Working with powers
| Y9 (04/99) | |||
| a) |
i) ii) |
36 32 |
very easy moderate |
| b) |
i) ii) |
25 169 |
easy easy |
| c) |
i) ii) |
153 9474 |
moderate moderate |
| Common error | Likely calculation | Likely reason | |
|
a) i) ii) |
12 10 |
6 × 2 5 × 2 |
Interprets ab as a × b |
|
b) i) ii) |
14 34 |
4 × 2 + 3 × 2 5 × 2 + 12 × 2 |
Interprets ab as a × b |
|
c) i) ii) |
27 96 |
1 × 3 + 5 × 3 + 3 × 3 9 × 4 + 4 × 4 + 7 × 4 + 4 × 4 |
Interprets ab as a × b |
| c) i) | 155 | 1 × 3 + 53 + 33 | Treats 13 as 1 × 3 instead of 1 |
EXTENSION:
a) i) What is special about the answers to b)? Answer: They are all perfect squares.
ii) Explore other pairs of numbers where a2 + b2 is a perfect square, i.e., Pythagorean triples.
Answers:
[3, 4, 5] [5, 12, 13] [7, 24, 25] [9, 40, 41] etc., i.e., [2n+1, 2n (n+1), 2n (n+1) +1]
for n = 1, 2, 3...
[8, 15, 17] [12, 35, 37] [16, 63, 65] etc., i.e., [4 (n+1), (2n+1) (2n+3), (2n+2)2 +1]
for n = 1, 2, 3...
Plus all multiples of each triple, i.e., [3×2, 4×2, 5×2] i.e., [6, 8, 10] etc.
b) i) Find all other 3 digit numbers that part c) i) works for. Answer: 371, 407
ii) Find all other 4 digit numbers that part c) ii) works for. Answer: 1634