4MA0 Higher June 2015 Paper 3R Q10
10
(a) \(A = 2^2 \times 3 \times 5^2\)
\(B = 2^3 \times 5\)
\(B = 2^3 \times 5\)
(i) Find the Highest Common Factor (HCF) of \(A\) and \(B\).
(ii) Find the Lowest Common Multiple (LCM) of \(A\) and \(B\).
(3)(b) \(\dfrac{8^2 \times 8^3}{8^4} = 2^n\)
Find the value of \(n\). (2)
Find the value of \(n\). (2)
(i)
| Scheme | Marks |
|---|---|
| \(2^2 \times 5\) | B1 |
Notes
B1: B1 for \(2^2 \times 5\) oe or 20
(ii)
| Scheme | Marks |
|---|---|
| \(2^3 \times 3 \times 5^2\) | B2 |
| (3) |
Notes
B2: B2 for \(2^3 \times 3 \times 5^2\) oe or 600
(B1 for any product using powers of 2 and 3 and 5 or at least 300, 600… and 40, 80, 120 …)
| Scheme | Marks |
|---|---|
| 8 (\(= 2^n\)) or \(2^3\) | M1 |
| 3 | A1 |
| (2) |
Notes
M1: M1 for one correct use of index laws eg. \(8^5 \div 8^4\)