AQA GCSE Mathematics (8300) – Paper 1 (Non-
Calculator) – Higher Tier
Q1
Simplify 72
Answer: 6 2
Explanation: 72 = 36 × 2 = 6 2
Q2
Write 0.07 as a fraction.
7
Answer: 90
Explanation: Let � = 0.0777. . ., 10� = 0.777. . ., 100� = 7.777. . ., subtract: 90� = 7, so � = 7/90
Q3
2 −2
Work out 3
9
Answer: 4
Explanation: Negative power → reciprocal: (3/2)2 = 9/4
Q4
Write 450 000 in standard form.
Answer: 4.5 × 105
Q5
Work out 3.4 × 106 ÷ 2 × 103
Answer: 1.7 × 103
Explanation: (3.4 ÷ 2) × 106−3 = 1.7 × 103
Q6
What is 25 × 23 as a single power of 2?
Answer: 28
Q7
37
Simplify 34
Answer: 33 = 27
Q8
Work out 5−2
1
Answer: 25
,Q9
3�2�3
Simplify fully 6��5
�
Answer: 2�2
Explanation: 3/6 = 1/2, �2−1 = �1 , �3−5 = �−2 = 1/�2
Q10
5
Rationalise the denominator of 3
5 3
Answer: 3
Q11
5
Write 8 as a percentage.
Answer: 62.5%
Q12
Increase £40 by 15%
Answer: £46
Explanation: 15% of 40 = 6, so 40 + 6 = 46
Q13
Decrease 200 by 12%
Answer: 176
Explanation: 12% of 200 = 24, so 200 − 24 = 176
Q14
Find 0.2% of 500
Answer: 1
Explanation: 0.2% = 0.002, ×500 = 1
Q15
Write 1.45 as a fraction in simplest form.
13 145−14 131
Answer: 9 or 90 = 90 wait correction: 1.4555. . . = 1 + 4/10 + 5/90 = (90 + 36 + 5)/90 = 131/
90? Check: Actually 1.45 = 1 + (45 − 4)/90 = 1 + 41/90 = 131/90 – but simpler: 1.45 = (145 −
14)/90 = 131/90. Yes.
Q16
7 5
Which is larger: 9 or 6?
5
Answer: 6
Explanation: 7/9 ≈ 0.777,5/6 ≈ 0.833
Q17
Work out 144 + 169
Answer: 25
, Q18
Express 84 as a product of prime factors.
Answer: 22 × 3 × 7
Q19
Find the HCF of 24 and 36.
Answer: 12
Q20
Find the LCM of 6 and 10.
Answer: 30
Q21
Solve 5� − 7 = 3� + 9
Answer: � = 8
Explanation: 5� − 3� = 9 + 7, 2� = 16, � = 8
Q22
Expand 3(2� − 5)
Answer: 6� − 15
Q23
Factorise �2 − 9
Answer: (� − 3)(� + 3)
Q24
Simplify 4�2 � × 3��3
Answer: 12�3 �4
Q25
�
Solve 3 + 5 = 8
Answer: � = 9
Q26
Solve 2(� + 4) = 18
Answer: � = 5
Q27
Factorise �2 + 7� + 12
Answer: (� + 3)(� + 4)
Q28
Factorise 6�2 − 11� − 10
Answer: (3� + 2)(2� − 5)
Calculator) – Higher Tier
Q1
Simplify 72
Answer: 6 2
Explanation: 72 = 36 × 2 = 6 2
Q2
Write 0.07 as a fraction.
7
Answer: 90
Explanation: Let � = 0.0777. . ., 10� = 0.777. . ., 100� = 7.777. . ., subtract: 90� = 7, so � = 7/90
Q3
2 −2
Work out 3
9
Answer: 4
Explanation: Negative power → reciprocal: (3/2)2 = 9/4
Q4
Write 450 000 in standard form.
Answer: 4.5 × 105
Q5
Work out 3.4 × 106 ÷ 2 × 103
Answer: 1.7 × 103
Explanation: (3.4 ÷ 2) × 106−3 = 1.7 × 103
Q6
What is 25 × 23 as a single power of 2?
Answer: 28
Q7
37
Simplify 34
Answer: 33 = 27
Q8
Work out 5−2
1
Answer: 25
,Q9
3�2�3
Simplify fully 6��5
�
Answer: 2�2
Explanation: 3/6 = 1/2, �2−1 = �1 , �3−5 = �−2 = 1/�2
Q10
5
Rationalise the denominator of 3
5 3
Answer: 3
Q11
5
Write 8 as a percentage.
Answer: 62.5%
Q12
Increase £40 by 15%
Answer: £46
Explanation: 15% of 40 = 6, so 40 + 6 = 46
Q13
Decrease 200 by 12%
Answer: 176
Explanation: 12% of 200 = 24, so 200 − 24 = 176
Q14
Find 0.2% of 500
Answer: 1
Explanation: 0.2% = 0.002, ×500 = 1
Q15
Write 1.45 as a fraction in simplest form.
13 145−14 131
Answer: 9 or 90 = 90 wait correction: 1.4555. . . = 1 + 4/10 + 5/90 = (90 + 36 + 5)/90 = 131/
90? Check: Actually 1.45 = 1 + (45 − 4)/90 = 1 + 41/90 = 131/90 – but simpler: 1.45 = (145 −
14)/90 = 131/90. Yes.
Q16
7 5
Which is larger: 9 or 6?
5
Answer: 6
Explanation: 7/9 ≈ 0.777,5/6 ≈ 0.833
Q17
Work out 144 + 169
Answer: 25
, Q18
Express 84 as a product of prime factors.
Answer: 22 × 3 × 7
Q19
Find the HCF of 24 and 36.
Answer: 12
Q20
Find the LCM of 6 and 10.
Answer: 30
Q21
Solve 5� − 7 = 3� + 9
Answer: � = 8
Explanation: 5� − 3� = 9 + 7, 2� = 16, � = 8
Q22
Expand 3(2� − 5)
Answer: 6� − 15
Q23
Factorise �2 − 9
Answer: (� − 3)(� + 3)
Q24
Simplify 4�2 � × 3��3
Answer: 12�3 �4
Q25
�
Solve 3 + 5 = 8
Answer: � = 9
Q26
Solve 2(� + 4) = 18
Answer: � = 5
Q27
Factorise �2 + 7� + 12
Answer: (� + 3)(� + 4)
Q28
Factorise 6�2 − 11� − 10
Answer: (3� + 2)(2� − 5)
