Surds: Fluency and Exam Drill - Worksheets, Questions and Revision

24 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

Download PDFJump to mark scheme (page 6)
« Previous: SurdsNext: Bounds »
Revision Library
revisionlibrary.co.uk
HIGHER

7.1D Surds: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculators not allowed · about 65 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.

Surds: Fluency and Exam Drill

Original content written for Revision Library. Styled on Edexcel 1MA1 GCSE Mathematics conventions.

This is a non-calculator practice set for Edexcel 1MA1 topic 7.1 (Surds). Work through the fluency questions first to secure the core skills of simplifying, combining and rationalising surds, then attempt the exam-style questions, finishing with two grade 9 stretch questions. Show all your working clearly, since method marks are available even when a final answer is not fully correct. Give all answers in their simplest surd form unless told otherwise.

1
Simplify √18 fully.
(Total for Question 1 is 1 mark)
2
Simplify √50 fully.
(Total for Question 2 is 1 mark)
3
Simplify √75 fully.
(Total for Question 3 is 1 mark)
4
Simplify √32 fully.
(Total for Question 4 is 1 mark)
5
Simplify √80 fully.
(Total for Question 5 is 1 mark)
6
Work out √3 * √12.
(Total for Question 6 is 1 mark)
7
Work out √20 * √5.
(Total for Question 7 is 1 mark)
8
Work out √48 / √3.
(Total for Question 8 is 1 mark)
9
Simplify 3sqrt(2) + 5sqrt(2).
(Total for Question 9 is 1 mark)
10
Simplify 7sqrt(5) - 2sqrt(5).
(Total for Question 10 is 1 mark)
11
Simplify √8 + √2 fully.
(Total for Question 11 is 2 marks)
12
Simplify √27 - √3 fully.
(Total for Question 12 is 2 marks)
13
Rationalise the denominator of 1/√5, giving your answer in its simplest form.
(Total for Question 13 is 2 marks)
14
Rationalise the denominator of 6/√3 fully.
(Total for Question 14 is 2 marks)
15
Expand and simplify (3 + √5)(5 - √5).
(Total for Question 15 is 3 marks)
16
Show that (6 + √7)(6 - √7) = 29.
(Total for Question 16 is 2 marks)
17
Rationalise the denominator of 1/(4 + √3), giving your answer in the form (a - √b)/c, where a, b and c are integers.
(Total for Question 17 is 3 marks)
18
A rectangular garden bed has length (6 + √11) m and width (6 - √11) m. Find the area of the garden bed, giving your answer as an integer.
(Total for Question 18 is 3 marks)
19
Simplify fully √90 + √40 - √10, showing each step of your working.
(Total for Question 19 is 3 marks)
20
In triangle ABC, the angle at B is 90 degrees. AB = √21 cm and BC = √54 cm. Work out the length of AC, giving your answer in the form ksqrt(n) cm, where k and n are integers.
Diagram NOT accurately drawn
A B C AB = √21 cm BC = √54 cm AC
(Total for Question 20 is 4 marks)
21
Show that (2 + √5)2 = 9 + 4sqrt(5).
(Total for Question 21 is 3 marks)
22
A student writes down the statement √16 + √9 = √16 + 9.
(a)Show, by evaluating both sides, that the statement above is not correct.(2)
(b)By simplifying √20 + √5 and √20 + 5 separately, show that √a + √b is not equal to √a + b in general.(3)
(Total for Question 22 is 5 marks)
23
Show that √7 + 2sqrt(10) = √5 + √2.
(Total for Question 23 is 3 marks)
24
Simplify (5 + 2sqrt(2))/(3 - 2sqrt(2)) fully, giving your answer in the form p + qsqrt(2), where p and q are integers.
(Total for Question 24 is 4 marks)
Mark scheme · 7.1D Surds: Fluency and Exam Drill

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24