Download MAT07NATT10025

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Topic test
Algebra and equations
•
Time allowed: 45 minutes
•
Calculators are not allowed.
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Part A: 20 multiple-choice questions (40 marks)
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Part B: 10 free-response questions (60 marks)
Name: _________________________________________
7 Which expression is equal to 6p – p?
A 6p2
B –5p
C 5p
D 6
8 Which expression is equal to 10ab2?
Part A
20 multiple-choice questions
2 marks each: 40 marks
Circle the correct answer.
A 100ab2
B 10 × a × b × b
C 10 × a × a × b × b
D 10ab × 10ab
1 Which expression is equal to w × w × w?
9 Solve 2y + 1 = 8.
A 3+w
B 3w
D w3
C w+3
A y = 3.5
B y=3
C y=4
D y = 4.5
2 Which expression is equal to 3 × u × u × 10?
10 If a = 4, what is the value of 3a + 4?
A 30u2
B 60u2
C 13u2
D 60u
A 11
B 38
C 16
D 18
3 Which expression is equal to 17 × 12?
11 Which expression represents the quotient of x and 5?
A 17 + 10 × 17 + 2
B 17 × 10 + 17 × 2
C 17 × 10 + 2
D 17 × 10 × 2
4 Which equation is false?
B a × a = a2
C a×b=b×a
D a+b=b+a
5 If x represents any number, which expression represents
C 5x
D
x
5
B –1
A 0
C 1
D 1k
13 Callum solved the equation 2a – 5 = 19 incorrectly,
like this:
3 less than that number?
B 3x – 3
B x 5
12 Which of the following is equal to k – k?
A a÷b=b÷a
x
A 3
A x5
2a – 5  19
C 3–x
D x–3
2a  19 – 5
Line 1
2a  14
Line 2
14
2
a 7
a
6 Solve x  19  28 .
Line 3
Line 4
In which line did Callum first make a mistake?
A x=8
B x = 47
C x=9
D x = 48
A Line 1
B Line 2
C Line 3
© Cengage Learning Australia Pty Ltd 2011
MAT07NATT10005
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Number and Algebra: Patterns and algebra, Linear and non-linear relationships
D Line 4
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14 If c = –6, find the value of 4c – 10.
B –34
A 12
C –12
b 30 × 70
D –20
c 25 × 9
15 Which is the correct formula for the perimeter (P) of a
rectangle with length l and width w?
A P=l+w
B P = lw
C P = 2l + 2w
D P = 4lw
22 (2 marks) Examine this number pattern, then write a
general rule for it using a variable.
9 ÷ (–9) = –1
4 ÷ (–4) = –1
16 Which one expression is not equal to the other three?
A 0÷a
17 Solve
B 0+a
C a–a
D 0×a
x
 8  20 .
3
A x = –4
7 ÷ (–7) = –1
1 ÷ (–1) = –1
23 (6 marks) If p represents any whole number, write an
algebraic expression for:
B x = 12
C x=4
D x = 36
18 If C = 3m – 4, what is the value of C when m = 7?
A C=9
10 ÷ (–10) = –1
B C=6
C C = 17
a the number multiplied by itself
b the difference between the number and 4
D C = 33
c the next consecutive whole number
19 Which one of the following expressions is not equal to
2p?
A p2
B p×2
C p+p
D 4p – 2p
24 (10 marks) Simplify each expression.
a 3×b÷4
20 If f = 3 and g = –1, which of the following is equal to
f 2 + g2?
A 5
B 8
C 10
D 7
Part B
10 free-response questions
60 marks
Show working where appropriate.
b h×h–2×d
c r×9+r×r
d 4m + 4m + 4m
21 (6 marks) Evaluate each expression.
a 2 × 18 × 5
e 18 × p ÷ (z + 1)
© Cengage Learning Australia Pty Ltd 2011
MAT07NATT10005
www.nelsonnet.com.au
Number and Algebra: Patterns and algebra, Linear and non-linear relationships
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25 (12 marks) If a = 6, b = 12 and c = –3, evaluate:
b how many times 5 divides into q
a a+c
c 10 more than triple b
b 10 – b
d 5 less than half of g
c
12
c
28 (8 marks) Solve each equation.
d 2c + 9
e 2bc
a
k
 21
3
b
d
–6=2
4
f 5a – b
c 4m + 8 = 36
26 (2 marks) Use the guess-and-check method to find the
solution to the equation 8p – 5 = 19. Show all working.
d
2n
 2
3
27 (8 marks) Write an algebraic expression for:
a n decreased by 2
© Cengage Learning Australia Pty Ltd 2011
MAT07NATT10005
www.nelsonnet.com.au
Number and Algebra: Patterns and algebra, Linear and non-linear relationships
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29 (2 marks) The number of hours of sleep recommended
A
for children has the formula H = 14 – , where H is
2
the number of hours and A is the age of the child in
years. Use the formula to find the number of hours of
sleep recommended for a 6-year-old child.
30 (4 marks) If you divide Alex’s age by 3 and subtract 2,
you get his daughter Ellen’s age, 9.
a Write an equation to find a, Alex’s age.
b Solve the equation from part a to find Alex’s age.
This is the end of the test.
Use the back for extra working space.
© Cengage Learning Australia Pty Ltd 2011
MAT07NATT10005
www.nelsonnet.com.au
Number and Algebra: Patterns and algebra, Linear and non-linear relationships
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Answers
Part A
1 D
9 A
17 D
2 A
10 C
18 C
3 B
11 D
19 A
4 A
12 A
20 C
5 D
13 A
6 C
14 B
7 C
15 C
8 B
16 B
Part B
21 a 180 b 2100
c 225
22 n   n   1 (other variables possible)
23 a p2
b p–4
c p+1
3b
24 a
4
b h  2d
c 9r  r 2
d 12m
e
25 a 3
26 p = 3
b –2
c –4
d 3
e –72
27 a n  2
b
c 3b  10
d
2
q
5
18 p
z 1
f 18
g
5
2
28 a k = 63 b d = 32
c m=7
d n = –3
29 H = 11, the number of hours required is 11 hours.
30 a
a
2 9
3
b Alex is 33
© Cengage Learning Australia Pty Ltd 2011
MAT07NATT10005
www.nelsonnet.com.au
Number and Algebra: Patterns and algebra, Linear and non-linear relationships