 Middle Years

2.06 Substitution

Worksheet
Substitution
1

Evaluate:

a

9 k when k = 6.

b

- 9 z when z = 5.

c

q \times 5 when q = 3.

d

3 c + 9 when c = 6.

e

8 x + 4 when x = 2.

f

45 - 7 x when x = 6.

g

6 n \times 10 when n = 2.

h

5 + k when k = 9.

i

z + 2 when z = - 7.

j

4 - t when t = 3.

k

p - 8 when p = 6.

l

\dfrac{r}{3} when r = 12.

m

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

2

Evaluate:

a

c^{2} when c = 9.

b

s^{3} when s = 5.

c

k^{2} when k = - 7.

d

k^{3} when k = - 9.

3

Evaluate:

a

\dfrac{5 k}{24} when k = 8.

b

\dfrac{15}{8 k} when k = 3.

c

\dfrac{4 k}{5} when k = 15.

4

Evaluate the expression \dfrac{45}{2 n} when:

a

n = 9

b

n = 47

5

Evaluate:

a

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

b

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

c

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

d

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

e

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

f

\dfrac{36}{uv} when u = - 2 and v = 3.

g

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

h

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

i

3 y + 5 w when y = 6 and w = 5.

j

6 x + 4 y + 6 when x = 3 and y = 5.

k

4 x - 2 y - 6 when x = 3 and y = 2.

l

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

m

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

n

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

o

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

p

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

q

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

r

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

s

\dfrac{m v^{2}}{2} when m = 8 and v = - 15.

6

Evaluate:

a

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

b

3 j + 5 k + 6 l when j = 3, k = 8, and l = 7.

c

6 a - 3 b + 4 c when a = 8, b = 6, and c = 7.

d

a b c when a = 8, \, b = 9 and c = 6.

e

2pqr when p = 3, \,q = 4 and r = 5.

f

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

7

18.6 - 3 x when x is equal to 4.1. Round your answer to one decimal place.

8

Evaluate \dfrac{11 s - 39}{3 r} when r = - 1.6 and s = 2.8. Round your answer to three decimal places.

9

Evaluate 6 x - 3 y when:

a

x = 5 and y = 5.

b

x = 7 and y = 4.

c

x = 8 and y = \dfrac{1}{3}.

10

If x = 3, evaluate:

a

3 x^{2}

b

\left( 4 x\right)^{2}

c

- 2 x^{2} + \left( 3 x\right)^{2}

11

Evaluate x^{2} + 6 x + 9 when:

a

x = 2

b

x = 5

12

Evaluate the expression m n when:

a

m = 7 and n = 9.

b

m = 4 and n = 3.5.

c

m = \dfrac{1}{8} and n = 72.

13

Evaluate the expression \dfrac{p q}{- 8 r} when:

a

p = 5, \, q = - 3 and r = - 9.

b

p = - 9, \, q = 21 and r = 3.

14

Evaluate the expression \dfrac{a b}{5 c} when:

a

a = 2, b = 3 and c = 4.

b

a = 4, b = 16 and c = 2.

15

Evaluate u + a t when:

a

u = 18, a = 2 and t = 4.

b

u = 37, a = 2 and t = 14.

16

Evaluate the expression u + v w when:

a

u = 59, v = 3 and w = 15.

b

u = 14, v = 5.5 and w = 3.6.

Applications
17

What is the largest whole number value that you can substitute for p so that the expression 81 - p^{2} is positive?

18

What is the smallest whole number value that you can substitute for p so that the expression 64 - p^{2} is negative?

19

The area, A, of triangle is given by the following formula:

A = \dfrac{b h}{2}

where h is the height of the triangle and b is the length of its base.

a

Find the area of a triangle that has a base of 7 cm and a height of 5 cm.

b

Find the area of a triangle that has a base of 25 cm and a height of 16 cm.

20

Energy can be measured in many forms. A quantity of energy is given in units of Joules (J).

The kinetic energy, E, of an object in motion is calculated using the following formula:

E = \dfrac{m v^{2}}{2}

where m is the mass of the object in kilograms and v is the speed of the object in metres per second.

Find the kinetic energy, E, of an object with a mass of 6 kg, travelling at a speed of 19 metres per second.

21

When the heating system in a house is on a setting of s, the temperature, T, of the house within the first 30 minutes can be estimated by using the formula T = a + \dfrac{s t}{10} where a is the initial temperature and t is the number of minutes since turning the heating system on. Calculate the temperature of the room after 18 minutes if the initial temperature is - 3 degrees Celsius and the setting on the heater is 5.

22

Valerie stands at the top of a cliff and launches a tennis ball across the valley. To estimate the vertical position, y, of the ball compared to herself she uses the formula: y = 14.7 t - \dfrac{9.8}{2} t^{2} where v is the initial vertical velocity and t is the number of seconds since the ball is launched.

a

Find the vertical position of the ball after:

i

2 seconds

ii

3 seconds

iii

8 seconds

b

At which of the above times as the ball above Valerie?