Name: _________________________________
Mathletics Diagnostic Test
Year 8 - National Curriculum
8803
Number and Algebra
Suggested Time: 60 minutes
50 marks
Name:
Teacher:
Date:
All questions are worth one mark.
Sub-strand and content elaborations are based on Version 1.2 ACARA Australian National Mathematics Curriculum Year 8 | March 2011
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 1 - Number and Place Value
ACMNA182
a What is the value of 6 0 ?
6
A
B
undefined
0
1
0
B
6
C
10
D
4
B
64
0
32
D
96
B
1
0
-1
D
5
0
5°
C
5÷2
D
5²
D
b 2² x 2³ = 2ª Find a.
0
5
c Calculate 2² x 2³ .
A
16
d 4² ÷ 4³ = 4ª Find a.
A
3
e 5² ÷ 5² is equivalent to:
A
5¹
Space for working
ACMNA182
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 2 - Number and Place Value
ACMNA183
a 1+5x9-4=
42
Answer:
b9+4÷ 1+8=
21
Answer:
c 1 + 5 (9 - 4) + 1 =
27
Answer:
d 1 + 5 (9 - 4 (1 + 8) + 1) =
-129
Answer:
e 1 + 5 (-9 + 4 (1 - 8 ( 1 + 5) + 5) - 3) =
-899
Answer:
ACMNA183
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 3 - Real Numbers
ACMNA184/186
a What is the difference between a 'terminating' and a 'recurring' decimal?
A terminating decimal is one that does not repeat, it ends eg: 0.5
A recurring decimal repeats infinitely eg: 2/3 = 0.66666666 (repeats)
Answer:
b Which fraction would result in a recurring decimal?
A
1/4
C
3/4
B
1/2
0
2/3
c Describe the difference between a 'rational' and an 'irrational' number.
A rational number can be written as a ratio and as a fraction.
Any number that is not rational is irrational.
Irrational numbers can not be written as fractions.
Answer:
d Which of the following is a rational number?
0
√9
C
√2
B
π
D
√3
e Can the square root of a perfect square ever be irrational?
No, all square roots of perfect squares are rational.
Answer:
ACMNA184/186
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 4 - Real Numbers
ACMNA187
a Calculate the discount if the original price was $50 and the discount is 6%.
A
$
0.60
0
$
3.00
C
$
6.00
D
$
8.33
b What is the percentage markup on an item that cost $98 and sells at $104?
0
6.12%
B
12.24%
C
8.12%
D
4.12%
c If GST in Australia is 10%, how much GST would be added to a product that cost the
retailer $46?
0
$
4.60
B
$ 36.00
C
$ 41.40
D
$
0.46
d A product costs $42 to manufacture and the wholesaler sells it for $53, what is the
profit made by the wholesaler?
$11.00
Answer:
e GST in Australia is 10%. An item costs $56 including GST, what is the value of the
GST?
$5.09
Answer:
ACMNA187
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 5 - Real Numbers
ACMNA188
Use the information below to answer questions a and b.
a Australia is in the Oceania region. Comparing Australia to Asia, why do you think the growth
rates are so different?
Asia is a developing region with high fertility rates and improving access
to medical facilities.
Answer:
b Again, comparing Australia to Asia, why do you think Asia's growth rate is declining and
Australia's is very slowly increasing?
Asia's growth rate may decline as it self-regulates to a more sustainable
level. Australia is fairly stable at low increase rates.
Answer:
c A grazier has 388 sheep and 2328 cattle. What is the ratio of sheep to cattle on the farm?
A
582:97
0
97:582
C
291:48.5
D
2328:388
d 0 On this same farm, the cattle drink 3 times more water than the sheep. If all the sheep drink
9312L of water per day, how many litres does each cow drink per day?
A
e
7L
0
72 L
C
8L
D
can't tell
When the cattle are lactating, their water consumption doubles. What is the new ratio of
water consumption for lactating cattle to sheep?
0
6:1
B
24:2
0
6:1
D
can't tell
ACMNA188
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 6 - Money and Financial Mathematics
ACMNA189
a
A
b
A
c
d
e
A book shop sells a textbook for $70 and makes a loss of 2.1%. Calculate the cost
price of the book.
$67.90
B
$74.20
C
$65.80
0
$71.50
A new mobile phone is coming out on the market and promises to be sold 'at cost'
for the first two weeks. If the price then increases to $288, and the company
needs to make a 20% profit, what was the cost price to the nearest $?
$238
B
$480
0
$240
D
$242
One method that retail stores use to offer discounted products is the 'buy one get
one free' model. This represents an effective discount of
A
100% off both items
0
50% off both products when
combined together
B
50% off the first item, the
second for free
D
75% off the combined price
Select the offer with the greatest discount on a $47 meal.
A
GST free
C
15% off
0
$10 cashback
D
$5 rebate
Which offer represents the greatest dollar value discount?
A
20% discount on $300
C
10% discount on $150
0
25% discount on $250
D
30% discount on $200
ACMNA189
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 7 - Patterns and Algebra
ACMNA190
a
Which expression best represents the area of the rectangle below?
a
c
b
b
A
c
A
axbxc
0
a(b+c)
B
a + b+ c
D
b + c(a)
For the rectangle above, calculate the area in cm² if a = 4, b = 5 and c = 6.
15
0
44
b=4
D
29
c = 20
A
118 = c x b + a
0
120 = (c + b)a
B
122 = (c x a) + b
D
117= (c x b) + a
Which of the equations below are correct when the values below are used?
x=5
e
120
Which of the equations below are correct when the values below are used?
a=5
d
C
y=3
z=6
0
45 = (z+y)x
C
42= (z/y) + x
B
21 = (z+y)x
D
47 = (z/y) + x
Expand the following equation:
5a(a + 20) =
5a² + 20a
Answer:
ACMNA190
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 8 - Patterns and Algebra
ACMNA191
a
b
Factorise 28a - 32
A
a(28 - 32)
C
7(4a - 8)
B
a=4
0
4(7a - 8)
Factorise 4x + 4.
4(x + 1)
Answer:
c
Factorise 15x +5
5(3x + 1)
Answer:
d
Factorise 20x -5
5(4x - 1)
Answer:
e
Factorise 6x² - 2x
2x(3x - 1)
Answer:
ACMNA191
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 9 - Patterns and Algebra
ACMNA192
a
b
c
Simplify
e
A
33hk - 7
C
22h + 11k+ 7
0
14h + 19k - 7
D
11h -15k + 8
Simplify 114wzy ÷ 6wz
A
20wzy
C
19wz
0
19y
D
20y
a
3
Simplify,
0
d
5h + 2k - 7 + 17k + 9h
+
8a
15
Simplify
a
5
B
2a
15
6a
15
C
D
2a
8
-5(2a - 8)
A
10a + 40
0
-10a + 40
B
10a - 40
D
-10a - 40
Factorise 18a - 45
A
9(5 - 2a)
C
-9(2a + 5)
B
-9(2a - 5)
0
9(2a - 5)
ACMNA192
/5
Section 10 - Linear and Non-Linear Relationships
ACMNA193/194
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Use the following information to answer the questions below.
In the linear equation y = mx + b
b is the y-intercept on the Cartesian plane
m is the gradient (slope) of the line plotted on the Cartesian plane
x and y are the co-ordinates of a point on the line
a
Label the x and y axes. (1 mark)
b
Plot the x and y co-ordinates shown in the table on the graph below.
Use this graph to answer question c.
10y-axis
x
-5
-4
-3
-2
-1
0
1
2
3
4
5
8
6
4
y
-1
0
1
2
3
4
5
6
7
8
9
x-axis
2
0
-6
-4
-2
0
2
4
6
-2
c
If b = 4, calculate the value of the gradient (m) of the line you have plotted.
0
1
C
4
B
5
D
-1
Section 10 Continued
Use the graph below to answer the following questions
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
25
20
15
10
5
0
-6
-4
-2
0
2
4
6
-5
-10
-15
-20
-25
d
The slope of this line is negative, which means that the value of 'm' will be negative
in the linear equation y = mx + b.
Which equation matches the line graphed above?
e
A
y = 4x + 1
C
m = -4
0
y = -4x + 1
D
y = -4x +21
Where does the line cut the y-axis on the graph above?
ie: what is the y-intercept?
A
-4
C
-3
B
-4
0
1
ACMNA193/194
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011