Higher November 2023 Paper 3 Q7
7 The first two cube numbers are 1 and 8
Show that
the 3rd cube number can be written as the sum of three different prime numbers. [3 marks]
\[\boxed{\phantom{000}} \;=\; \boxed{\phantom{000}} \;+\; \boxed{\phantom{000}} \;+\; \boxed{\phantom{000}}\]| Answer | Mark | Comments |
|---|---|---|
| 27 in the box on the left side of calculation | B1 | accept \(3^3\) for 27 throughout |
| Three different prime numbers in the boxes on the right side of calculation | M1 | |
| \(27 = 3 + 5 + 19\) or \(27 = 3 + 7 + 17\) or \(27 = 3 + 11 + 13\) | A1 | numbers in the boxes on the right side of calculation can be in any order SC2 \(27 = 2 + 2 + 23\) or \(27 = 5 + 5 + 17\) or \(27 = 7 + 7 + 13\) or \(27 = 5 + 11 + 11\) |
Additional guidance
| SC2 is for using a repeated prime number | |
| \(27 = 3 + 5 + 17\) | B1M1A0 |
| \(27 = 7 + 11 + 9\) | B1M0A0 |
| \(27 = 1 + 3 + 23\) | B1M0A0 |
| List of prime numbers with right side boxes empty or incorrect | M0 |