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8.04 Substitution

Worksheet
Substitution
1

Find the value of:

a

9 + m when m = 8

b

14 + v when v = 15

c

n - 2 when n = 5

d

n - 8 when n = 44

e

\dfrac{n}{7} when n = 14

f

\dfrac{u}{9} when u = 54

g

- \dfrac{20}{x} when x = 5.

h

u \times 5 when u = 6

i

n \times 9 when n = 8

j

z + 2 when z = - 7.

k

4 - t when t = 3.

l

p - 8 when p = 6.

m

2x + 9 when x = 4

n

c^{2} when c = 9.

o

s^{3} when s = 5.

p

k^{2} when k = - 7.

q

k^{3} when k = - 9.

r

y^2 when y = -2

s

x^2 - 4x when x = 3

t

\dfrac{x+10}{4} when x = 2

u

\dfrac{3x}{4} when x = 8

v

2 \left( x+7 \right) when x = 4

w

\left( x+2 \right) \left( x - 1 \right) when x = -3

x

4y^2 + 9 when y = 2

2

For each formula find the value of y for the given value of x:

a

y = 6 x - 9, when x = 12.

b

y = \dfrac{x}{9} + 6, when x = 63.

c

y = 4-3x, when x = 7.

d

y = 14x+\dfrac{18}{5}, when x = \dfrac{1}{10}.

3

Find the value of:

a

s t when s = 7 and t = - 8.

b

4 x y when x = - 6 and y = - 5.

c

m + n when m = 7 and n = 12

d

4 x + 2 y + 3 when x = 5 and y = 4

e

m + n when m = 6 and n = - 4.

f

5 + a + b when a = - 7 and b = 4.

g

p + q + r when p = 5, \,q = 9 and r = 6.

h

x^2 - 4y when x = -2 and y = 5

i

8a + 4b - 9 when a = 2 and b = 5

j

\dfrac{a}{b} when a = 56 and b = - 8.

k

\dfrac{m n}{15} when m = 12 and n = 20.

l

abc when a = 3, b = -2 and c = -1

m

m - n when m = 2 and n = - 9.

n

7 - p - q when p = 4 and q = 5.

o

- 5 - s + t when s = 8 and t = 15.

p

\dfrac{p}{2 q} when p = - 28 and q = - 7.

q

4 \left(p + q\right) when p = 7 and q = 8.

r

7 x + y when x = 6 and y = - 36.

s

- 4 \left(s - t\right) when s = 6 and t = 15.

t

m - 2 n when m = - 19 and n = - 7.

4

Consider the following formulae:

a

q = p + 7

i

Complete the table:

p123456
q8910
ii

Find the value of q when p = 30.

b

q = 3 p

i

Complete the table:

p123456
q369
ii

Find the value of q when p = 20.

c

q = 6 p + 4

i

Complete the table:

p123456
q101622
ii

Find the value of q when p = 40.

d

n = m - 7

i

Complete the table:

m101112131415
n345
ii

Find the value of n when m = 20.

e

q = 5 p - 3.

i

Complete the table:

p123456
q2712
ii

Find the value of q when p = 20.

f

q = p^{2} + 5.

i

Complete the table:

p123456
q6914
ii

Find the value of q when p = 20.

Applications
5

Find the next three numbers in the following sequences:

a

11, 22, 33, 44, \ldots

b

15, 23, 31, 39, \ldots

c

32, 27, 22, 17, \ldots

d

9, 16, 25, 36, \ldots

6

Vanessa is making the sequence to the right out of tiles. She creates a table comparing the sequence number of a shape to the number of tiles needed to make it:

\text{Sequence}\\ \text{number } (S)123456
\text{No. tiles } (T)357
a

Write an algebraic rule for the number of tiles, T, in terms of the sequence number, S.

b

Use your rule to complete the table of values.

7

James is making snowflakes out of hexagonal tiles:

James creates a table comparing the width of a snowflake to the number of tiles needed to make it:

\text{Width } (W)135791113
\text{No. tiles } (T)171319
a

Write an algebraic rule for the number of tiles, T, in terms of the snowflake's width, W.

b

Use your rule to complete the table of values.

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Outcomes

MA4-9NA

operates with positive-integer and zero indices of numerical bases

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