Higher June 2023 Paper 1 Q7
7
\[2^a \times 3 \times 5^2 = 600\]Work out the value of \(a\).
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 – evaluation and division | ||
| \((5^2 =)\ 25\) or \((3 \times 5^2 =)\ 75\) or \(600 \div 3\) or 200 or \(600 \div 5^2\) or 24 | M1 | oe oe eg \(3 \times 200 = 600\) oe eg \(25 \times 24 = 600\) |
| \(600 \div 3 \div 5^2\) or 8 | M1dep | oe eg \(8 \times 75 = 600\) |
| 3 with M1 awarded and not from incorrect working | A1 | |
| Alternative method 2 – product of prime factors | ||
| 600 written as a product of factors where at least one factor is prime | M1 | eg 2 and 300 or 5 and 120 or 2 and 2 and 150 may be seen on a factor tree or in repeated division allow one strand to be incorrect if a previous value completes the product eg \(20 \times 30\) followed by \(2 \times 10 \times 5 \times 8\) implies \(2 \times 10 \times 30\) for M1 |
| 2 and 2 and 2 and 3 and 5 and 5 | M1dep | may be seen on a factor tree or in repeated division |
| 3 with M1 awarded and not from incorrect working | A1 | |
Additional guidance
| \(8 \times 3 \times 25 = 600\) and answer 3 | M1M1A1 |
| \(2^3\) on answer line with M2 awarded | M1M1A0 |
| Answer 3 on answer line with no working | M0M0A0 |
| Do not allow \(600 \div 3 \times 5^2\) for M2 in alt 1 unless recovered, but do allow \(\dfrac{600}{3 \times 5^2}\) or \(600 \div (3 \times 5^2)\) |