 Middle Years

Worksheet
Addition and subtraction of algebraic terms
1

Identify the following parts of the algebraic term:

a

The number 3 in the term 3 x.

b

The letter x in the term 6 x.

c

The number 7 in the expression 5 x + 7.

d

The number 5 in the term 4- 5 x.

e

The letter u in the term -12 u.

f

The number 8 in the expression 8 +6z.

2

State whether the following pairs are like terms or unlike terms:

a

10 p and 5 p

b

3 and y

c

5 n^{2} and 8 n

d

5 p and 5

e

10 a and - 9 a

f

2 a b and 6 b a

g

15 p and 15 q

h

8 and 8z

i

7 m^{2} and 7 m

j

8z and -8z

k

12 b and - 21 b

l

13 xy and 14 yx

3

Simplify:

a
2 a + 5 a
b
10 x + 6 x
c
4 b + 3 b
d
12 y - 3 y
e
3 c + 4 c + 7 c
f
15 x - 6 x - 2 x
g
19 b - 12 b - 6 b
h
-3 n + 6 n + 3 n
i
8x - 3x + 7x
j
4xy+10xy-9xy
k
10ab+3ab-8ba
l
x + 9 + 7
m
9 x + 4 x
n
12 p - 9 p
o
2 u^{2} + 9 u^{2}
p
4 m - 4 m
q
8 p - 7 p
r
12 n - 9 m - 7 n
s
6 x - 9 x
t
- 5 m - 10 m
u
- 5 x^{2} - 2 x^{2}
v
- 5 p q + \left( - 4 p q \right)
w
7 x - \left( - 10 x \right) - 8 x
x
- 6 x - 5 x - 3 + 8
4

Simplify:

a
8 x + 6 y - 2 y - 4 x
b
10 m + 9 n + 5 m + 10 n
c
10 x - 9 y - 7 x + 11 y
d
11 m + 8 n + 14 m
e
9 x y + 12 y x
f
6 p + 8 q - 6 p
g
9 p^{2} - 11 p + 11 p^{2}
h
7n^2 + n^2 - 4m + 2m^2 - 5n^2
i
8x+9y-5x+10y
j
7a+11a-9b+b
k
12x^2+10x-9x-5x^2
l
8x-7y-6z+10z
m
15y-8y^2+10y-y^2
n
19a-8b+4c-8a+b
o
2ab-7c+ab+9c
p
12j+9k-7k+11j
q
18x-9y+7x+11y
r
11y-6z+y+6z
s
13m+2n-8m+10n
t
-3s+4t-6t+9s
5

Simplify:

a
5x+2y-8x+6z-3y+4z
b
2xy+5yz+4xz-8xy+2xz-3yz
c
8x^2+10x-6+4x^2-x+11
d
20-9x+4y+6y-7x+21
e
9mn+8m-7n+7n-10m+2mn
f
-6+8x^2-9+5x+16x^2
g
11s+6t+3st-2ts+t-4s
h
13ab-8bc+6ba-9b+11cb
i
10 x + 9 y - 3 y - 2 x
j
10 p - 7 q + 10 - 3 p + 7 q - 3
k
10 p q + 4 p^{2} q - 8 q p + 7 p^{2} q
l
20x^2 - 12 x^2 + 10x^2 - x^2
m
6 z x y + 4 x z y + 10 x y z + 12 x y + 11 y x
n
- 2 x + 2 y - 6 y - 10 x
o
- 4 r k + 3 r - 6 k - 2 r k
p
- 6 v w - 4 v^{2} w + 2 v^{2} w - 8 w v
q
- 5 m + n - \left( - 7 m \right) - 6 n - 2 m + 7
r
-2m+n-\left(-6m\right)-3n-4m+5
6

State whether the following expressions are equal to 11y:

a

9 + y + 10 y - 9

b

6 y - 5 y

c

5 y + 6 y

d

11 + y

e

9 y+3y-1

f

10 y + 1

7

State whether the following expressions is equal to 8 r + 9:

a

9 + 8 r

b

9 r + 8

c

17 r

d

72 r

e

9 r + 8 - r + 1

f

10 r + 2 - 2r + 7

8

State whether the following expressions is equal to 9 r t + 8:

a

5 r + 4 t + 8

b

8 + 4 r t + 5 r t

c

9 r + 8 t

d

17 r t

Applications
9

An isosceles triangle has 2 sides of length 5 \text{ cm}. If the third side has a length of a \text{ cm}, write an expression for the perimeter of the triangle.

10

Laura decides to put a bird feeder in her back garden. The first day she sees 6 birds use the feeder. The next day she sees 12 birds, and on the third day she sees 18 birds.

a

If the number of birds continues to follow the pattern, calculate how many birds will Laura see on the fourth day.

b

If the pattern continues, write an expression for the number of birds Laura will see after y days.

11

A tap has not been turned off properly, and water is dripping into the bucket underneath it. After 1 hour, the water level in the bucket is 3 \text{ cm}. After 2 hours the water level is at 6 \text{ cm}, and after 3 hours the water level is at 9 \text{ cm}.

a

If the tap is turned off after x hours, write an expression in terms of x for the water level in the bucket at this time.

b

Describe the expression as it relates to the water level.

12

Tracy saves all of her 5 cent coins and 10 cent coins. After some time, she loses track of how many coins she has.

If p represents the number of 5 cent coins and q represents the number of 10 cent coins, write an expression for the total value of the coins that Tracy has.

13

Uther likes to go kayaking, and on Saturday he takes his boat down to the lake which is 300 \text{ m} away from his house. After 1 minute of paddling he is 370 \text{ m} away from his house. After 2 minutes he is 440 \text{ m} away, and after 3 minutes he reaches 510 \text{ m} away.

a

Uther paddles for t minutes in total before he changes direction. Write an expression for how far he is from his house at this time.

b

Describe the expression as it relates to Uther's paddling pace.

14

To get to school in the morning, Sally walks for 7 minutes to the bus stop and then waits for 2 minutes for the bus to arrive. She then catches the bus the rest of the way to school.

a

If the bus trip takes y minutes, write an expression in terms of y for the total length of time it takes Sally to get to school.

b

Explain what the constant in your expression represents.