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6.02 Substitution into expressions

Worksheet
Evaluate algebraic expressions with one variable
1

Evaluate each of the following expressions for the given value:

a

m - 2 for m = - 7

b

x - 2 for x = 8

c

7 a + 18 for a = - 3

d

8 x + 4 for x = 2

e

45 - 7 x for x = 6

f

\dfrac{n}{9} for n = 8

g

\dfrac{6}{w} for w = 3

h

\dfrac{4 k}{5} for k = 15

i

\dfrac{r}{5} for r = - 20

j

\dfrac{15}{r} for r = - 3

k

\dfrac{5 c}{- 36} for c = - 4

l

\dfrac{4 y - 1}{y - 1} for y = 6

m

18.6 - 3 x for x = 4.1

n

5.1 + v for v = - 10

2

Evaluate each of the following expressions for the given value:

a

y + 5 for:

i

y = 3

ii

y = 6

b

m + 6 for:

i

m = - 5

ii

m = -7

c

\dfrac{45}{2 n} for:

i
n = 9
ii
n = 47
d

\dfrac{- 36}{5 n} for:

i
n = - 4
ii
n = 37
3

Evaluate each of the following expressions for the given value:

a

y^{2} for y = 4

b

r^{2} for r = - 2

c

7 a^{2} for a = - 3

d

3 x^{2} + 5 for x = 2

e

25 - z^{2} for z = 8

f

5w^{3} for w = -2

g

\dfrac{z^{3}}{z^{2} - 6} for z = 4

h

\dfrac{3 x + 2}{x^{2} - 4 x - 12} for x = 7

4

Evaluate x^{2} - 9 x + 18 for:

a

x = 2

b

x = 4

5

If x = 3, evaluate:

a

3 x^{2}

b

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

c

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

6

Find the largest whole number that can be substituted to p so that the expression 81 - p^{2} is positive.

Evaluate algebraic expressions with more than one variable
7

Evaluate each of the following expressions for the given values:

a

a + b for a = 5 and b = 1.1

b

a - b for a = - 2 and b = 7.9

c

u + v + 25 for u = 32 and v = 48

d

- 9 m n + 2 n for m = - 7 and n = 8

e

s \left(12 - t\right) for s = - 3 and t = 10

f

4 r \times 3 s + 38 for r = - 5 and s = 3

g

\dfrac{4 a \times 5}{9 b} for a = 7 and b = 21

h

\dfrac{2 a \times 9}{5 b} for a = 25 and b = - 2

i

\dfrac{a}{1 - r} for a = 3 and r = \dfrac{1}{10}

j

5 a \times 6 b for a = \dfrac{1}{5} and b = 4

k

6 r \times 4 s for r = - \dfrac{1}{6} and s = 7

l

\dfrac{y+z}{2z} for y = 0.8 and z = 0.2

8

Evaluate each of the following expressions for the given values:

a

m n for:

i

m = 7 and n = 9

ii

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

iii

m = 4 and n = 3.5

b

r s for:

i

r = 3 and s = - 5

ii

r = \dfrac{1}{5} and s = - 35

iii

r = - 5 and s = 3.2

c

3 x - 4 y for:

i

x = 4 and y = 8

ii

x = \dfrac{1}{3} and y = 5

iii

x = 2 and y = 7.8

d

6 x - 3 y for:

i

x = 5 and y = 5

ii

x = 7 and y = 4

iii

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

e

x \left( 3 y + 4\right) + 42 for:

i

x = 4 and y = - 2

ii

x = - 43 and y = - 1

iii

x = 10 and y = 5

9

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

10

Evaluate each of the following expressions for the given values:

a

5 j k l for j = 4, k = 3 and l = 5

b

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

c

w + z + y for w = 26, z = -27, and y = -39

d

\left(u + v\right) \left(w - y\right) for u = 5, v = 8, w = 2 and y = 10

11

Evaluate each of the following expressions for the given values:

a

u + v w for:

i

u = 59, v = 3 and w = 15

ii

u = 14, v = 5.5 and w = 3.6

b

w + z y for:

i

w = - 60, z = 7 and y = 8

ii

w = - 98, z = 10 and y = 11

c

\dfrac{a b}{5 c} for:

i

a = 2, b = 3 and c = 4

ii

a = 4, b = 16 and c = 2

d

\dfrac{p q}{- 8 r} for:

i

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

ii

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

12

Evaluate each of the following expressions for the given values:

a

\left( r h\right)^{2} for r = 2 and h = 3

b

\left( p q\right)^{2} for p = 6 and q = - 2

c

v^{2} + u for u = - 49 and v = 2

d

x \left(2 - 4 y^{2}\right) for x = - 2 and y = - 2

e

a \left(b - 13\right) + b^{2} for a = - 9 and b = 10

f

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

13

If m = - 3 and n = 4, evaluate:

a

m n - \left(m - n\right)

b

m^{2} + 9 n

Applications
14

Adam sells chocolates to raise money for charity. Each chocolate sold earns \$6 for the charity.

a

If Adam sells q chocolates, write an algebraic expression for the amount of money he raises.

b

Find the amount raised if he sold 4 chocolates.

c

Find the amount raised if he sold 5 chocolates.

d

Is it possible to raise exactly \$50 if Adam sells chocolates at \$6?

15

Valentina's hens produce 5 eggs each day.

a

If Valentina collects the eggs from her hens for y days, write an algebraic expression for the total number of eggs.

b

Find the number of eggs Valentina will have after 30 days.

16

John sells chocolates in two different sized boxes. He also sells bulk amounts in packages to supermarkets.

  • Small boxes contain x chocolates
  • Large boxes contain y chocolates
  • Packages contain k boxes of chocolates
a

Write an algebraic expression for the total number of chocolates required for each or the following orders:

i

2 small and 5 large boxes.

ii

3 small boxes and five indivudual chocolates.

iii

One bulk package of large boxes.

iv

5 packages of small boxes and 3 packages of large boxes.

b

If small boxes contain 10 chocolates, large boxes contain 20 chocolates and packages contain a dozen boxes, find the total number of chocolates required for the each order in part (a).

17

Justin uses a watering can to give each of his plants an equal amount of water.

a

If his watering can contains m\text{ mL} of water and he has n plants, write an algebraic expression for how much water is given to each plant.

b

As n increases, do the plants receive more or less water?

18

Robert visits a carnival that costs \$5 to enter, and each ride costs \$1 per person.

a

If Robert decides to go on b rides, write an algebraic expression for the total amount he spends at the carnival.

b

If Robert goes on 6 rides, calculate the amount of money he spend in total.

19

At a movie screening x adults and y children attend.

a

Write an algebraic expression for the total number of people who attended the screening.

b

The price of adult tickets are \$12 and children's tickets are \$8, write an expression for the total takings on ticket sales for the screening.

c

If 20 adults and 25 children attended, calculate the total takings on ticket sales for the screening.

20

At an event there are a motorcycles and b cars. Assuming all the motorcycles have two wheels and all the cars have four wheels:

a

Write an algebraic expression for the total number of wheels at the event.

b

Write an algebraic expression for the average number of wheels per vehicle at the event.

c

Find the average number of wheels per vehicle if there were 8 motorcycles and 32 cars at the event.

21

Vanessa has \$700 in her bank account. She only uses the account to pay her mobile phone bill each month.

a

If each monthly bill is \$14, write an algebraic expression for how much Vanessa has in her account after c months.

b

Find the amount of money she will have in her account after she pays her bill for 4 months.

22

Laura has a piggy bank in which she collects 20c and 50c coins. After some time, she loses track of how many coins are in the piggy bank.

a

Let m represent the number of 20c coins and n represent the number of 50c coins. Write an algebraic expression for the total value of Laura’s coins in cents.

b

Laura breaks her piggy bank and discovers that she has thirteen 20c and twenty-seven 50c coins. Find the total value of these coins in dollars.

23

Water is dripping from a tap into a large bucket, so that:

  • After 1 hour, the water level in the bucket is 5 cm

  • After 2 hours the water level is at 10 cm

  • After 3 hours the water level reaches 15 cm

a

If the tap continues to leak at the same rate and stops after a hours, write an algebraic expression for the water level in the bucket at this time.

b

If the tap stopped leaking after b minutes, write an algebraic expression for the water level in the bucket at this time.

c

If the tap stopped leaking after 3.5 hours, calculate the water level in the bucket at this time.

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Outcomes

ACMEM035

substitute numerical values into algebraic expressions; for example, substitute different values of x to evaluate the expressions 3x/5, 5(2x-4)

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