Chapter 5: Algebra
Test A (40 marks)
Name:
Part A - Multiple-choice questions (io marks)
1 In the expression 8^ + 5^ +7+ 6y2, the coefficient ofy is:
AO
D
6
B
E
1
C
5
8
2 Which of the following expressions does not contain a constant term?
A 4.V + 9 B 7-3y C 5(.v-l)
D 2x[y-7) E 3^ + 8 + 67
3 If x is a whole number between 1 and 10, which of these statements is false?
A x must be smaller than x + 2
B x must be smaller than x-2
C x must be smaller than 2x
D 2x must be an even number
E x+2 could be an odd number
4 A number is substituted for a in the expression 8 + 0 and the result is 13. What is
the value of a?
A
D
21
7
B
E
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C
9
5
1
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Which of these following expressions can be simplified further by adding like
terms?
B
4 + b-a
D
6.?? + ab + 6
1 ab + 2b-ba
9a - SZ? + 9 + 3ab
%b-ba + l
6 2xa + Z7^5 can be written as:
B
2a+
/ b^
D
2a-\-b
2[a + b}
2a .
—
+b
5
a+—
5
6 at .
The simplified form of —— is:
9yz
A
2xy
2yz
D ^
9z
B
6xy
2xy
9z
3z
2x_
3z
8 Which expression is not equivalent to the area of the rectangle shown?
A 5.V + 15
B 5(^ + 3)
D 3(A' + 5) + 2.V
E 8.v +3-3.V + 5
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C 8 + 5.V + 7
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Which expression does not expand to 12a + 24b?
A 2[6a + 12b) B 3(8/} +4a)
C 6(2fl+ 4b)
D S[3b + 2a) E 4(30 + 6b)
10 Which of these expressions represents the total cost in dollars of hiring a plumber
for five hours if the plumber charges a $20 call-out fee and then $x per hour?
Sx
B
20 + x
D 50 + 20)
E
20 + x + S
A
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Part B - Short-answer questions (12 marks]
1 Write an expression for each of the following without using multiplication or
division signs.
a a is doubled and then subtracted from 5
b 3 more than b is divided by c
(1 + 1 = 2 marks)
2 If,Y = 4 andy = 9, find the value of the following expressions.
16
— + y-S
x
b 2x2-3y
\[xy
(3x1 = 3 marks)
3 Simplify the following by collecting like terms,
a
Sp+7-Sp+6
b 9e -2f -4 + 7f-6e
c 2s + 7st + 3-4t -ts + Ss
(3x1 = 3 marks)
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FOR THE AUSTRALIAN
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Write the following expressions without multiplication or division signs. Simplify
your answer if possible.
Gay. be-x 2d
b 9^-^18^
(2x1 = 2 marks)
5 Use the distributive law to expand the following,
a 4(/77 + 6/;j
b 3p(7-2q)
(2x1 = 2 marks)
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Part C - Extended-response questions (18 marks]
1 Consider the rectangle shown:
3 b
a
a i Write a simplified expression for the perimeter of the rectangle.
ii Find the perimeter of the rectangle if a = 7 and /? = 9.
b i Write two equivalent expressions for the area of the rectangle, only one of
which includes brackets.
ii Find the area of the rectangle if a = 8 and b = 4.
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c The length and width of the rectangle are now doubled.
i Draw the new rectangle, showing its dimensions using the pronumerals
a and b.
ii Write a simplified expression for the area of the new rectangle.
((1 + 1) + (2 + 1) + (1 + 1) = 7 marks)
2 Sally is planning a party for her birthday, and needs to hire a venue and organise
catering. A company called Complete Celebrations combines the cost of venue hire
and catering for $10 per person.
Alternatively, Sally can hire out a hall with Perfect Parties for $70, and that
company will provide catering at a cost of $5 per person.
a i Write an expression for the total cost for /? people with Complete
Celebrations.
ii Complete the following table for the total cost with Complete
Celebrations.
Number of people
10
12
14
16
18
20
Total cost ($)
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b i Write an expression for the total cost for n people with Perfect Parties.
ii Complete the following table for the total cost with Perfect Parties.
Number of people
10
12
14
16
18
20
Total cost ($)
c i When do the two companies charge the same amount?
ii When is it cheaper for Sally to use Complete Celebrations?
iii When is it cheaper for Sally to use Perfect Parties?
((1 + (6 x Vz)) + (1 + (6 x Vz)) + (3 x 1) = 11 marks)
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