Preliminary Mathematics Worksheet
Substitution
NSW Syllabus Ref: 1.3

(c) Mathematics Plus, 2002


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Question 1

If x = 5, find the exact value of these expressions:

I

II

III

(a)

2x + 3

(a)

3x2 - 25

(a)

4(x - 2)2

(b)

(2x - 1)(3x + 2)

(b)

(x - 5)(3x + 1)1/2

(b)

(c)

2x2 � 3x

(c)

10x5 � 2x3

(c)


Question 2

If x = 2 and y = - 5, evaluate these expressions:

I

II

III

(a)

3x + y

(a)

3(x + y)

(a)

10 - (x + y)

(b)

5(2x + y)

(b)

(3x - y)(4x + 3y)

(b)

(2x2 + y)(x + y2)

(c)

x3 + y3

(c)

(c)

(d)

5(x + y)2

(d)

(d)

Question 3

Given that y = 3x2 - 2x + 5, find the exact value of y for these values of x.

I

II

III

(a)

x = 3

(a)

x = - 2

(a)

x = 1/2

(b)

x = 2.8

(b)

x = 2� 3

(b)


Question 4

Find the value of if x = 4/9, y = - 2/3 and z = 4/7.


Question 5

Given that s = ut + 1/2 at2, find the value of s when u = 30.2, t = 3 and a = 9.8.


Question 6

If , evaluate r when a = 5.5 and b = - 3.2. Give your answer correct to one decimal place.


Question 7

Given that p = 1/2m(v2 - u2), evaluate p when v = 3.5, u = 2.5 and m = 10.


Question 8

Find correct to one decimal place the value of if M = 10.7, m = 7.4 and g = 9.8.


Question 9

Given that A = P(1 + r)n, find correct to two decimal places the value of A when
P = 10 000, r = 0.08 and n = 12.5.


Question 10

If , evaluate V when r = 1.61, h = 3.52. Give your answer correct to two decimal places.


Question 11

Given that , find the value of d correct to three significant figures when T = 3.52 � 103 and r = 2.59 � 10-2.

 

 

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