Download practice exams for T4 year 9

NAME:
TEACHER:
WESTERN SPRINGS
COLLEGE
Year 9 Mathematics
2010 Examination
Time: 1 1/2 hours
Sections
Topic
Result
Algebra
Patterns and Graphs
Number
Angles
Answer ALL questions in the spaces provided in this booklet.
SINCOS Publications
Page 1
Show ALL working.
Year 9 Mathematics 2010
NAME:
TEACHER:
YEAR 9 MATHEMATICS, 2010
Algebra
QUESTION AND ANSWER BOOKLET
Answer ALL questions in the spaces provided in this booklet.
Achievement Criteria
For Assessor’s use only
Achievement
with Merit
Achievement
Carry out simple algebraic
manipulations and solve
simple equations.
Show ALL working.
Carry out more complex
algebra manipulations and
solve linear equations.
Overall Level of Performance
Achievement
with Excellence
Solve algebra problems
involving manipulation.
Total:
/ 50
=========================================================================
QUESTION TWO
QUESTION ONE
Simplify these expressions.
Using a variable (e.g. x or n) for unknown
numbers, write expressions for these
(a) 2k + 5m - k
descriptions.
___________________________
(a) A number is reduced by six.
___________________________
[1]
(b) d x d x d x d
___________________________
(b) A number that has been doubled, and then
had four added to it.
___________________________
[1]
[1]
(c) 5 x p
[1]
___________________________
[1]
(d) 2n x 7
(c) A number that has had three subtracted from
it, and the result multiplied by four.
___________________________
SINCOS Publications
[1]
Page 2
___________________________
(e) 15e x e
Year 9 Mathematics 2010
[1]
(e) 3n + 4 = 19
QUESTION THREE
(a) Factorise these expressions
________________________
(i) 5x + 5y
___________________________
n = ________________________
[1]
(ii) 6x + 12
___________________________
[2]
QUESTION FIVE
If x = 5, y = 2 and z = -1, evaluate (work out the
value of) these expressions.
[1]
(a) xy + 2
(iii) 8x - 20
___________________________
___________________________
[1]
[1]
(b) x – z
(b) Expand these expressions
___________________________
[1]
(i) 4(p + 2)
(c) 2y – x
___________________________
[1]
___________________________
(ii) 6(t – 1)
[1]
(d) x2 + z2
___________________________
[1]
___________________________
(iii) 10(4r – 6)
___________________________
[1]
[1]
QUESTION SIX
Expand and simplify
QUESTION FOUR
Solve these equations (work out what number n
stands for).
(a) 6 – n = 2
n = ________________________
[1]
[1]
[1]
[1]
___________________________
[3]
(d) 3(x + 2) – 2(x + 1)
___________________________
________________________
SINCOS Publications
___________________________
___________________________
(d) 2n – 1 = 9
n = ________________________
[1]
(c) 4(x + 1) + 2(x + 3)
(c) 3 + n = 11
n = ________________________
___________________________
(b) 7n(2n + 4)
(b) 4n = 20
n = ________________________
(a) 5p(3 + y)
___________________________
[2]
Page 3
Year 9 Mathematics 2010
[3]
QUESTION SEVEN
QUESTION TEN
Factorise these expressions:
(a) Amy wants to build a run for her chickens.
She has 40m of chicken-wire fencing. She
decides that she wants to build a rectangular
chicken run, where the longer sides are 2m more
than double the shorter sides.
(a) 12x – 18xy
___________________________
[1]
(b) x2 – 5x
___________________________
x
[1]
2x + 2
(c) ab + ad - ac
___________________________
[1]
Write and solve an equation to work out x. Use
it to state the length and width of the run.
QUESTION EIGHT
Equation: ______________________
Write an equation that fits each description.
Solve the equation.
Solve:
(a) An unknown number will equal 15 if you
double it and then subtract three.
_______________________
_______________________
x = ___________
Equation: ______________________
[1]
[2]
[1]
Length and width of chicken run:
Solve:
_______________________
_______________________________
_______________________
[1]
(b) A number that is increased by four, and then
the result tripled, gives an outcome of 48.
Equation: ______________________
Solve:
(b) Paul had doubled his money in a game, but
then lost $1. Eileen started by losing $4, but
then tripled all that she had.
[1]
Paul and Eileen both started with the same
amount of money. They also finished with
identical amounts.
_______________________
_______________________
[1]
[1]
Write an equation that will allow you to work
out what they started with.
QUESTION NINE
Equation: ______________________
[1]
Solve the following equations.
Solve your equation
4x + 8 = 2x + 12
_______________________
x+2=5
4
_______________________
3(2x-5) = 5(x+2)
_______________________
_______________________
They started with $ __________
SINCOS Publications
Page 4
Year 9 Mathematics 2010
[2]
NAME:
TEACHER:
YEAR 9 MATHEMATICS, 2010
Patterns and Graphs
QUESTION AND ANSWER BOOKLET
Answer ALL questions in the spaces provided in this booklet.
Achievement Criteria
For Assessor’s use only
Achievement
with Merit
Achievement
Describe simple arithmetic or
geometric patterns and plot and
interpret simple graphs.
Show ALL working.
Find terms and rules for
patterns and interpret linear
graphs.
Overall Level of Performance
Achievement
with Excellence
Solve algebra problems using
graphs and manipulation.
Total:
/40
=========================================================================
(c) Complete the rule that links the number of
QUESTION ONE
matchsticks (M) with the number of houses (H):
M = ______ H + _______
(d) How many straight lines would be required
to draw the design with 12 houses in a row?
Here is a design representing rows of houses
made from matchsticks.
(a) You can see the design for 1, 2 and 3
houses in a row. Draw the design for 4
houses in a row.
[1]
(b) Complete the table
Number of
houses (H)
1
2
3
4
SINCOS Publications
[2]
[2]
Number of
matchsticks (M)
6
11
Page 5
________________________
[1]
QUESTION TWO
Use the rule y = 2x + 1 to fill in the y values for
this table.
[4]
x
1
2
5
20
y
Year 9 Mathematics 2010
(b) Complete this table for the pattern
QUESTION THREE
Give the next two numbers in the following
sequences:
Pattern number
(a) 2, 5, 8, 11, _____ , ______
[1]
(b) 10, 8, 6, 4, _____ , ______
[1]
(c) 11, 14, 17, 20, _____ , ______
[1]
1
2
3
4
n
[2]
Total number of
diamonds
1
5
(c) Graph the first four ordered pairs from the
table as points.
[2]
QUESTION FOUR
C
B
A
D
E
(d) If you continued the pattern and made the
graph bigger, would the point (10, 42) be on
it? Explain.
Give the coordinates of the points closest to
these letters:
_______________________________________
A ( ____ , _____ )
B ( ____ , _____ )
_______________________________________
C ( ____ , _____ )
D ( ____ , _____ )
_______________________________________
E ( ____ , _____ )
[5]
___________________________________
[2]
QUESTION FIVE
Here is a pattern involving diamonds.
Pattern 1
2
3
(a) Describe in words how the pattern is made.
[1]
SINCOS Publications
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Year 9 Mathematics 2010
QUESTION SIX
QUESTION SEVEN
Cheyenne’s trip home can be modelled by the
equation:
y = -2x + 12
(a) Graph her trip on the grid below
[4]
y = distance from home (km)
This graph shows Jeannie’s distance from home
over time. X = how long she has been walking
for (in hours). Y = How far she is from home (in
kilometres).
(a) How far away from home was she when
she started walking?
____________________________
[1]
x = number of hours passed.
(b) What was her walking speed (rate in
km/h)?
Using the graph and the features of the graph:
____________________________
[1]
(c) If she had been running at 6km/h instead
of walking, describe how the graph
would have looked.
___________________________________
(b)How can you tell how far away from home
was she when she started her trip?
__________________________
[1]
(c)How can you tell how many hours does it take
her to get home?
___________________________________
__________________________
[1]
___________________________________
___________________________________
[2]
(d)What is her average speed for the trip? What
feature of the graph tells you this?
__________________________
(d) How far had she walked after 1 hour?.
[2]
SINCOS Publications
Page 7
__________________________
[2]
Year 9 Mathematics 2010
NAME:
TEACHER:
YEAR 9 MATHEMATICS, 2010
Number
QUESTION AND ANSWER BOOKLET
Answer ALL questions in the spaces provided in this booklet.
Achievement Criteria
For Assessor’s use only
Achievement
with Merit
Achievement
Solve problems involving
integers, decimals
and fractions.
Show ALL working.
Solve number problems.
Overall Level of Performance
Achievement
with Excellence
Solve number problems in
context involving several
steps.
Total:
/ 25
==========================================================================
QUESTION TWO
QUESTION ONE
Fill in the missing numbers on these number
lines.
Shade 72% of this square
[1]
(a)
-
0 1 2 3 4 5 6
3
[1]
(b)
4.997
4.999
QUESTION THREE
[2]
Rewrite these decimals in order from smallest to
largest.
0.08, 0.7, 8.0, 0.87, 7.8, 0.8, 0.78, 0.078
(c)
1
1.5
2
[1]
SINCOS Publications
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[2]
Year 9 Mathematics 2010
QUESTION FOUR
QUESTION SEVEN
Use the order of operations to work out this
problem. Show each working step.
Amanda wanted to buy a CD, but at $39.95, it
was a bit too dear. Later, she sees that CDs are
being discounted by 20%.
3 x (2 – 5) + (6 – 3)2 – 8 ÷ 2
(a) Write a calculation Amanda could do in her
head to estimate the size of the discount.
[1]
(b) What is the exact amount Amanda would
pay for the discounted CD?
[3]
QUESTION FIVE
[1]
QUESTION EIGHT
Fill in the missing numbers that will make the
fractions equivalent.
3
8
=
(b)
2
9
=
12
(c)
35
42
=
5
(a)
[1]
(a) Hemi earned $12.50 per hour. After an 8%
pay rise, what will his new pay rate be?
[1]
New Pay Rate: __________
24
[1]
QUESTION SIX
[2]
(c) As well as his $450 spending money, Hemi
also had to save $650 for his flights, $832 for
accommodation, $780 for food and $205 for
airport taxes. If he earns $12.50 per hour and is
only saving 35% of his pay, how many hours
will he need to work to save the money he
needs? (show all working)
Complete this table to show numbers that are
equivalent in value.
Fraction
Decimal
0.98
Percentage
98%
0.12
1
________________ hours
[3]
1.2
67.5%
[4]
SINCOS Publications
Page 9
Year 9 Mathematics 2010
NAME:
TEACHER:
YEAR 9 MATHEMATICS, 2010
Angles
QUESTION AND ANSWER BOOKLET
Answer ALL questions in the spaces provided in this booklet.
Achievement Criteria
For Assessor’s use only
Achievement
with Merit
Achievement
Solve simple angle problems.
Show ALL working.
Solve simple angle problems
and give reasons.
Overall Level of Performance
Achievement
with Excellence
Calculate angles giving
reasons.
Total:
/ 22
=========================================================================
QUESTION THREE
QUESTION ONE
Read the size of this angle off the protractor.
Give the size of the following angles. You do
not have to give a reason.
(a)
142o
A
It measures __________ degrees
[1]
A = _________________
(b)
QUESTION TWO
For each angle, write acute, obtuse, right or
reflex
68o
B
[3]
SINCOS Publications
[1]
Page 10
114o
B = _________________
[1]
Year 9 Mathematics 2010
(c)
63o
C
C = _________________
[1]
QUESTION FOUR
For the following questions, give the angle sizes
and give a reason (rule) for each one.
(a)
y
71o
x
x = ______________
[1]
Reason: ____________________________
____________________________
y = ______________
[1]
[1]
Reason: ____________________________
____________________________
[1]
(b)
105o
t
48o
s
s = ______________
[1]
Reason: ____________________________
____________________________
t = ______________
[1]
[1]
Reason: ____________________________
____________________________
SINCOS Publications
[1]
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Year 9 Mathematics 2010
QUESTION FIVE
QUESTION SIX
In the “Cat’s Cradle” string game, a lot of
parallel lines can be created.
Discuss whether lines AB and CD are
parallel to each other.
Here are some diagrams based on cat’s cradles.
Your job is to work out the size of the angle
marked A. Number (1, 2, etc.) any angles in the
diagram you used to help solve the problem.
Give a reason for each one.
A
(a)
115˚
63˚
B
D
C
A
150 o
Angle Number Size Reason
A = __________________
[3]
(b)
32 o
48 o
A
Angle Number Size Reason
A = __________________
[4]
SINCOS Publications
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Year 9 Mathematics 2010