Download Year 7 Diagnostic

Name: ___________________________________________
Mathletics Diagnostic Test
Year 7 - National Curriculum
813
Number and Algebra
Suggested Time: 90 minutes
83 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 7 | March 2011
© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 1 - Number and Place Value
ACMNA149
a Which of the following numbers is prime?
A
28
B
58
18
D
13
C
157
D
13
C
3, 3, 11
D
2, 3, 3, 13
15
D
30
D
15
D
5
C
b Which of the following numbers is composite?
A
109
B
145
c What are the prime factors of 78?
A
3, 9, 9
B
2, 3, 13
d What is the lowest common multiple of 3 and 5?
A
12
B
20
C
e What is the lowest common multiple of 3, 4 and 6?
A
60
B
12
C
30
f What is the highest common factor of 136 and 30?
A
4
B
2
C
9
ACMNA149
/6
© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 2 - Number and Place Value
ACMNA150
a What is the square of 2?
Answer:
b What is the square root of 121?
Answer:
c What is 3 2 ?
Answer:
d What is √ 144
?
Answer:
e If 13 2 = 169 and 15 2 = 225, then the square root of 196 is most likely:
Answer:
f If 160
2
= 25600 and 162
2
= 26244, then the square root of 25921 is most likely:
Answer:
ACMNA150
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© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 3 - Number and Place Value
ACMNA151
a Which of the following demonstrates Distributive Law?
A
(a + b) + c = a + (b + c)
B
a x (b + c) = a x b + a x c
C
a+b=b+a
b Which law best describes: a - c = c - a ?
A
Commutative Law
C
Distributive Law
B
Associative Law
D
These laws don't apply
to subtraction
c When can you not use associative law?
A
subtraction
B
addition
d Which equation is correct?
A
(a + b) - c = a - (b + c)
B
(a - b) - c = a - (b - c)
C
(a + b) + c = a + (b + c)
e Calculate 2 x (5 + 8) =
Answer:
f Calculate (2 x 5) x 8 =
Answer:
ACMNA151
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© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 4 - Number and Place Value
ACMNA280
a Which number has the highest value?
A
99,241
B
84,067
C
82,976
D
84,067
C
96,649
D
101,951
b Which number has the lowest value?
A
103,072
B
98,145
c Calculate 7324 + 932.
Answer:
d Calculate 3388 + 932.
Answer:
e Calculate 4845 - 960.
Answer:
f Calculate 5515 - 932.
Answer:
ACMNA280
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© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 5 - Real Numbers
ACMNA152
Use the fraction wall below to answer the following questions.
a Which fraction is equivalent to 2/4?
A
1
2
B
2
8
C
4
9
D
1
3
b Write at least two equivalent fractions for 2/4.
Answer:
c Find 1/5 + 2/5.
Answer:
d Find 3/6 + 5/10.
Answer:
ACMNA152
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© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 6 - Real Numbers
ACMNA153
1
3
a
9
24
A
b
3
7
1
3
3
6
3
6
-
2 1/2
B
38
7
C
43
7
B
11
7
C
3
14
B
1 2/3
C
5/6
B
3
6
B
1/2
D
10
24
D
36
7
D
4
14
=
1
6
1
8
D
5/12
C
6
6
D
7
6
C
1 1/2
D
=
2
6
5
8
A
+
C
8
24
=
2 1/2
A
f
1
7
4
7
A
e
+
B
11
24
=
40
7
A
d
1
7
5
A
c
=
=
5
ACMNA153
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© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 7 - Real Numbers
ACMNA154/155
a
A
b
2
4
A
d
A
e
3
4
=
2+3
4+4
2
4
÷
3
4
2
4
x
3
5
÷
2-3
4-5
3
5
B
2÷4
4÷3
B
2÷5
4÷3
B
2x5
4x3
C
2x3
4x4
C
2÷3
4÷4
C
2x3
4x5
C
2÷3
4÷5
D
4x3
2x4
D
4x3
2x4
D
4x3
2x5
D
4x3
2x5
=
2+3
4+5
2
4
B
2÷4
4÷3
=
2x4
4x3
A
c
x
=
Express 25 millilitres as a fraction of 1 litre.
Answer:
f
Express 10 minutes as a fraction of 1 hour.
Answer:
ACMNA154/155
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© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 8 - Real Numbers
ACMNA156/157
a
Round 61.5311 to 2 decimal places.
Answer:
b
Round 14.7513 to 3 decimal places.
Answer:
c
Convert the fraction 16/100 to a decimal.
Answer:
d
What percentage of 0.15 is 1?
Answer:
e
Jackson is entitled to receive a 5% staff discount. If the original price was $100, how
much is the discounted price?
Answer:
f
Nicola wants to donate 15% of her savings to charity. If she has saved $90, how much
is she wanting to donate?
Answer:
ACMNA156/157
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© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 9 - Real Numbers
ACMNA173
a
If Sarah eats 3/10 of a cake and Matthew eats twice as much as Sarah, how much
cake did Matthew eat?
Answer:
b
Cindi needs to make lemonade for a school fundraiser. The ratio of lemons to
water to sugar is 1:1:3 . If she has 35 lemons, how much water and sugar will
she need?
Answer:
c
For every 35 lemons, Cindi can sell 105 cups of lemonade for $1.50 per cup.
How much money will she raise if she sells all of the lemonade?
Answer:
d
It takes one person one day to dig a 5m x 5m x 5m hole. How long will it take 6
people, working at the same rate, to dig a 20m x 20m x 20m hole?
Answer:
‽ answer might not be a whole number
ACMNA173
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© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 10 - Money and Financial Mathematics
ACMNA174
a
b
c
d
Which is the best buy? Choose the item(s) with the best value for money.
There may be more than one answer.
A
440 grams of tinned
tomatoes for $2.
C
110 grams of tinned
tomatoes for $4.
B
300 grams of tinned
tomatoes for $3.
D
200 grams of tinned
tomatoes for $1.
Which is the best buy? Choose the item(s) with the best value for money.
There may be more than one answer.
A
2 kilograms of flour
for $3.
C
2.5 kilograms of flour
for $5.
B
4 kilograms of flour
for $2.
D
1.5 kilograms of flour
for $4.
Which is the best buy? Choose the item(s) with the best value for money.
There may be more than one answer.
A
250 litres of petrol for
$300.
C
400 litres of petrol for
$400.
B
800 litres of petrol for
$100.
D
600 litres of petrol for
$200.
Which is the best buy? Choose the item(s) with the best value for money.
There may be more than one answer.
A
170 bricks for $30.
C
180 bricks for $20.
B
150 bricks for $20.
D
160 bricks for $30.
ACMNA174
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© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 11 - Patterns and Algebra
ACMNA175
a
A
b
A
c
d
A
e
The 2 in 2a is referred to as a __________
variable
formula
C
constant
D
pronumeral
B
5a
C
4+a
D
a
a+a+a+a =
4a
4
(a + 5) + (7a + 8) =
A
(a + 8a) + (5 + 7)
C
20a
B
21a
D
(a + 7a) + (5 + 8)
If a = 8, then 2a =
10
B
16
C
28
D
280
Which of the following equations does not describe a number pattern increasing
by 5?
A b = 5a + 2
f
B
B b = 19 + 5a
C b=a+5
D b = 5a - 5
If the rule describing a number pattern is d = 4c - 5, what will the value of d be
when c = 60?
A
95
B
233
C
240
D
235
ACMNA175
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© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 12 - Patterns and Algebra
ACMNA176/177
a
If speed = distance / time, calculate the speed when d = 144 and t = 4.
speed (km/h) = s
A
b
0.03 km/h
distance (km) = d
B
c
A
d
A
e
A
D
140 km/h
36 km/h
If force = mass x acceleration, calculate the acceleration when F = 92 and m = 2.
force (N) = F
A
C
576 km/h
time (h) = t
B
46
acceleration (m/s 2 ) = a
mass (kg) = m
C
0.02
D
184
17.83
D
19
g = 18
D
g = 19
90
If y = mx + c, calculate 'y' when m = 2 and x = 6 and c = 7.
4.333
B
Solve for g:
g = 20.5
C
15
17g - 16 = 15g + 20
B
C
g = 21
Make B the subject of the formula
B=
A
P+R
B
B=
A
P-R
C
P=
A
R
-
B=
A
R
-P
B
D
B=
A
R
+P
Which value for m makes 16m - 14 < 16 true?
f
A
m = 5.5
B
m=4
C
m=0
D
m=3
ACMNA176/177
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© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 13 - Linear and non-linear relationships
ACMNA178
a
6
5
Which are the correct co-ordinates of
the point?
4
3
2
1
A
(-5, 2)
B
(2, -5)
C
(2, 5)
D
(5, -2)
0
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
b
6
5
Which are the correct co-ordinates of
the point?
4
3
2
A
(-4, -4)
B
(-4, 5)
C
(-5, 4)
D
(5, -4)
1
0
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 13 - continued
c
Plot the point (-6,6) on the graph.
6
5
4
3
2
1
0
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
-1
-2
-3
-4
-5
-6
d
Plot the following points on the graph.
x
-4
-2
0
2
4
y
-7
-5
-3
-1
1
20
15
10
5
0
-20
-10
0
10
-5
-10
-15
-20
© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
20
6
Name: ___________________________________________
e
Plot the following points on the graph.
x
-6
-4
-2
0
2
y
0
-2
-4
-6
-8
20
15
10
5
0
-20
-10
0
10
20
-5
-10
-15
-20
ACMNA178
/5
© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 14 - Linear and non-linear relationships
ACMNA179
Represent the following equation on the balance beam below, using boxes to
represent 'x' and '2'. For example to represent x + 2 you would need to draw one
x box and two one's boxes.
eg: x + 2 =
x
1
1
a
Represent 4x + 3 = 7 on the balance below using boxes to show x and units of 1.
b
Draw what the other side of the balance would look like if you were to find x.
x
c
Explain what you did to both sides of the balance to find x.
Answer:
© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
?
Name: ___________________________________________
Section 14 - continued
ACMNA179
d
Describe a strategy you could use to solve the following:
"I'm thinking of a number. When I subtract 3 from my number, multiply the result
by 8, then divide this result by 3, I get 16. What is my number?"
Answer:
e
Using the following - substitute the values to choose the correct equation.
c=9
a=3
b=3
f
A
28 = c x b + a
C
32 = (c x a) + b
B
30 = (c x b) + a
D
27= (c x b) + a
Using the following - substitute the values to choose the correct equation.
y=4
x=2
z = 12
A
5 = (z/y) + x
C
7 = (z/y) + x
B
3 = (z/y) + x
D
2= (z/y) + x
ACMNA179
/6
© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
Name: ___________________________________________
Section 15 - Linear and non-linear relationships
ACMNA180
The following questions refer to the graph below:
Distance From Home (km)
Travel Graph
a
b
c
d
20
15
10
5
0
1
2
3
4
5
6
Time (mins)
At 3 minutes, how far is Sam from home?
A
can't tell
C
5 km
B
10 km
D
15 km
During which time frame was Sam not moving at all?
A
between 1 and 4 minutes
C
between 4 and 5 minutes
B
between 5 and 6 minutes
D
can't tell
During which time frame was Sam travelling the fastest?
A
between 6 and 7 minutes
C
between 1 and 4 minutes
B
between 4 and 5 minutes
D
can't tell
At how many minutes did Sam begin to travel back home?
A
at 4 minutes
C
at 5 minutes
B
at 6 minutes
D
can't tell
© 3P Learning - Mathletics National Curriculum Assessment Series - 2011
7
Name: ___________________________________________
Section 15 - continued
ACMNA180
The following questions refer to the graph below:
Monthly evaporation compared with rainfall (mm)
for open pan water storage
2000
1800
1600
1400
1200
1000
800
Evaporation
600
Rainfall
400
200
0
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
e
In which year was there the most water retained in the water storage area?
Explain your answer.
Answer:
f
In which year was evaporation the greatest? Explain why you chose that year.
Answer:
ACMNA180
/6
© 3P Learning - Mathletics National Curriculum Assessment Series - 2011