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Middle Years

6.04 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

u \times 5 when u = 6

h

n \times 9 when n = 8

i

2x + 9 when x = 4

j

y^2 when y = -2

k

x^2 - 4x when x = 3

l

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

m

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

n

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

o

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

p

4y^2 + 9 when y = 2

2

Find the value of:

a

m + n when m = 7 and n = 12

b

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

c

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

d

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

e

\dfrac{5xy}{9} when x = 3 and y = 6

f

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

3

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}.

Tables of values
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.

5

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.

6

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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