Unit 10
9 marks · NormalThis question is about simplifying surds and combining algebraic fractions.
Simplify the following expression, giving your answer as a surd in its simplest form:
Express as a single algebraic fraction and simplify as far as possible:
Let . Substitute this value into your answer for part (b) and write your answer as a surd in its simplest form.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) 3\sqrt{5} + 4\sqrt{5} - \sqrt{5} = 6\sqrt{5}
(b) \frac{2y + (y-4)}{y+3} = \frac{3y-4}{y+3}
(c) \frac{3\sqrt{5} - 4}{\sqrt{5} + 3}
Common mistakes: Not simplifying all surds fully; Adding numerators without common denominators; Not substituting or simplifying with surds
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Attempts to break down and simplify all surds, e.g., writes .
A1 (a) · 2 marks · Obtains fully simplified answer .
M2 (b) · 1 mark · Attempts to add algebraic fractions over a common denominator.
A2 (b) · 2 marks · Correctly combines to .
M3 (c) · 1 mark · Attempts substitution of into the part (b) answer. (follow-through)
A3 (c) · 2 marks · Simplifies expression in surd form to . (follow-through)
Worked solution
(a) ; , so:
(b) The denominators are already the same, so add numerators: :
(c) Substituting :