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Homework Sheet - Indices 1. Write down the value of: a) 62 b) 92 c) (–3)2 d) (12–4)2 c) (–3)3 d) (8–3)3 c) √25 d) √49 c) 3√27 d) 3√8 2. Write down the value of: a) 23 b) 103 3. Write down the value of: a) √100 b) √4 4. Write down the value of: a) √1000 b) 3√125 3 5. Put these numbers in ascending order: 23, √4, 12, √27, 3 1.5 6. Here is a list of integers: 1, 4, 6, 8, 12, 15, 36, 50, 64, 100, 125 a) Joe says that there are 5 square numbers in the list. He is correct. Which are the square numbers? b) Sian says that there aren’t any odd cube numbers in the list. She is wrong. Which are the odd cube numbers? c) Mel says that the difference between the last two numbers in the list is a square number. (i) Show that she is correct. (ii) There are two other pairs of adjacent numbers in the list where the difference is also a square number. What are the two pairs of numbers? 7. Calculate the answers to these: a) √4 + 4 + 42 b) 3√64 – 3√8 c) (–3)2 – (–3)3 8. Write the answers to the following in index form: a) 32 × 34 b) 56 ÷ 54 9. Arran says that 6.52 is 13, but his friend Zak says it’s got to be over 40. Explain who is correct and why. 10. There are two integers under 100 which have a perfect square root and also a perfect cube root. What are the two integers? Indices Answers and Mark Scheme Q Answer Mark 1(a) 36 B1 1(b) 81 B1 1(c) 9 B1 1(d) 64 B1 2(a) 8 B1 2(b) 1 000 B1 2(c) -27 B1 2(d) 125 B1 3(a) 10 B1 3(b) 2 B1 3(c) 5 B1 3(d) 7 B1 4(a) 10 B1 4(b) 5 B1 4(c) 3 B1 4(d) 2 B1 5. 12, 1.5, √4, √27, 3 23 B2 Comments B1 for order B1 for working out 6(a) 1, 4, 6(b) 1, 125 36, 64, 100 B2 B1 for 3 or 4 B1 + B1 6(c)(i) 125 – 100 = 25 (= 52) M1 + A1 M1 for 125 – 100 = 25 6(c)(ii) 100 – 64 = 36 = 62 M2 + A2 M1 for 100 – 64 = 36 & 12 – 8 = 4 = 22 M1 for 12 – 8 = 4 Q Answer Mark 7(a) 2 + 4 + 16 = 22 M1 + A1 7(b) 8–2=6 M1 + A1 7(c) 9 + 27 = 36 M1 + A1 8(a) 36 B1 8(b) 52 B1 Zak is correct as 6.52 means 6.5 x 6.5 which must be more than 6 x 6 (= 36) and less than 7 x 7 (= 49). Arran has just added 6.5 to get 13 B3 1 and 64 have perfect square roots (1 and 8) and perfect cube roots (1 and 4) B2 9. 10. Comments B1 for > 36 B1 for < 40 B1 for Aaron has added 6.5 + 6.5 B1 for 1 B1 for 64