Unit 10
9 marks · NormalThis question connects knowledge of number types and algebraic fractions.
Write the number in its simplest surd form and state whether it is rational or irrational.
Simplify the following algebraic fraction as much as possible:
If , write your answer to part (b) 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.
Show answer
(a) , which is irrational because 2 is not a perfect square.
(b) for
(c) with : numerator , denominator .\ So the answer is:\
Common mistakes: Not simplifying the surd fully; Incorrectly factorising a squared binomial; Not checking value substitution
Show mark scheme and worked solution
Marking points
A1 (a) · 1 mark · Simplifies as .
B1 (a) · 1 mark · Correctly classifies as irrational with a valid reason.
M1 (b) · 2 marks · Correctly factorises numerator and denominator.
A2 (b) · 2 marks · Fully simplifies to for .
M2 (c) · 1 mark · Attempts correct substitution of . (follow-through)
A3 (c) · 2 marks · Simplifies the numerator and denominator to the correct fraction in terms of surds. (follow-through)
Worked solution
(a) , which is irrational because 2 is not a perfect square.
(b) , . Fraction simplifies to for .
(c) Substitute :
Simplified answer: