Chapter 3: Algebra Test A
Number and algebra: Patterns and algebra
Chapter 3:Algebra
Test AName:______
FLUENCYMark
1 / For the expression −5xy2 +2y + 8y2 + 6 the coefficient of the third term is:
A5
B2
C8
D6
E5
Answer:C / 1
2 / The coefficient of x2 in the expression + + is:
A5
B4
C
D3
E
Answer:C / 1
3 / What is simplified?
A
B
C
D
E
Answer:D / 1
4 / Mel had $60 in her purse. She spent $(x + 10). The amount left is:
A$(x− 50)
B$(60 −x)
C$(70 −x)
D$(x− 70)
E$(50 −x)
Answer:E / 1
5 / Which of the following is a like term with 3x2y?
A3
Bxy
C3xy
Dyx2
Ey2x
Answer:D / 1
6 / The volume V of a sphere is given by the formula , where is the radius of the cone. The volume if r = 2 is:
A8.38
B25.13
C33.51
D75.40
E100.53
Answer:C / 1
7 / What is −10xy2 + 7xy2 simplified?
A−3xy2
B3xy2
C3x2y
D3x2y4
E17xy2
Answer:A / 1
8 / What is 2ab 3ab simplified?
A5ab
B5ab2
C6ab2
D6a2b
E6a2b2
Answer:E / 1
9 / Which of the following expressions is equal to?
A
B
C
D
E
Answer: B / 1
10 / When factorised 6(a−b) + x(a−b) equals:
A6 −x(a + b)
B(6 −x)(a + b)
C6(a + b−x)
D(6 + x)(a−b)
E(6 + x)(a + b)
Answer:D / 1
UNDERSTANDING
11 / Answer the following for each expression.
(i)State the number of terms.
(ii)State the constant (if there is one).
(iii)State the term with the smallest coefficient.
(a)3x2 4x + 5
(b)y3 4 −y
(c)6ab2 + 7b2 + 2a2b
Answers:
(a)
(i)There are 3 terms.
[1 mark]
(ii)The constant term is 5.
[1 mark]
(iii)The term with the smallest coefficient is −4x.
[1 mark]
(b)
(i)There are 3 terms.
[1 mark]
(ii)The constant term is 4.
[1 mark]
(iii)The term with the smallest coefficient is −y.
[1 mark]
(c)
(i)There are 3 terms.
[1 mark]
(ii)There is no constant term.
[1 mark]
(iii)The term with the smallest coefficient is .
[1 mark] / 9
12 / A class of x students goes to the beach. One-third of the class swims in the ocean while one-fifth of the class plays beach volleyball.
(a)Write an expression to represent the number of students who swam.
(b)Write an expression to represent the number of students who played beach volleyball.
(c)Write an expression to represent the total number of students who either swam or played beach volleyball.
Answers:
(a)
[1 mark]
(b)
[1 mark]
(c)
[1 mark] / 3
13 / Alex buys pencils at cents and biros at cents.
(a)How much did he spend?
(b)Factorise the expression.
Answers:
(a)
[1 mark]
(b)
[1 mark] / 2
14 / Expand and simplify the following expressions.
(a)
(b)
(c)
Answers:
(a)
[1 mark]
[1 mark]
(b)
[1 mark]
[1 mark]
(c)
[1 mark]
[1 mark] / 6
15 / Identify from the following expressions, which of them can be factorised using the grouping in pairs method? Factorise where applicable.
A
B
C
D
E
Answer:
A and D are the only ones.
B is the difference of 2 squares.
[1 mark]
C cannot be factorised into pairs.
E is a perfect square.
[1 mark]
A:
[1 mark]
[1 mark]
D:
[1 mark]
[1 mark] / 6
REASONING
16 / Jackie is making her own cards. She is using a rectangular piece of paper with dimensions 12 cm high and 9 cm wide. She has put p cm margins on the top and bottom of the paper and margins of q cm on the left and right sides of the paper.
(a)Write an expression for the height of the paper on which he is able to write.
(b)Write an expression for the width of the paper on which he can write.
(c)Write an expression for the area of the paper inside the margins.
(d)If , what is the area allowed for writing?
Answers:
(a) cm
[1 mark]
(b)
[1 mark]
(c)
[1 mark]
(d)
[1 mark] / 4
17 / A rectangular food pallet is (2x + 3) metres long and (y− 4) metres wide.
© Kutlayev Dmitry/Shutterstock.com
(a)Write an expression for the perimeter.
(b)Write an expression for the area.
(c)If x = 3 m and y = 8 m, what is the area?
(d)Using the answer from (c), find how many boxes of oranges, 60 cm long and 50 cm wide, you can fit on the pallet so that the minimum space is left over (no overhanging).
Answers:
(a)
[1 mark]
(b)
[1 mark]
(c)
[1 mark]
(d)
[1 mark]
A total of 120 boxes of oranges can fit on a pallet. / 4
18 / A rectangular mattress top has a length of 5y cm and a width of 2y cm.
(a)Write an expression for its perimeter.
(b)Write an expression for its area.
(c)If all sides are increased by z cm, write an expression for the new perimeter and expand.
(d)Find the perimeter when y = 5 cm, z = 3 cm.
(e)Write an expression for the new area and expand.
(f)Find the area when
Answers:
(a)
[1 mark]
(b)
[1 mark]
(c)
[1 mark]
(d)
[1 mark]
(e)
[1 mark]
(f)
[1 mark] / 6
PROBLEM SOLVING
19 / A rectangular swimming pool is (2y + 3) m long and 5y m wide. It is surrounded by a steel fence that is q m from the edge of the pool.
(a)Write an expression for the perimeter of the pool.
(b)Write an expression for the area of the pool.
(c)Write an expression for the length of the fence along the length of the pool.
(d)Write an expression for the width of the fence.
(e)Write an expression for the perimeter of the fence around the pool.
(f)Write an expression for —the area enclosed by the fence.
(Do not expand.)
(g)Find the area between the pool and the fence. (Do not expand.)
(h)Find the area between the pool and the fence when and.
Answers:
(a)
[1 mark]
(b)
[1 mark]
(c)
[1 mark]
(d)
[1 mark]
(e)
[1 mark]
(f)
[1 mark]
(g)
[1 mark]
(h)
[1 mark] / 8
20 / Pavika found a small photo frame and decided to put one of her favourite photos in it. The width of the metal surround is cm. Unfortunately, the glass of the photo frame is damaged and will need to be replaced.
(a)Write expressions for the height and width of the glass.
(b)Write an expression for the perimeter of the glass.
(c)If the perimeter of the glass is 22 cm, what is the height and width of the glass?
(d)Show that an expression for the area of the glass is .
(e)Calculate the area when the width of the metal is 1.2cm.
Answers:
(a)
[1 mark]
(b)
[1 mark]
(c)
[1 mark]
[1 mark]
(d)
[1 mark]
(e)
[1 mark] / 6
Total marks: 64
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