marks b) 2 marks

6. January 2022 Paper 1H, Question 15 3 marks

7. June 2019 Paper 2H, Question 17 a) 3 marks b) 2 marks

 30

8. January 2023 Paper 1H, Question 17 3 Marks

9. June 2018 Paper 2H, Question 16 a) 3 marks b) 2 marks

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10. January 2022R Paper 2HR, Question 20 4 marks

11. January 2023 Paper 1HR, Question 19 a) 3 marks b) 3 marks

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Volume & Surface Area: Prisms and Cylinders

1. June 2019 Paper 1HR, Question 1 3 Marks

2. January 2019 Paper 2HR, Question 2 4 Marks

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3. June 2019 Paper 2H, Question 4 2 Marks

4. November 2020 Paper 2H, Question 9 5 Marks

5. January 2020 Paper 2HR, Question 13 3 Marks

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Mark scheme : Algebra

Question 1 Question 11
(𝑥 + 1)2 + 1 (3𝑦 − 1)(𝑦 − 7)

Question 12
Question 2
( 4𝑥 − 3) ( 4𝑥 + 1)
(𝑥 − 2)2 + 1

Question 13
Question 3
𝑥 = 5 or 𝑥 = −7
(𝑥 + 3)2 + 1
Question 14
Question 4 1
𝑥 = − 2 or 𝑥 = −6
(𝑥 − 3)2 +7
(2𝑥 + 1) (𝑥 + 6) = 0
Question 5
1 2 5 Question 15
(𝑥 + 2) − 4
7
𝑥 = 2 or 𝑥 = 2

Question 6 (𝑥 − 2)(2𝑥 − 7) = 0

3 2 29
(𝑥 + ) − Question 16
2 4
1
𝑥 = 7 or 𝑥 = − 3
Question 7 (𝑥 − 7)(3𝑥 + 1) = 0
(𝑦 + 4𝑘)2 −16𝑘2 + 4

Question 17
Question 8
𝑥 = 3.91 or 𝑥 = 0.43
(3𝑥 + 4)(𝑥 + 1)
Question 18
Question 9 𝑥 = 3 or 𝑥 = 1
(2𝑥 + 3)(3𝑥 + 2)
Question 19
𝑥 = 2.45 or 𝑥 = −2.45
Question 10
Question 20
(𝑥 − 6)(4𝑥 − 1)
15𝑥5 − 10𝑥2
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Question 21 Geometry & Data

15𝑦5 −6𝑝 𝑦3 − 6𝑦3 Question 1
6
Question 22 Question 2
𝑥2 + 6𝑥 + 5 13
Question 3
Question 23 10
2𝑥2 + 9𝑥 + 7 Question 4
11
Question 24 Question 5
1 43.6mm
𝑞 = 4 𝑥2
Question 6
77.5cm
Question 7
Question 25
12 𝑦 =64.5 °
𝑝= 𝑦 Question 8
𝑥 =15.2cm
Question 26 Question 9
3
𝑥 =
2 √4
1
124cm 2
𝑧9 Question 10
41.9mm 2
Question 11
Question 27
199.5cm 2
28672
𝑎= 𝑐4
Question 12
39.29cm
Question 13
Question 28
𝑝 =8cm
300% Question 14
Question 29
162cm 3
100% Question 15
264cm 3
Question 30 Question 16

𝑦=
25 6859m 3
𝑥2

Question 17
35cm
 36

Question 18
288cm 2 Question 28
1
(4𝑦 + 𝑦 + 1)(3𝑦 + 1) = 135
Question 19 2

3293.6cm 3 (5𝑦 + 1)(3𝑦 + 1) = 270

Question 20 15𝑦2 + 3𝑦 + 5𝑦 + 1 = 270

195.9cm 3 15𝑦2 + 8𝑦 − 269 = 0

Question 29
Question 21
351.9cm 2
0 = (2𝜋)𝑟2 + (2𝜋(19.4))𝑟 − 1823
0 = (2𝜋)𝑟2 + (38.8𝜋)𝑟 − 1823
Question 22
−(38.8𝜋) ± √(38.8𝜋)2 − 4(2𝜋)(−1823)
527.8cm 2 𝑟 = 2(2𝜋)
= 9.902 … 𝑜𝑟 − 29.302 …
Question 23 ➃ Radius must be positive
49.5cm 3 𝑟 = 9.902 … so 2𝑟 = 19.8

Question 24
240cm 3
Question 30

Question 25 𝑎2 + 𝑏2 = 𝑐2
(𝑥 + 1)2 + (𝑥 + 2)2 = (6)2
ℎ = 11.2cm
Question 26
2𝑥2 + 6𝑥 + 5 = 36
6𝑥(3𝑥 + 4) = 60
2𝑥2 + 6𝑥 − 31 = 0
3𝑥2 + 4𝑥 − 10 = 0
−(6) ± √(6)2 − 4(2)(−31)
𝑥 =
Question 27 2(2)
= 2.7131 … 𝑜𝑟 −5.7131 …
1
2
(2𝑥 + 2 + 2𝑥 + 1)(𝑥) = 105 so 𝑥 = 2.71 cm

4𝑥2 + 3𝑥 = 210
4𝑥2 + 3𝑥 − 210 = 0
 37

Recent Past Paper Questions

Quadratics
Q1. January 21R Paper 2, Question 9, [3 marks]

Q2. Jan 20R Paper 1, Question 6, [3 marks]

Q3. SAM 3H, Question 6, [ a) 2 marks, b) 3 marks ]

Q4. June 18 Paper 1, Question 3, [9 marks]

 38

Q5. June 22R Paper 1, Question 5, [5 marks]

Q6. Jan 21 Paper 1, Question 9, [5 marks]

Q7. January 2023 Paper 1HR, Question 8 [5 marks]

Q8. June (Nov) 20, Paper 1, Question 7, [8 marks]

 39

Q9. Jan 20 Paper 2, Question 7, [5 marks]

Q10. May 18 Paper 1, Question 11, [6 marks]

 40

Q11. SAM 3H, Question 15, [7 marks]

Q12. Jan 19 Paper 2, Question 15, [6 marks]

Q13. Specimen Paper 1H, Question 21, [6 marks]

 41

Proportion

1. January 2019 Paper 1H

2. June 2020 Paper 1H

3. June 2020 Paper 2HR

 42

4. Specimen Paper 1H

5. SAMs Paper 4H

6. January 2022 Paper 1H

 43

7. June 2019 Paper 2H

8. January 2023 Paper 1H

9. June 2018 Paper 2H

 44

10. January 2022R Paper 2HR

11. January 2023 Paper 1HR

 45

Volume & Surface Area : Prisms and Cylinders

1. June 19 Paper 1HR, Question 1

2. January 2019 Paper 2HR, Question 2

3. June 2019 Paper 2H, Question 4

4. November 2020 Paper 2H, Question 9

5. January 2020 Paper 2HR, Question 13