Surds: Simplifying & Rationalising (Grade 11) — Worksheet & Memo

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Grade 11 · Exponents & Surds

Surds: Simplifying & Rationalising (Grade 11)

EXAM-STYLE CLASS TEST

Marks

Duration

55 minutes

Questions

Name:

Class:

Date:

Mark

/ 36

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
√50 in simplest surd form is …
(1)
A)5√2
B)2√5
C)25√2
D)√25
1.2
√12 + √27 = …
(1)
A)5√3
B)√39
C)6√3
D)5√6
1.3
√8 × √2 = …
(1)
A)4
B)√10
C)16
D)2√2
1.4
Rationalise the denominator of 3√5.
(1)
A)3√55
B)3√5√5
C)35
D)√155
1.5
Rationalise the denominator of 2√3 − 1.
(1)
A)√3 + 1
B)√3 − 1
C)2(√3 + 1)4
D)2√3 + 2
1.6
The CONJUGATE of √7 + 2 is …
(1)
A)√7 − 2
B)−√7 + 2
C)√7 + 2
D)2 + √7
1.7
If √x = 5, then x = …
(1)
A)25
B)5
C)√5
D)10
1.8
√47 lies between which TWO integers?
(1)
A)6 and 7
B)7 and 8
C)23 and 24
D)5 and 6
1.9
(√5)² − (√3)² = …
(1)
A)2
B)√2
C)8
D)√15
1.10
For √(x − 3) to be REAL, x must satisfy …
(1)
A)x ≥ 3
B)x > 3
C)x ≤ 3
D)x ≥ −3

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[11 MARKS]

Simplify the following WITHOUT the use of a calculator. Leave your answers in simplest surd form.

2.1
12 + 27 − 3
(4)
2.2
(5 − 2)(5 + 2)
(3)
2.3
72 − 50 + 8
(4)

Question 3

[15 MARKS]

Rationalise the denominators and answer the questions that follow.

3.1
41 + 2
(5)
3.2
33 − 1
(5)
3.3
Determine, without a calculator, between which two consecutive integers 72 lies.
(3)
3.4
Explain why 9 + 16 ≠ 25.
(2)

TOTAL: 36 marks

This question paper consists of 3 questions.