plumiLaws of indices: OCR GCSE Maths questions
Every OCR GCSE Maths exam question on N7 Laws of indices, 2017–2025, with its mark scheme and examiner’s report.
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All 38 questions on Laws of indices, as a list
- June 2025, Paper 4, Q10 (3 marks): Find the value of k. 3 k 25 ( 5 ) # 19 5 = 4 5 k =
- June 2025, Paper 5, Q14 (6 marks): (a) Find the value of 42 . (a) (b) Simplify. _ i – 3 2 8 3 x 9 x # (b)
- June 2025, Paper 6, Q5 (2 marks): A teacher asks their class which of the following values is the smallest. 1 3 2 - - 10 - 2 4 One student says - is the smallest because 2 is smaller than 4 and
- November 2024, Paper 5, Q21 (5 marks): (a) Work out. 1 1 3 d n 8 (a) x y (b) 2 4 16 # = x Show that y 2 . = - 2
- November 2024, Paper 6, Q14 (4 marks): N 4 a . = m. Write the following in the form ka - 1 = a N (a) 3 = a (b) N2
- June 2024, Paper 4, Q7 (3 marks): Write the following in order of size, smallest first. 2 - 2 2 - 0.2 2 10 # Show how you decide. , , smallest
- June 2024, Paper 6, Q16 (4 marks): Write in the form kx 4 3 x
- November 2023, Paper 4, Q21 (3 marks): Solve. 1 5 x 1 3 - x , where x ≠ 0 = 6 3 x 4 x = for question 22
- November 2023, Paper 5, Q3 (4 marks): (a) Simplify. 2 5 3 a 4 a # (a) (b) Factorise fully. 2 - 4 x 12 x (b)
- November 2023, Paper 5, Q20 (2 marks): Work out. 1 - 36 2
- June 2023, Paper 5, Q16 (6 marks): (a) Work out. 2 643 (a) p 5 o o (b) 0 13 . + = q 9 p where q is a fraction in its lowest terms. Find the value of p and the value of q. (b) p = q =
- June 2023, Paper 5, Q18 (3 marks): p m m , where p 2 0 , m 2 0 and p m . = ! 5 . Show that the value of x is 3
- June 2023, Paper 6, Q17 (4 marks): The kth term of a sequence is r k, where r 0 . ! The sixth term is equal to three times the second term. Find the value of r, giving your answer correct to 3 de
- November 2022, Paper 5, Q9 (4 marks): A student says that they have placed the following values in order starting with the smallest. a k 2 -4 1 1 0 25 . 10 Has the student done this correctly? Show
- November 2022, Paper 6, Q9 (3 marks): Given that ( 2 ) 8 2 , find the value of k. = # k =
- June 2022, Paper 5, Q4 (3 marks): (a) Complete this statement by writing the missing power in the box. # 72 784 = 2 (b) Use your answer to part (a) to find the value of 784. (b)
- June 2022, Paper 6, Q4 (4 marks): You are given that k 8 7 10 2 a a a # = 5 5 ma where k and m are integers. Find the value of k and the value of m. k = and m =
- November 2021, Paper 4, Q3 (1 mark): Simplify. 12 4 x x '
- November 2021, Paper 5, Q2 (2 marks): (a) Azmi is given this question. Write 40 as a product of prime factors. Give your answer in index form. Azmi’s answer is 2 2 2 5 . # # # Is Azmi correct? Expla
- November 2020, Paper 5, Q11 (4 marks): (a) Work out. 1 - 16 2 (a) (b) Simplify. 6 3 # (b)
- November 2020, Paper 5, Q14 (5 marks): Simplify. 1 2 (a) 4 a 3 a 2 # (a) J 2 3 N 2 a K O (b) KK OO - 3 a L P (b)
- November 2019, Paper 5, Q3 (6 marks): Martina has answered some questions on algebra. In each question, she has made an error. Describe her error and give the correct answer to each problem. Simplif
- November 2019, Paper 5, Q17 (3 marks): Show that can be expressed as a3 . a # a
- November 2019, Paper 6, Q14 (3 marks): Write 8
- June 2019, Paper 4, Q1 (3 marks): Calculate. 210 3 2 2 10 5 + Give your answer correct to 3 significant figures.
- June 2019, Paper 4, Q17 (3 marks): Show that ( ) ( ) 1 . a a = 3 2 #
- June 2019, Paper 5, Q2 (6 marks): (a) Simplify fully. 8 5 3 a 2 a # 2 a (a) (b) Solve. x 6 10 - 1 = 5 (b) x =
- June 2019, Paper 5, Q11 (3 marks): (a) Simplify fully. 200 (a) (b) Evaluate. 1 83 (b)
- June 2019, Paper 6, Q11 (8 marks): You are given that 3 # 11 270 3 2 5 and 177147 3 = = # (a) (i) Find the lowest common multiple (LCM) of 270 and 177 147. Give your answer using power notation a
- November 2018, Paper 4, Q8 (10 marks): (a) Two numbers, P and Q, are written as products of their prime factors. 5 2 3 4 4 P 2 3 5 11 Q 2 3 5 7 = # # # = # # # (i) Find the lowest common multiple (LC
- November 2018, Paper 5, Q1 (5 marks): Work out. 1 3 - (a) 64 2 # (a) 5 4 (b) 4 3 . 10 3 8 . 10 + # # Give your answer in standard form. (b)
- June 2018, Paper 4, Q2 (1 mark): k =
- June 2018, Paper 5, Q12 (3 marks): Carol says that 64 . = 2 32 p 1 - in the form q Explain her error and give the correct value of 64 . 2
- June 2018, Paper 5, Q20 (9 marks): In the following equation, n is an integer greater than 1. _ i n = 2 k 2 (a) (i) Find k when n = 7. (a)(i) k = (ii) Find n when k = 64. (ii) n = 14 (b) Show tha
- June 2018, Paper 6, Q4 (5 marks): 1 9 (b) Write 125 25 as a power of 5. # (b)
- November 2017, Paper 4, Q2 (3 marks): (a) Simplify. 6 2 (i) a a ' (a)(i) b5 3 (ii) ( ) (ii) (b) Factorise. 2 6 x x - (b)
- November 2017, Paper 5, Q16 (6 marks): (a) Write 12 75 in the form k 3. + (a) (b) Work out. 3 - 16 4 (b)
- June 2017, Paper 5, Q15 (7 marks): (a) Simplify fully. (i) 50 2 + (a)(i) 10 (ii) 6 (ii) - 2 (b) There are two errors in Sam’s method for finding the value of 64 3 shown below. Find the cube root
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