Higher January 2021 Paper 2 Q14
14
(a) Solve \(\dfrac{9a - 7}{5} - \dfrac{3a - 7}{4} = 4.55\)
Show clear algebraic working. (3)
Show clear algebraic working. (3)
(b) Make \(c\) the subject of the formula \(p = \sqrt{\dfrac{ac + 8}{3 + c}}\) (4)
| Scheme | Marks |
|---|---|
eg \(20 \times \dfrac{9a - 7}{5} - 20 \times \dfrac{3a - 7}{4} = 20 \times 4.55\) (= 91) or eg \(4(9a - 7) - 5(3a - 7) = 20 \times 4.55\) or eg \(\dfrac{4(9a - 7)}{20} - \dfrac{5(3a - 7)}{20}\) (= 4.55) or eg \(\dfrac{4(9a - 7) - 5(3a - 7)}{20}\) (= 4.55) | M1 |
| eg \(36a - 28 - 15a + 35 = 20 \times 4.55\) or \(21a = 84\) oe | M1 |
| Working required Answer: 4 | A1 |
| (3) |
Notes
M1: For clear intention to multiply all terms by 20 (or 4 × 5) or a multiple of 20 oe or to express LHS as two fractions over 20 (or 4 × 5) or a multiple of 20 oe or as a single fraction with a denominator of 20 (or 4 × 5) or a multiple of 20 oe
if expanded numerator, allow one error
M1: Expanding brackets and multiplying by denominator with no more than one sign error
A1: dep on M1
| Scheme | Marks |
|---|---|
| \(p^2 = \dfrac{ac + 8}{3 + c}\) | M1 |
| \(3p^2 + cp^2 = ac + 8\) | M1 |
| \(cp^2 - ac = 8 - 3p^2\) or \(3p^2 - 8 = ac - cp^2\) | M1ft |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(c = \dfrac{8 - 3p^2}{p^2 - a}\) | A1 |
| (4) | |
| (7 marks) |
Notes
M1: for removing square root
M1: for multiplying by denominator and expanding in a correct equation
M1ft: for gathering terms in \(c\) on one side and other terms the other side
ft their equation dep on 2 terms in \(c\) and two other terms
A1: or \(c = \dfrac{3p^2 - 8}{a - p^2}\)