All topics · Chapter 5
Surds
13 exam-style questions at four levels. Type your working one line at a time and it is marked line by line — method marks and accuracy marks, like the ECZ scheme.
Foundation5 questions
Simplify √50.
ECZ Paper 1 · 2 marks · Foundation level
Simplify √18.
ECZ Paper 1 · 2 marks · Foundation level
Simplify √8 × √2.
ECZ Paper 1 · 2 marks · Foundation level
Simplify 2√3 + 5√3.
ECZ Paper 1 · 2 marks · Foundation level
Which ONE of these numbers is a surd? √4, √9, √10, √16. Give a reason for your answer.
ECZ Paper 1 · 2 marks · Foundation level
Application4 questions
Simplify √27 + √12.
ECZ Paper 1 · 3 marks · Application level
Expand and simplify √2(√8 + √2).
ECZ Paper 1 · 3 marks · Application level
Rationalise the denominator of 1/√5.
ECZ Paper 1 · 2 marks · Application level
Rationalise the denominator of 6/√3, giving your answer in its simplest form.
ECZ Paper 1 · 3 marks · Application level
Analysis2 questions
Mastery2 questions
A rectangle has length (3 + √2) cm and width (3 − √2) cm. (a) Show that the area of the rectangle is 7 cm². (b) Work out the perimeter of the rectangle, in cm.
ECZ Paper 2 · 4 marks · Mastery level
(a) Simplify √72 + √50 − √32. (b) Rationalise the denominator of 14/√2, giving your answer in its simplest form. (c) What do you notice about your answers to (a) and (b)?
ECZ Paper 2 · 6 marks · Mastery level
Working through the whole syllabus? The full topic list and our weekly revision routine put this chapter in context.