Download Year 6 Diagnostic

Name: _________________________________
Mathletics Diagnostic Test
Year 6 - National Curriculum
4367
ANSWER KEY
Number and Algebra
Suggested Time: 50 minutes
40 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 6 | March 2011
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 1 - Number and Place Value
ACMNA122
a A prime number is divisible by:
an even
A number
B a factor of 2
a composite
C number
0 1 and itself
b A composite number is a:
product of its
0 prime factors
only a perfect
B square
only a triangle
C number
only divisible by 1
D and itself
c Which number below is both a triangle number and a perfect square?
0
36
B
25
C
45
D
3
d What are the prime factors of 100?
A 5
B
4 and 6
0 2 and 5
D odd numbers
e Which of the following are all square numbers?
A 12, 14, 16
B
4, 6, 8
C
20, 30, 40
0
9, 49, 121
Space for working
ACMNA122
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 2 - Number and Place Value
ACMNA123/124
a On the numberline below, show 1 less than 6.
Students should indicate 5 on the number line.
0
Teacher Discretion
b What is 1100 divided by 20?
A 1080
B
50
C
60
0
55
c What strategy could you use to answer (b) if you didn't have a calculator, or you
wanted to check your answer?
Teacher discretion
Answer:
d In the Snowy Mountains, the temperature during the day can often drop 6 degrees. If
the temperature in the day is 1 degrees, what will the temperature overnight be?
Draw your answer on the number line below.
Students should indicate -5 degrees.
0o
e In the Australian outback in winter, the day time temperatures can rise 10 degrees. If
the night time temperature is -2 degrees, what would the day time temperature be?
Draw your answer on the number line below.
Students should indicate 8 degrees.
0o
ACMNA123/124
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 3 - Fractions and Decimals
ACMNA125/126/127
a Below is a number line showing halves. Write the equivalent fractions in quarters
above. The first one is done for you.
Write your answers in the boxes on the number line below.
1/4
0
2/4
3/4
1/2
1
2
b Which fraction is equivalent to 4/8?
A
3/5
0
1/2
B
3/4
D
1/4
c My friend has a watermelon which has been cut into 6 pieces. If I get half, and my
sister gets 1/3 how much is left?
1/3 or 2/6
Answer:
d What is 4/12 of 48?
A
18
0
16
B
32
D
15
A
11
0
9
B
8
D
18
e What is 3/9 of 27?
ACMNA125-127
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 4 - Fractions and Decimals
ACMNA128/129
a What is 2.4 + 0.3?
A
2.1
0
2.7
C
3.7
D
1.7
B
0.36
C
-1.82
D
1.18
b What is 0.96 - 0.78?
0
0.18
c A relay of 35 kms is being run by 4 athletes. How far does each athlete run?
A
7.75 km
B
17.5 km
C
9.75 km
0
8.75 km
d If 4 chocolates sell for $4.28, then how much would each chocolate sell for?
$1.07
Answer:
e Since the smallest Australian coin is the 5c piece, if you wanted to buy all 4
chocolates (from question d), how much would you actually have to pay the
shopkeeper?
$4.30
Answer:
ACMNA128/129
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 5 - Fractions and Decimals
ACMNA130/131
a
b
What is 36.15 ÷ 5 equivalent to?
A
3615 ÷ 50
C
361.5 ÷ 500
0
3615 ÷ 500
D
3615 ÷ 5000
What is 14.35 x 5 equivalent to?
A
(1435 x 5) ÷ 10
0
(1435 x 5) ÷ 100
B
(1435 x 5) x 100
D
(143.5 x 5) ÷ 100
c Write down a way you could multiply 2.3 x 0.6 without a calculator?
Teacher Discretion - eg: I could multiply 23 by 6, which would
give 138 and then divide by 100.
Answer:
d
e
Choose the answer below that is equivalent to 3/21.
A
14.29 or 14%
C
1.43 or 1.4%
0
0.14 or 14%
D
0.14 or 1.4%
Choose the answer below that is equivalent to 42.86%.
0
9/21 or 0.43
C
9/21 or 4.29
B
9/21 or 42.86
D
90/2100 or 0.43
`
ACMNA130/131
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 6 - Money and Financial Mathematics
ACMNA132
a
0
b
A
c
d
e
A bookshop is selling old stock at a discount of 50%. How much would a book
cost if it was originally $17?
$8.50
B
$7.50
C
$9.50
D
$9.00
A new mobile phone is coming out on the market and promises to be sold at a
10% discount for the first two weeks. If the cost price is $273, what will you pay if
you buy in the first two weeks?
$240.70
0
$245.70
C
$27.30
D
$250.70
A store is offering 25% off all clothing. If you have $51 worth of clothing that you
want to buy, how much will you actually pay?
A
$12.75
0
$38.25
B
$40.25
D
$36.25
One item with the price tag of $49 is marked at 10% off, the other with a price tag
of $24 is marked as 50% off. How much would you actually pay for both items?
A
$58.10
0
$56.10
B
$54.10
D
$16.90
Two items cost $72.49 and $ 36.24. How much would you pay if there is a
discount of 25% on both items?
A
$65.24
C
$27.18
B
$54.37
0
$81.55
ACMNA132
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 7 - Patterns and Algebra
ACMNA133
Questions a - c relate to the square sequence pictured below.
a
Draw what the next picture in the sequence would look like.
20 blocks
a
b
b
The table below relates to the sequence of images in question a.
Which numbers are going to be in sequence 4, 6 and 7?
A
c
d
20, 27, 32
B
20, 28, 33
C
20, 27, 33
0
20,28,32
For the above sequence, which is the best expression to represent the pattern?
A
?=n+4
C
? = 4n +3
0
? = 4n + 4
D
? = 4n + 1
A very famous sequence of numbers is called the 'Fibonacci Sequence'.
0, 1, 1 , 2, 3, 5, 8, 13, 21, 34, ….
What would be the next two numbers in the sequence?
e
A
43, 55
C
67, 89
0
55, 89
D
43, 66
Write a sentence to describe the maths that makes up the Fibonacci sequence.
Answer:
Teacher discretion: "Keep adding the previous two numbers
together"
ACMNA133
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011
Name: _________________________________
Section 8 - Patterns and Algebra
ACMNA134
a
Which equation is written correctly?
9=3x2+1
b
A
9 = (3 x 2) + 1
C
9 = (3 x 2 + 1)
B
9 = (3 x 2) - 1
0
9 = 3 x (2 + 1)
Which equation is written correctly?
8 x 8 + 3 - 1 = 87
c
0
8 x (8 + 3) - 1 = 87
C
8 x 8 + (3 - 1) = 87
B
8 x (8 + 3 - 1) = 87
D
(8 x 8 + 3) - 1 = 87
Which equation is written correctly?
32 = 64 x 8 + 8
d
A
32 = 64 x 8 + 8
C
32 = 64 x (8 ÷ 8 + 8)
B
32 = (64 x 8) + 8
0
32 = 64 x 8 ÷ (8 + 8)
Rewrite the equation below with the brackets in the right place to make the
equation correct.
8=2x3+1
8 = 2 x (3 + 1)
Answer:
e
Which equation is written correctly?
32 = 8 x 4
A 32 = 24 + 1
0 32 = 8 x (3 + 1)
C 32 = (8 x 3 + 1)
D 32 = 8 x (3 + 2)
ACMNA134
/5
© 3P Learning Pty Ltd - Mathletics National Curriculum Assessment Series - 2011