plumiIndex laws: AQA Level 2 Further Maths questions
Every AQA Level 2 Further Maths exam question on 2.18 Index laws, 2021–2025, with its mark scheme and examiner’s report.
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All 16 questions on Index laws, as a list
- June 2025, Paper 1, Q8 (1 mark): Work out x x 3 9 2 1 2 as a power of x. Circle your answer. x7 x12 x15 x27
- June 2025, Paper 2, Q7 (5 marks): (a) 25a + 1 = 2a Work out the value of a. a = 7 (b) ( ) = 2 7 3 3 3 3 c c − − ÷ Work out the value of c. c =
- June 2024, Paper 1, Q21 (5 marks): ( ) + + = x x x− 4 1 3 1 2 8 Work out the possible values of x. Answer
- June 2024, Paper 2, Q14 (3 marks): P is the point on the graph y = 3 –x that has x-coordinate –2 Q is a point on the graph y = 1152 × x 1 2 y-coordinate of P = y-coordinate of Q Work
- June 2024, Paper 2, Q16 (3 marks): Simplify ( ) x x x x + 3 3 3 Give your answer in the form + a b c x x where a, b and c are integers. Answer
- June 2023, Paper 1, Q15 (4 marks): Solve – x x 2 1 3 2 2 = x2 + x Answer
- June 2023, Paper 2, Q13 (6 marks): (a) Circle the expression equivalent to 3x –7 7 3 x − 7 1 3x − 7 1 3x 7 3 x 13 (b) Simplify fully ( ) 8 2 3 12 4 w w Answer 13 (c) y × 3 y = d c y where c and d
- June 2022, Paper 1, Q13 (3 marks): Simplify fully (6x 3y –2 + 9x 5y) ÷ 3x 2y –3 Answer
- June 2022, Paper 2, Q22 (4 marks): Using powers of 2 or otherwise, work out the non-zero value of x for which ( ) x x 16 = x 3 2 1 You must show your working. Answer
- November 2021, Paper 1, Q13 (3 marks): Here is a sketch of y = kx where k > 0 A 2, 1 316 is a point on the curve. 13 (a) Work out the value of k. Answer 13 (b) B is a point on the curve with
- November 2021, Paper 1, Q22 (4 marks): Solve – = x 56 26 2 4 8 30 x =
- November 2021, Paper 2, Q7 (4 marks): (a) a is a value greater than 1 Work out the value of m for which (am) 4 = (a5) 2m m = 7 (b) w3x2y5 = w13x7 Write y in terms of w and x. Give your answer in its
- Specimen, Paper 1, Q1 (4 marks): (a) 6 4 m y y y y × = Circle the value of m. – 2 1.5 2 3 1 (b) an × a5 = a5 Work out the value of n. Answer 1 (c) (c5)p = (c2)6 Work out the value of p. Answer
- Specimen, Paper 1, Q18 (3 marks): Solve x − = 2 3 1 12 4 x =
- Specimen, Paper 2, Q15 (4 marks): Here is a sketch of the curve x y ab− = where a and b are positive constants. (0, 3) and (2, 0.48) lie on the curve. x (2, 0.48) y O (0, 3) Not drawn accurately
- Specimen, Paper 2, Q17 (4 marks): By multiplying both sides of the equation by x 1 2 Solve x x x − − = 3 1 1 2 2 2 2 3 7 for x > 0 Give your answer to 3 significant figures. You must show your w
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