EDEXCEL GCSE MATHS · HIGHER TIER
Exam Practice: Surds
Surds · Number · Lesson 7 of 7 · 15 marks · 25 minutes
Name Date
Answer all questions. Show your working. All questions are non-calculator.
Question 1 NON-CALCULATOR [1 mark]
Write √45 in the form k√5, where k is an integer.
Question 2 NON-CALCULATOR [2 marks]
Rationalise the denominator of 12/(√3). Give your answer in its simplest form.
Question 3 NON-CALCULATOR [3 marks]
Expand and simplify (2 + √3)(4 − √3). Give your answer in the form a + b√3, where a and b are integers.
Question 4 NON-CALCULATOR · SHOW THAT [3 marks]
Show that √98 + √8 = 9√2
Question 5 NON-CALCULATOR [3 marks]
The diagram shows the right-angled triangle ABC. AB = √5 cm and BC = √11 cm. Work out the length of AC.
Question 6 NON-CALCULATOR [3 marks]
A rectangle has length (3 + √5) cm and width (3 − √5) cm. Work out the area of the rectangle.
Answers
Check your answer only once you have written one.
Question 1 [1 mark]
√45 = √9 × √5 = 3√5
▸ 3√5 B1
Question 2 [2 marks]
12/(√3) × √3/(√3) = 12√3/3 = 4√3
▸ Multiplying the top and the bottom by √3 M1
▸ 4√3 A1
Question 3 [3 marks]
8 − 2√3 + 4√3 − 3 = 5 + 2√3
▸ At least 3 of the 4 terms correct: 8, −2√3, 4√3, −3 M1
▸ All 4 terms correct M1
▸ 5 + 2√3 A1
Question 4 [3 marks]
√98 = √49 × √2 = 7√2. √8 = √4 × √2 = 2√2. 7√2 + 2√2 = 9√2.
▸ √98 = 7√2 or √8 = 2√2 M1
▸ Both simplified correctly M1
▸ Correctly added to reach 9√2 A1
Question 5 [3 marks]
AC² = (√5)² + (√11)² = 5 + 11 = 16, so AC = √16 = 4 cm.
▸ (√5)² + (√11)² or 5 + 11 M1
▸ √16 M1
▸ 4 (cm) A1
Question 6 [3 marks]
(3 + √5)(3 − √5) = 9 − 3√5 + 3√5 − 5 = 4 cm²
▸ Area = (3 + √5)(3 − √5) M1
▸ At least 3 of the 4 terms correct: 9, −3√5, +3√5, −5 M1
▸ 4 (cm²) A1