02 - Indices And Surds

St Joseph’s Institution Secondary Four Mathematics REVISION − INDICES & SURDS Name:_____________________________________ (

Q1)

Q2)

a)

Simplify

b)

Simplify

12 + 75 − 48 + 147

c)

Simplify

4x 2 − 4 − x 2 − 1

d)

x −6 − y −6 Simplify −3 x − y −3

e)

Simplify

2 − 2− 2 .

2 + 2− 2 ×

3 n +1 − 3 n −2 3 n −1 − 3 n +2

Rationalise the following 5 a) 2+3 5

b)

c)

Q3)

) Class: ___________

4+2 5 1+ 2 + 5 1+ 2 + 3 1− 2 + 3

The sides AB and BC of a triangle, right-angled at B, are of length 3 2 + 5 and 2 + 2 5 respectively. Find i) the area of the triangle; ii) the value of AC 2 .

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© Jason Ingham 2009

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1

Q4)

A hollow closed rectangular tank is constructed of a thin sheet of metal of negligible thickness. The length of the tank is twice the width. The external surface area of the tank is 48 m2. If the width is 1+ 2 m , find the exact value of the height of the tank and the volume of the tank.

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Q5)

Q6)

a)

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2

)

 13   in the form of a + b 3 , where a and b Express 1 + 3 −  4 + 3   are integers to be determined. 9 n +2 − 3 2n +2 = 2 a 3 b , where a and b are integers, find the 25 value of a and express b in terms of n.

b)

Given that

a)

Given that

b)

Find the values of m and of n if 1 3  −  1 2 5 25     125 2 +   − 5   4  × 2 = 2 m + n 5  5 +2 5  64   16     where m and n are integers.

2 3 −1

2 54 + 1

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)

a b + c 3 , where a, b and c are 4 2 3 +2 2 2 integers that are to be determined. +

=

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Q7)

)

Without using calculators, express

2

2 3 −3 2 4 3−2 3

)

in the form of a + b 6 .