Year 8 Mathematics Algebra
Name
Date
Part A — Multiple Choice
4 questions
1
\(2ab + b \times 5a\) simplified is:
1 mark
Working
2
The simplified form of \(\dfrac{24x^2yz}{32xy}\) is:
1 mark
Working
3
Which of the following expressions is not equivalent to the others?
1 mark
Working
4
When fully simplified, \(\dfrac{4xy + 2xy}{2x}\) is equal to:
1 mark
Working
Part B — Short Answer
16 marks
1
If \(x = -4\) and \(y = 9\), use substitution to solve the following expressions.
a
\(3y - x\) 2 marks
Working
Answer
b
\(2x^2 - \sqrt{y}\) 2 marks
Working
Answer
c
\((xy) + \dfrac{y}{3}\) 2 marks
Working
Answer
d
\(50 - 10(y + x)\) 2 marks
Working
Answer
2
Simplify the following expressions.
a
\(3x \times 4xy\) 2 marks
Working
Answer
b
\(\dfrac{21ab}{14b}\) 2 marks
Working
Answer
c
\(\dfrac{21c^2d}{35c}\) 2 marks
Working
Answer
d
\(\dfrac{12x}{6x} \times 2x\) 2 marks
Working
Answer
3
Expand the following.
a
\(5(m - 3n)\) 1 mark
Working
Answer
b
\(2w(w + 4x)\) 1 mark
Working
Answer
4
Determine the ? in each of the following.
a
\(4a \times \mathbf{?} = 32abc\) 1 mark
Working
? =
b
\(\dfrac{8ab}{\mathbf{?}} = 4\) 1 mark
Working
? =
Part C — Extended Response
6 marks
1
Consider the rectangle shown below.
6 marks
4
b
a
a
i
Write a simplified expression for the perimeter of the rectangle.
Remember: perimeter is the sum of all the sides.
Working
Perimeter =
ii
Find the perimeter of the rectangle if \(a = 6\) and \(b = 10\).
Working
Perimeter =
b
Write two equivalent expressions for the area of the rectangle — one with brackets and one without brackets.
With brackets
Without brackets
c
The length and width of the rectangle are now doubled.
i
Draw the new rectangle below, labelling its dimensions using the pronumerals \(a\) and \(b\).
ii
Write a simplified expression for the area of the new rectangle.
Working
Area =
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