1. Algebraic Manipulation – Higher – GCSE Questions – AQA
These questions are the same format as previous GCSE exams.
COPY means they use the exact same numbers as the original GCSE question.
Otherwise, they are clone questions using different numbers.
The worksheets are provided in 2 sizes.

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3. 5𝑥+4 5𝑥+15 5(𝑥+4) 5𝑥−4 5𝑥+4 5𝑥+15 5(𝑥+4) 5𝑥−4 5𝑥+4 5𝑥+15 5(𝑥+4) 5𝑥−4
AQA Higher: June 2018 Paper 3, Q15
AQA Higher: June 2018 Paper 3, Q15 1
Amy has 𝑥 beads.
Billy has four more beads than Amy.
Carly has five times as many beads as Billy.
Circle the expression for the number of beads that Carly has. 1
Amy has 𝑥 beads.
Billy has four more beads than Amy.
Carly has five times as many beads as Billy.
Circle the expression for the number of beads that Carly has.
[1 mark]
[1 mark]
5𝑥+4
5𝑥+15
5(𝑥+4)
5𝑥−4
5𝑥+4
5𝑥+15
5(𝑥+4)
5𝑥−4
AQA Higher: June 2018 Paper 3, Q15
AQA Higher: June 2018 Paper 3, Q15 1
Amy has 𝑥 beads.
Billy has four more beads than Amy.
Carly has five times as many beads as Billy.
Circle the expression for the number of beads that Carly has. 1
Amy has 𝑥 beads.
Billy has four more beads than Amy.
Carly has five times as many beads as Billy.
Circle the expression for the number of beads that Carly has.
[1 mark]
[1 mark]
5𝑥+4
5𝑥+15
5(𝑥+4)
5𝑥−4
5𝑥+4
5𝑥+15
5(𝑥+4)
5𝑥−4

5. AQA Higher: November 2017 Paper 1, Q10
Three identical isosceles triangles are joined to make this trapezium.
Each triangle has base 𝑏 cm and perpendicular height ℎ cm 1
Three identical isosceles triangles are joined to make this trapezium.
Each triangle has base 𝑏 cm and perpendicular height ℎ cm
𝑏 cm
𝑏 cm
Not drawn
accurately
Not drawn
accurately
ℎ cm
ℎ cm
1 (a)
Work out an expression, in terms of 𝑏 and ℎ , for
the area of the trapezium.
Give your answer in its simplest form.
1 (a)
Work out an expression, in terms of 𝑏 and ℎ , for
the area of the trapezium.
Give your answer in its simplest form.
[2 marks]
[2 marks]
Answer
cm2
Answer
cm2
1 (b)
This diagram shows the same trapezium.
1 (b)
This diagram shows the same trapezium.
Not drawn
accurately
Not drawn
accurately
𝑏 cm
𝑏 cm
𝑠 cm
𝑠 cm
[2 marks]
[2 marks]
𝑏 : 𝑠 = 2 : 3
Work out an expression, in terms of 𝑏,
for the perimeter of the trapezium.
𝑏 : 𝑠 = 2 : 3
Work out an expression, in terms of 𝑏,
for the perimeter of the trapezium.
Answer cm
Answer cm

7. AQA Higher: June 2017 Paper 3, Q3 AQA Higher: June 2017 Paper 3, Q3
Rearrange 𝑡= 𝑦 𝑥 to make 𝑥 the subject.
Circle your answer. 1
[1 mark]
𝑥 = 𝑦 3𝑡
𝑥 = 3𝑡 𝑦
𝑥 = 𝑡 3𝑦
𝑥 = 3𝑦 𝑡
Rearrange 𝑡= 𝑦 𝑥 to make 𝑥 the subject.
Circle your answer. 1
[1 mark]
𝑥 = 𝑦 3𝑡
𝑥 = 3𝑡 𝑦
𝑥 = 𝑡 3𝑦
𝑥 = 3𝑦 𝑡
Rearrange 𝑠= 2𝑥 𝑔 to make 𝑥 the subject.
Circle your answer. 2
[1 mark]
𝑥 = 2𝑔 𝑠
𝑥 = 2𝑠 𝑔
𝑥 = 2 𝑔𝑠
𝑥 = 𝑔𝑠 2
Rearrange 𝑠= 2𝑥 𝑔 to make 𝑥 the subject.
Circle your answer. 2
[1 mark]
𝑥 = 2𝑔 𝑠
𝑥 = 2𝑠 𝑔
𝑥 = 2 𝑔𝑠
𝑥 = 𝑔𝑠 2
Rearrange 𝑔= 𝑘 3ℎ to make ℎ the subject.
Circle your answer. 3
[1 mark]
ℎ = 6𝑘 ℎ
ℎ = 6𝑘 𝑔
ℎ = 𝑘 6𝑔
ℎ = 𝑘 3𝑔
Rearrange 𝑔= 𝑘 3ℎ to make ℎ the subject.
Circle your answer. 3
[1 mark]
ℎ = 6𝑘 ℎ
ℎ = 6𝑘 𝑔
ℎ = 𝑘 6𝑔
ℎ = 𝑘 3𝑔
AQA Higher: June 2017 Paper 3, Q3
AQA Higher: June 2017 Paper 3, Q3
Rearrange 𝑡= 𝑦 𝑥 to make 𝑥 the subject.
Circle your answer. 1
[1 mark]
𝑥 = 𝑦 3𝑡
𝑥 = 3𝑡 𝑦
𝑥 = 𝑡 3𝑦
𝑥 = 3𝑦 𝑡
Rearrange 𝑡= 𝑦 𝑥 to make 𝑥 the subject.
Circle your answer. 1
[1 mark]
𝑥 = 𝑦 3𝑡
𝑥 = 3𝑡 𝑦
𝑥 = 𝑡 3𝑦
𝑥 = 3𝑦 𝑡
Rearrange 𝑠= 2𝑥 𝑔 to make 𝑥 the subject.
Circle your answer. 2
[1 mark]
𝑥 = 2𝑔 𝑠
𝑥 = 2𝑠 𝑔
𝑥 = 2 𝑔𝑠
𝑥 = 𝑔𝑠 2
Rearrange 𝑠= 2𝑥 𝑔 to make 𝑥 the subject.
Circle your answer. 2
[1 mark]
𝑥 = 2𝑔 𝑠
𝑥 = 2𝑠 𝑔
𝑥 = 2 𝑔𝑠
𝑥 = 𝑔𝑠 2
Rearrange 𝑔= 𝑘 3ℎ to make ℎ the subject.
Circle your answer. 3
[1 mark]
ℎ = 6𝑘 ℎ
ℎ = 6𝑘 𝑔
ℎ = 𝑘 6𝑔
ℎ = 𝑘 3𝑔
Rearrange 𝑔= 𝑘 3ℎ to make ℎ the subject.
Circle your answer. 3
[1 mark]
ℎ = 6𝑘 ℎ
ℎ = 6𝑘 𝑔
ℎ = 𝑘 6𝑔
ℎ = 𝑘 3𝑔

9. AQA Higher: November 2017 Paper 3, Q9
Rearrange 𝑣=𝑢+𝑎𝑡 to make 𝑡 the subject of the formula.
1 (a)
Rearrange 𝑣=𝑢+𝑎𝑡 to make 𝑡 the subject of the formula.
[2 marks]
[2 marks]
Answer
Answer
1 (b)
Complete this table with consistent metric units.
1 (b)
Complete this table with consistent metric units.
[2 marks]
[2 marks]
Distance
Time
Speed
Acceleration m s
Distance
Time
Speed
Acceleration m s
AQA Higher: November 2017 Paper 3, Q9
AQA Higher: November 2017 Paper 3, Q9
1 (a)
Rearrange 𝑣=𝑢+𝑎𝑡 to make 𝑡 the subject of the formula.
1 (a)
Rearrange 𝑣=𝑢+𝑎𝑡 to make 𝑡 the subject of the formula.
[2 marks]
[2 marks]
Answer
Answer
1 (b)
Complete this table with consistent metric units.
1 (b)
Complete this table with consistent metric units.
[2 marks]
[2 marks]
Distance
Time
Speed
Acceleration m s
Distance
Time
Speed
Acceleration m s

11. AQA Higher: November 2017 Paper 3, Q5
Multiply out and simplify 𝑥−5 2
[2 marks] 1
Multiply out and simplify 𝑥−5 2
[2 marks]
Answer
Answer 2
Multiply out and simplify 𝑥−3 2
[2 marks] 2
Multiply out and simplify 𝑥−3 2
[2 marks]
Answer
Answer
AQA Higher: November 2017 Paper 3, Q5
AQA Higher: November 2017 Paper 3, Q5 1
Multiply out and simplify 𝑥−5 2
[2 marks] 1
Multiply out and simplify 𝑥−5 2
[2 marks]
Answer
Answer 2
Multiply out and simplify 𝑥−3 2
[2 marks] 2
Multiply out and simplify 𝑥−3 2
[2 marks]
Answer
Answer

13. AQA Higher: May 2017 Paper 1, Q26 AQA Higher: May 2017 Paper 1, Q26
Expand and simplify 𝑥−5 2𝑥+5𝑦 2
[4 marks] 1
Expand and simplify 𝑥−5 2𝑥+5𝑦 2
[4 marks]
Answer
Answer
AQA Higher: May 2017 Paper 1, Q26
AQA Higher: May 2017 Paper 1, Q26 1
Expand and simplify 𝑥−5 2𝑥+5𝑦 2
[4 marks] 1
Expand and simplify 𝑥−5 2𝑥+5𝑦 2
[4 marks]
Answer
Answer

15. AQA Higher: November 2017 Paper 3, Q15
3𝑥2𝑦3 1
[1 mark]
Circle the highest common factor (HCF) of 6𝑥3𝑦2 and 9𝑥𝑦2
3𝑥2𝑦
6𝑥2𝑦2
3𝑥𝑦2
3𝑥2𝑦3 1
[1 mark]
Circle the highest common factor (HCF) of 6𝑥3𝑦2 and 9𝑥𝑦2
3𝑥2𝑦
6𝑥2𝑦2
3𝑥𝑦2
4𝑥𝑦2 2
[1 mark]
Circle the highest common factor (HCF) of 6𝑥3𝑦 and 4𝑥𝑦4
2𝑥𝑦
4𝑥𝑦
2𝑥2𝑦3
4𝑥𝑦2 2
[1 mark]
Circle the highest common factor (HCF) of 6𝑥3𝑦 and 4𝑥𝑦4
2𝑥𝑦
4𝑥𝑦
2𝑥2𝑦3
8𝑥3𝑦 3
[1 mark]
Circle the highest common factor (HCF) of 24𝑥3𝑦 and 8𝑥2𝑦2
8𝑥2𝑦
8𝑥𝑦
4𝑥2𝑦
8𝑥3𝑦 3
[1 mark]
Circle the highest common factor (HCF) of 24𝑥3𝑦 and 8𝑥2𝑦2
8𝑥2𝑦
8𝑥𝑦
4𝑥2𝑦
AQA Higher: November 2017 Paper 3, Q15
AQA Higher: November 2017 Paper 3, Q15
3𝑥2𝑦3 1
[1 mark]
Circle the highest common factor (HCF) of 6𝑥3𝑦2 and 9𝑥𝑦2
3𝑥2𝑦
6𝑥2𝑦2
3𝑥𝑦2
3𝑥2𝑦3 1
[1 mark]
Circle the highest common factor (HCF) of 6𝑥3𝑦2 and 9𝑥𝑦2
3𝑥2𝑦
6𝑥2𝑦2
3𝑥𝑦2
4𝑥𝑦2 2
[1 mark]
Circle the highest common factor (HCF) of 6𝑥3𝑦 and 4𝑥𝑦4
2𝑥𝑦
4𝑥𝑦
2𝑥2𝑦3
4𝑥𝑦2 2
[1 mark]
Circle the highest common factor (HCF) of 6𝑥3𝑦 and 4𝑥𝑦4
2𝑥𝑦
4𝑥𝑦
2𝑥2𝑦3
8𝑥3𝑦 3
[1 mark]
Circle the highest common factor (HCF) of 24𝑥3𝑦 and 8𝑥2𝑦2
8𝑥2𝑦
8𝑥𝑦
4𝑥2𝑦
8𝑥3𝑦 3
[1 mark]
Circle the highest common factor (HCF) of 24𝑥3𝑦 and 8𝑥2𝑦2
8𝑥2𝑦
8𝑥𝑦
4𝑥2𝑦

17. AQA Higher: November 2017 Paper 2, Q16
Factorise fully 8𝑥3−2𝑥
[2 marks]
1 (a)
Factorise fully 8𝑥3−2𝑥
[2 marks]
Answer
Answer
1 (b)
Factorise fully 5𝑥2−10𝑥+5
[2 marks]
1 (b)
Factorise fully 5𝑥2−10𝑥+5
[2 marks]
Answer
Answer
AQA Higher: November 2017 Paper 2, Q16
AQA Higher: November 2017 Paper 2, Q16
1 (a)
Factorise fully 8𝑥3−2𝑥
[2 marks]
1 (a)
Factorise fully 8𝑥3−2𝑥
[2 marks]
Answer
Answer
1 (b)
Factorise fully 5𝑥2−10𝑥+5
[2 marks]
1 (b)
Factorise fully 5𝑥2−10𝑥+5
[2 marks]
Answer
Answer

19. AQA Higher: November 2017 Paper 1, Q5
Factorise 𝑥2 −49
[1 mark]
1 (a)
Factorise 𝑥2 −49
[1 mark]
Answer
Answer
1 (b)
Solve 5𝑥+7>1+3𝑥
[2 marks]
1 (b)
Solve 5𝑥+7>1+3𝑥
[2 marks]
Answer
Answer
AQA Higher: November 2017 Paper 1, Q5
AQA Higher: November 2017 Paper 1, Q5
1 (a)
Factorise 𝑥2 −49
[1 mark]
1 (a)
Factorise 𝑥2 −49
[1 mark]
Answer
Answer
1 (b)
Solve 5𝑥+7>1+3𝑥
[2 marks]
1 (b)
Solve 5𝑥+7>1+3𝑥
[2 marks]
Answer
Answer

21. AQA Higher: May 2018 Paper 1, Q3 AQA Higher: May 2018 Paper 1, Q3
Circle the expression that is equivalent to 4𝑏+2𝑏×𝑏−3𝑏 1
Circle the expression that is equivalent to 4𝑏+2𝑏×𝑏−3𝑏
6𝑏2−3𝑏
2𝑏2−𝑏
−6𝑏2
2𝑏2+𝑏
[1 mark]
6𝑏2−3𝑏
2𝑏2−𝑏
−6𝑏2
2𝑏2+𝑏
[1 mark] 2
Circle the expression that is equivalent to 7𝑏−2𝑏×2𝑏−𝑏 2
Circle the expression that is equivalent to 7𝑏−2𝑏×2𝑏−𝑏
5𝑏2
6𝑏−4𝑏2
10𝑏2−𝑏
7𝑏−2𝑏2
[1 mark]
5𝑏2
6𝑏−4𝑏2
10𝑏2−𝑏
7𝑏−2𝑏2
[1 mark] 3
Circle the expression that is equivalent to 4𝑏×2𝑏−𝑏×3𝑏 3
Circle the expression that is equivalent to 4𝑏×2𝑏−𝑏×3𝑏
−12𝑏3
12𝑏3
3𝑏2
5𝑏2
[1 mark]
−12𝑏3
12𝑏3
3𝑏2
5𝑏2
[1 mark]
AQA Higher: May 2018 Paper 1, Q3
AQA Higher: May 2018 Paper 1, Q3 1
Circle the expression that is equivalent to 4𝑏+2𝑏×𝑏−3𝑏 1
Circle the expression that is equivalent to 4𝑏+2𝑏×𝑏−3𝑏
6𝑏2−3𝑏
2𝑏2−𝑏
−6𝑏2
2𝑏2+𝑏
[1 mark]
6𝑏2−3𝑏
2𝑏2−𝑏
−6𝑏2
2𝑏2+𝑏
[1 mark] 2
Circle the expression that is equivalent to 7𝑏−2𝑏×2𝑏−𝑏 2
Circle the expression that is equivalent to 7𝑏−2𝑏×2𝑏−𝑏
5𝑏2
6𝑏−4𝑏2
10𝑏2−𝑏
7𝑏−2𝑏2
[1 mark]
5𝑏2
6𝑏−4𝑏2
10𝑏2−𝑏
7𝑏−2𝑏2
[1 mark] 3
Circle the expression that is equivalent to 4𝑏×2𝑏−𝑏×3𝑏 3
Circle the expression that is equivalent to 4𝑏×2𝑏−𝑏×3𝑏
−12𝑏3
12𝑏3
3𝑏2
5𝑏2
[1 mark]
−12𝑏3
12𝑏3
3𝑏2
5𝑏2
[1 mark]

23. AQA Higher: November 2017 Paper 1, Q3
Circle the expression that is equivalent to 2 𝑏 2 2
[1 mark] 1
Circle the expression that is equivalent to 2 𝑏 2 2
[1 mark] 4𝑏
4 𝑏 4
2 𝑏 2
4 𝑏 2 4𝑏
4 𝑏 4
2 𝑏 2
4 𝑏 2 2
Circle the expression that is equivalent to 5 𝑏 5 2
[1 mark] 2
Circle the expression that is equivalent to 5 𝑏 5 2
[1 mark]
25 𝑏 7
7 𝑏 7
10 𝑏 10
25 𝑏 10
25 𝑏 7
7 𝑏 7
10 𝑏 10
25 𝑏 10 3
Circle the expression that is equivalent to 4 𝑏 3 2
[1 mark] 3
Circle the expression that is equivalent to 4 𝑏 3 2
[1 mark]
8 𝑏 6
6 𝑏 5
16 𝑏 5
16 𝑏 6
8 𝑏 6
6 𝑏 5
16 𝑏 5
16 𝑏 6
AQA Higher: November 2017 Paper 1, Q3
AQA Higher: November 2017 Paper 1, Q3 1
Circle the expression that is equivalent to 2 𝑏 2 2
[1 mark] 1
Circle the expression that is equivalent to 2 𝑏 2 2
[1 mark] 4𝑏
4 𝑏 4
2 𝑏 2
4 𝑏 2 4𝑏
4 𝑏 4
2 𝑏 2
4 𝑏 2 2
Circle the expression that is equivalent to 5 𝑏 5 2
[1 mark] 2
Circle the expression that is equivalent to 5 𝑏 5 2
[1 mark]
25 𝑏 7
7 𝑏 7
10 𝑏 10
25 𝑏 10
25 𝑏 7
7 𝑏 7
10 𝑏 10
25 𝑏 10 3
Circle the expression that is equivalent to 4 𝑏 3 2
[1 mark] 3
Circle the expression that is equivalent to 4 𝑏 3 2
[1 mark]
8 𝑏 6
6 𝑏 5
16 𝑏 5
16 𝑏 6
8 𝑏 6
6 𝑏 5
16 𝑏 5
16 𝑏 6

25. AQA Higher: June 2017 Paper 3, Q12 AQA Higher: June 2017 Paper 3, Q12
𝑎𝑥𝑏 3 =27𝑥21 where 𝑎 and 𝑏 are positive integers.
Work out 𝑎 and 𝑏 1
𝑎𝑥𝑏 3 =27𝑥21 where 𝑎 and 𝑏 are positive integers.
Work out 𝑎 and 𝑏
[2 marks]
[2 marks]
𝑎 =
𝑏 =
𝑎 =
𝑏 =
AQA Higher: June 2017 Paper 3, Q12
AQA Higher: June 2017 Paper 3, Q12 1
𝑎𝑥𝑏 3 =27𝑥21 where 𝑎 and 𝑏 are positive integers.
Work out 𝑎 and 𝑏 1
𝑎𝑥𝑏 3 =27𝑥21 where 𝑎 and 𝑏 are positive integers.
Work out 𝑎 and 𝑏
[2 marks]
[2 marks]
𝑎 =
𝑏 =
𝑎 =
𝑏 =

27. AQA Higher: November 2017 Paper 3, Q21
𝑁 is a number.
As a product of prime factors in index form 𝑁 = 2 × 34 × 𝑦3
Work out 3𝑁2 as a product of prime factors in index form.
Give your answer in terms of 𝑦. 1
𝑁 is a number.
As a product of prime factors in index form 𝑁 = 2 × 34 × 𝑦3
Work out 3𝑁2 as a product of prime factors in index form.
Give your answer in terms of 𝑦.
[3 marks]
[3 marks]
Answer
Answer
AQA Higher: November 2017 Paper 3, Q21
AQA Higher: November 2017 Paper 3, Q21 1
𝑁 is a number.
As a product of prime factors in index form 𝑁 = 2 × 34 × 𝑦3
Work out 3𝑁2 as a product of prime factors in index form.
Give your answer in terms of 𝑦. 1
𝑁 is a number.
As a product of prime factors in index form 𝑁 = 2 × 34 × 𝑦3
Work out 3𝑁2 as a product of prime factors in index form.
Give your answer in terms of 𝑦.
[3 marks]
[3 marks]
Answer
Answer

29. AQA Higher: November 2017 Paper 2, Q11
4𝑥2 8𝑥2 + 4
4𝑥2 8𝑥2 + 4 1
Circle the expression that is equivalent to 1
Circle the expression that is equivalent to
𝑥2 2𝑥2 +4
𝑥2 2𝑥2 + 1
𝑥2 8𝑥2 +1
2𝑥2 4𝑥2 +1
[1 mark]
𝑥2 2𝑥2 +4
𝑥2 2𝑥2 + 1
𝑥2 8𝑥2 +1
2𝑥2 4𝑥2 +1
[1 mark]
5𝑥2 20𝑥2 −15
5𝑥2 20𝑥2 −15 2
Circle the expression that is equivalent to 2
Circle the expression that is equivalent to
𝑥2 4𝑥2 −2
4𝑥2 4𝑥2 −3
𝑥2 5𝑥2 − 3
𝑥2 4𝑥2 − 3
[1 mark]
𝑥2 4𝑥2 −2
4𝑥2 4𝑥2 −3
𝑥2 5𝑥2 − 3
𝑥2 4𝑥2 − 3
[1 mark]
AQA Higher: November 2017 Paper 2, Q11
AQA Higher: November 2017 Paper 2, Q11
4𝑥2 8𝑥2 + 4
4𝑥2 8𝑥2 + 4 1
Circle the expression that is equivalent to 1
Circle the expression that is equivalent to
𝑥2 2𝑥2 +4
𝑥2 2𝑥2 + 1
𝑥2 8𝑥2 +1
2𝑥2 4𝑥2 +1
[1 mark]
𝑥2 2𝑥2 +4
𝑥2 2𝑥2 + 1
𝑥2 8𝑥2 +1
2𝑥2 4𝑥2 +1
[1 mark]
5𝑥2 20𝑥2 −15
5𝑥2 20𝑥2 −15 2
Circle the expression that is equivalent to 2
Circle the expression that is equivalent to
𝑥2 4𝑥2 −2
4𝑥2 4𝑥2 −3
𝑥2 5𝑥2 − 3
𝑥2 4𝑥2 − 3
[1 mark]
𝑥2 4𝑥2 −2
4𝑥2 4𝑥2 −3
𝑥2 5𝑥2 − 3
𝑥2 4𝑥2 − 3
[1 mark]

31. AQA Higher: June 2018 Paper 2, Q13
Show that, for 𝑥 ≠ –1 1
Show that, for 𝑥 ≠ –1
6𝑥2 − 24 2𝑥 simplifies to the form a𝑥 + b where a and b are integers.
6𝑥2 − 24 2𝑥 simplifies to the form a𝑥 + b where a and b are integers.
[3 marks]
[3 marks]
Answer
Answer
AQA Higher: June 2018 Paper 2, Q13
AQA Higher: June 2018 Paper 2, Q13 1
Show that, for 𝑥 ≠ –1 1
Show that, for 𝑥 ≠ –1
6𝑥2 − 24 2𝑥 simplifies to the form a𝑥 + b where a and b are integers.
6𝑥2 − 24 2𝑥 simplifies to the form a𝑥 + b where a and b are integers.
[3 marks]
[3 marks]
Answer
Answer

34. AQA Higher: November 2017 Paper 1, Q10
Three identical isosceles triangles are joined to make this trapezium.
Each triangle has base 𝑏 cm and perpendicular height ℎ cm
𝑏 cm
Not drawn
accurately
ℎ cm
1 (a)
Work out an expression, in terms of 𝑏 and ℎ , for
the area of the trapezium.
Give your answer in its simplest form.
[2 marks]
Answer
cm2
1 (b)
This diagram shows the same trapezium.
Not drawn
accurately
𝑏 cm
𝑠 cm
[2 marks]
𝑏 : 𝑠 = 2 : 3
Work out an expression, in terms of 𝑏,
for the perimeter of the trapezium.
Answer cm

49. Area = (½ b × h) × 3 3𝑏ℎ 2 𝑏 𝑠 = 2 3 3𝑏 = 2𝑠 b b 3b + 2s 2s = 3b
AQA Higher: November 2017 Paper 1, Q10 1
Three identical isosceles triangles are joined to make this trapezium.
Each triangle has base 𝑏 cm and perpendicular height ℎ cm
𝑏 cm
Not drawn
accurately
ℎ cm
1 (a)
Work out an expression, in terms of 𝑏 and ℎ , for
the area of the trapezium.
Give your answer in its simplest form.
[2 marks]
Area = (½ b × h) × 3
3𝑏ℎ 2
Answer
cm2
1 (b)
This diagram shows the same trapezium.
Not drawn
accurately
𝑏 𝑠 = 2 3
𝑏 cm
𝑠 cm
3𝑏 = 2𝑠
[2 marks] b b
𝑏 : 𝑠 = 2 : 3
Work out an expression, in terms of 𝑏,
for the perimeter of the trapezium.
3b + 2s
2s = 3b
3b + 3b = 6b 6b
Answer cm

60. AQA Higher: November 2017 Paper 3, Q21
𝑁 is a number.
As a product of prime factors in index form 𝑁 = 2 × 34 × 𝑦3
Work out 3𝑁2 as a product of prime factors in index form.
Give your answer in terms of 𝑦.
[3 marks]
3 2 × 34 × 𝑦3 2
3 22 × 38 × 𝑦6
3 × 22 × 38 × 𝑦6
22 × 39 × 𝑦6
22 × 39 × 𝑦6
Answer

63. tom@goteachmaths.co.uk Questions? Comments? Suggestions?
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