Higher June 2022 Paper 1 Q11
11
(a) Factorise \(9x^2 - 4y^2\) (2)
(b) Express \(\dfrac{7}{8} - \dfrac{x + 3}{4x}\) as a single fraction in its simplest form. (3)
| Scheme | Marks |
|---|---|
| \((3x \pm 2y)(3x \pm 2y)\) or \((3x)^2 - (2y)^2\) | M1 |
| \((3x + 2y)(3x - 2y)\) | A1 |
| (2) |
| Scheme | Marks |
|---|---|
\(\dfrac{7(4x)}{32x} - \dfrac{8(x + 3)}{32x}\) oe or \(\dfrac{7(4x)}{8(4x)} - \dfrac{8(x + 3)}{8(4x)}\) oe or \(\dfrac{28x}{32x} - \dfrac{8(x + 3)}{32x}\) oe or \(\dfrac{28x}{32x} - \dfrac{8x + 24}{32x}\) oe or \(\dfrac{28x - 8(x + 3)}{32x}\) oe or \(\dfrac{7x}{8x} - \dfrac{2(x + 3)}{8x}\) oe or \(\dfrac{7x - 2(x + 3)}{8x}\) oe | M1 |
\(\dfrac{28x - 8x - 24}{32x}\) oe or \(\dfrac{20x - 24}{32x}\) oe or \(\dfrac{7x - 2x - 6}{8x}\) oe or \(\dfrac{20x}{32x} - \dfrac{24}{32x}\) oe or \(\dfrac{28x}{32x} - \dfrac{8x}{32x} - \dfrac{24}{32x}\) oe | M1 |
| \(\dfrac{5x - 6}{8x}\) | A1 |
| (3) | |
| (5 marks) |
Notes
M1: for two correct fractions with common denominator
or
a single correct fraction
M1: for correct fraction(s) with bracket(s) expanded and dealing with the negative signs
A1: or \(\dfrac{-6 + 5x}{8x}\)