Surds

Surds – Differentiated Worksheet with Worked Solutions (Pearson Edexcel IGCSE 9–1, Higher Tier)

This worksheet develops the surds content of the Pearson Edexcel International GCSE (4MA1) Higher Tier specification. Students start with simplifying surds and build up to exam-style problems in shape and real-life contexts. The pack has two PDFs: the student worksheet and a separate set of full worked solutions. It works well for classwork, homework, independent revision and exam preparation.

The worksheet has five colour-coded levels, each on its own page with a matching border and a clear grade label, so students know how hard the work is before they begin. Every question has a square grid for working out and an answer line, and all the questions are designed to be answered without a calculator.

Green – Practice (Grade 5): six questions on simplifying surds such as √50 and √48, multiplying surds, and adding and subtracting surds after simplifying them.
Amber – Further practice (Grade 6): six questions on expanding single and double brackets containing surds, including a difference of two squares and squaring a bracket, with answers in the form a + b√n.
Red – Developing understanding (Grade 7): six questions on rationalising the denominator. They move from simple denominators such as 6/√3 to denominators of the form 3 − √5 and √7 + 2, which need the conjugate.
TIF – Problem solving (Grade 8): six exam-style shape problems where students find an exact height, width, radius or length:
the width of a rectangle and the height of a triangle, both needing rationalising
the radius of a circle
the radius and curved surface area of a cylinder
the hypotenuse of a triangle with surd sides
the height and area of an equilateral triangle
TIEF – Real-life challenge (Grade 9): four illustrated problems that show where surds appear in everyday life:
the √2 ratio behind A4 and A5 paper
the gradient and exact length of a wheelchair ramp
the dimensions of a solar panel
the radius of a pizza with double the area

The worked solutions show one step per line going down the page, and give each part of an answer on its own line so students can follow every stage of the method. They highlight key techniques such as finding the largest square factor, using the conjugate to rationalise, recognising the difference of two squares, and giving exact answers in simplest surd form.