Higher June 2024 Paper 3 Q17
17
(a) \(a\) and \(b\) are different prime numbers.
\(a^3 \times b^2 = 200\)
Work out the value of \(\quad a^4 \times b\) [3 marks]
(b) \(c\) and \(d\) are different prime numbers.
Circle the equation for which \(\quad c^4 \times d^2 \times e \quad\) is a cube number. [1 mark]
- \(e = cd\)
- \(e = c^2d\)
- \(e = c^2d^2\)
- \(e = c^3d^3\)
| Answer | Mark | Comments |
|---|---|---|
| 80 | B3 | B2 \((200 =)\ 2^3 \times 5^2\) or \(2^4 \times 5\) oe or \(16 \times 5\) or \(200 \times 2 \div 5\) B1 \(a = 2\) and \(b = 5\) or 2, 2, 2, 5, 5 seen on a factor tree or 25 or 8 |
Additional guidance
| For B1, 25 or 8 must be chosen from any lists of square or cube numbers | |
| \(2 \times 2 \times 2 \times 5 \times 5\) | B2 |
| \(5^3 \times 2^2\) | B0 |
| Answer | Mark | Comments |
|---|---|---|
| \(e = c^2d\) | B1 |