Foundation June 2025 Paper 2 Q12
12
(a) Make \(y\) the subject of \(\quad w = 3y - d\) (2)
Diego buys \(b\) boxes of crayons and \(p\) packets of crayons.
There are 12 crayons in each box.
There are 3 crayons in each packet.
Diego buys a total of \(T\) crayons.
(b) Write down a formula for \(T\) in terms of \(b\) and \(p\) (3)
| Scheme | Marks |
|---|---|
\(w + d = 3y\) oe or \(-3y = -w - d\) oe or \(\dfrac{w}{3} = y - \dfrac{d}{3}\) oe or \(\dfrac{w + d}{3}\) oe or \(y = w + d \div 3\) | M1 |
Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: \(y = \dfrac{w + d}{3}\) | A1 |
| (2) |
Notes
M1: for a correct first step
A1: oe eg \(y = \dfrac{-d - w}{-3}\) or \(y = \dfrac{w}{3} + \dfrac{d}{3}\) oe or
\(y = (w + d) \div 3\)
(must see \(y\) = … on answer line or in working)
| Scheme | Marks |
|---|---|
| \(T = 12b + 3p\) | B3 |
| (3) | |
| (5 marks) |
Notes
B3: for \(T = 12b + 3p\) oe
[accept \(T = 12 \times b + 3 \times p\)]
B2 for \(12b + 3p\)
or \(T = 12b + xp\)
or \(T = yb + 3p\)
or a correct equation with other letters
eg \(T = 12m + 3n\)
B1 for \(12b + xp\) or \(12b\) or \(yb + 3p\) or \(3p\) or
\(12p + 3b\) or \(T = kb + cp\) where \(k \neq 0\) or \(k \neq 12\) and \(c \neq 0\) or \(c \neq 3\)
Accept upper or lower case for \(T\), \(b\) and \(p\) including a mixture of these for B3, B2 and B1