Higher June 2023 Paper 1 Q10
10 Sunita is \(x\) years old.
Beth is one year younger than Sunita.
Joel is double Sunita’s age.
The mean of their ages is 5
How old is Joel? [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 – algebra based on Sunita’s age | ||
| \(5 \times 3\) or 15 | M1 | may be implied by their algebraic total of the three ages being divided by 3 |
| \(x - 1\) or \(2x\) or \(4x - 1\) | M1 | oe expressions any letter throughout |
| \(x +\) their \((x - 1) +\) their \(2x =\) their 15 or \(4x - 1 =\) their 15 | M1dep | oe equation eg \(\dfrac{x + x - 1 + 2x}{3} = 5\) dep on M1M1 |
| \((x =)\ 4\) | M1dep | correct solution to their equation if the solution has a decimal part allow truncation or rounding to the nearest whole number |
| 8 | A1 | |
| Alternative method 2 – algebra based on Joel’s age | ||
| \(5 \times 3\) or 15 | M1 | may be implied by their algebraic total of the three ages being divided by 3 |
| \(\dfrac{y}{2}\) or \(\dfrac{y}{2} - 1\) or \(2y - 1\) | M1 | oe expressions any letter throughout \(2y - 1\) must not come from \(y + y - 1\) |
| \(y +\) their \(\dfrac{y}{2} +\) their \(\left(\dfrac{y}{2} - 1\right) =\) their 15 | M1dep | oe equation eg \(\dfrac{y + \frac{y}{2} + \frac{y}{2} - 1}{3} = 5\) dep on M1M1 |
| \(2y +\) their \(y +\) their \((y - 2) = 2 \times\) their 15 or \(4y - 2 = 30\) or \(2y - 1 = 15\) | M1dep | their equation with no denominator |
| 8 | A1 | |
| Alternative method 3 – trial and improvement | ||
| \(5 \times 3\) or 15 | M1 | may be implied by their total of the three ages being divided by 3 |
| Trial of three numbers which fit the criteria, with either their sum correctly evaluated or their sum divided by 3 | M1 | eg \(2 + 1 + 4 = 7\) or \((2 + 1 + 4) \div 3\) condone missing brackets |
| Second trial of three numbers which fit the criteria, with either their sum correctly evaluated or their sum divided by 3 | M1dep | dep on previous M1 eg \(3 + 2 + 6 = 11\) or \((3 + 2 + 6) \div 3\) condone missing brackets |
| 4, 3 and 8 selected as their final combination | M1dep | any order implies M4 |
| 8 | A1 | |
Additional guidance
| Up to M4 may be awarded for correct work seen in multiple attempts even if not subsequently used | |
| Correct expressions, but the sum of the three ages is equated to 5 eg \(4x - 1 = 5\) | M0M1M0M0A0 |
| In alt 1, the correct value of \(x\) or the correct age for Joel for their two terms for Beth and Joel, with one correct, implies the first 4 marks eg \(x\) and \(x + 1\) and \(2x\), with \(x = 3.5\) or answer 7 | M1M1M1M1A0 |
| In alt 2, the correct value of \(y\) for their two terms for Sunita and Beth, with one correct, implies the first 4 marks eg \(y\) and \(\dfrac{y}{2}\) and \(\left(\dfrac{y}{2} + 1\right)\), with \(y = 7\) or answer 7 | M1M1M1M1A0 |
| In alt 1 and alt 2, condone missing brackets in equations if not recovered for up to M1M1M1 eg \(x + x - 1 + 2x \div 3 = 5\) not recovered | M1M1M1M0A0 |