4MA0 Higher June 2016 Paper 3R Q20
20
(a) Simplify fully \(\dfrac{50x^2 - 8}{10x - 4}\)
Show clear algebraic working. (3)
Show clear algebraic working. (3)
(b) Given that \(a\) is a positive integer, show that \[\sqrt{3a}\left(\sqrt{12a} + a\sqrt{3a}\right)\] is always a multiple of 3 (3)
| Scheme | Marks |
|---|---|
\(\dfrac{2(5x + 2)(5x - 2)}{2(5x - 2)}\) or \(\dfrac{(5x + 2)(5x - 2)}{5x - 2}\) or \(\dfrac{(5x - 2)(10x + 4)}{2(5x - 2)}\) or \(\dfrac{(10x - 4)(5x + 2)}{2(5x - 2)}\) oe | M2 |
| \(5x + 2\) | A1 |
| (3) |
Notes
M2: Factorising numerator and denominator in a correct quotient
M1 for \(2(25x^2 - 4)\) or a correctly factorised numerator or denominator or \(\dfrac{25x^2 - 4}{5x - 2}\)
A1: dep on at least M1
| Scheme | Marks |
|---|---|
| \(\sqrt{12a \times 3a} + a\sqrt{3a \times 3a}\) or better | M1 |
| \(6a + 3a^2\) | A1 |
eg \(3(2a + a^2)\) or \(3a(2 + a)\) or \(\dfrac{6a + 3a^2}{3} = 2a + a^2\) or explanation that \(6a\) and \(3a^2\) are multiples of 3 so overall expression is a multiple of 3 Answer: Show | B1ft |
| (3) |
Notes
M1: For correct expansion or
\(\sqrt{12a} = 2\sqrt{3}\sqrt{a}\) or \(\sqrt{12a} = 2\sqrt{3a}\)
or \(6a\) or \(3a^2\) from correct working
B1ft: dep on at least M1