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this document. Marks are only
guidelines.
We have categorized each question into
one of the 4 achievement chart
(A/C)
categories: Knowledge/Understanding
(K)
, Thinking
and Inquiry
(T)
, Application
(A)
and
Communication
(C)
. You can change or
modify the categories as you see fit.
GRADE 10 PRINCIPLES OF MATHEMATICS
(ACADEMIC)
@
MPM 2D
Total Marks:
INSTRUCTIONS:
A/C
[K]
《
1. Calculators may be
used.
2. Read all
instructions carefully in order to maximize your
mark.
Part A
–
Multiple Choice 25 Marks
(25 questions * 1 mark each)
For each of the following questions in
this section,
circle the
letter
representing the
correct answer.
1.
A
linear
system of two
equations that has one solution
represents two lines that
are:
a)
parallel
b)
coincident
c)
intersecting
d)
none of these
2.
The midpoint of RS is
M(8, -1). If point S has coordinates (11, 4) what
are the
coordinates of
point
R
、
3.
4.
|
a)
(3, -6)
b)
(15,
-6)
c)
(5, -6)
d)
(3, 9)
The
midpoint
of the line segment
with
end points
A(-8, 8) and
B(6, 4) is:
a)
(0, 10)
b)
(1, 2)
c)
(7, 2)
d)
(-1, 6)
The
equation
of a horizontal
line
passing through the
point (4, 2) is:
a)
x
?
2
b)
y
?
4
c)
y
?
2
d)
x
?
4
5.
The
equation
of a line with a
slope
of
m
?
5
and a
y intercept
of 8
is:
a)
y
?
5
x
?
8
b)
y
?
?
5
x
?
8
c)
y
?
?
5
x
?
8
d)
y
?
8
x
?
5
1
6.
The
slopes of 2 lines are -7 and
.
These lines are said to
be:
7
a)
parallel
b)
perpendicular
c)
coincident
d)
none of these
7.
The
slope
of a line segment
passing through
2 points
(10,- 4) and (-2, -16) is:
】
8.
9.
】
a)
1
b)
2
c)
-1
d)
-2
The
length
of a line segment
with
end points
(-6, 7) and
(-1, -5) is:
a)
12
b)
5
c)
13
d)
169
The
diameter
of a circle whose
equation
is
x
2
?
y
2
?
289
is:
a)
15
b)
16
c)17
d)
none of these
10. The
equation
of a circle with a
centre of (0,
0)
that also passes through the
point (-8, -6
)
is:
a)
x
2
?
y
2
?
10<
/p>
b)
x
2<
/p>
?
y
2
?
100
c)
x<
/p>
2
?
y
2
?
14
d)
x
2
?
y
2
?
48
11. The
y-intercept
of the line
2
x
?
5
y
?
10
?
0
is:
a)
2
b)
-2
c)
10
d)
5
}
12. The
slope
of the line
4
x
?
2
y
?
1
?
0
is:
a)
2
b)
-2
c)
1
d)
13. If
(-3, y) is a solution
to the
equation
x
?
2
y
?
13
,
what is the value of y
a)
3
b)
6
c)
5
d)
'
14. The
product
?
?
3
x
2
y
3
z
??
?
4
x
2
y
3
z
?
is equal to:
a)
12
xy
6
z
2
b)
1
2
x
4
y
6<
/p>
z
2
c) <
/p>
?
12
xy
6<
/p>
z
2
d)
15. A
simplified
expression
for
?
2
m
?
n
?
?
?
?
5
m
?
n
?
is:
a)
7
m
b)
7
m
?
2
n
c)
?
3
m
d)
0
8
12
x<
/p>
4
y
0
z
0
7
m
?
2
n
?
27
a<
/p>
2
bc
4
16.
A
simplified expression
for
is:
?
9
abc
2
)
a)
3
ac
b)
3
abc
c)
3
ac
2
d)
3
a
2
c
2
17. The
slope
of
the line, which is
perpendicula
r to the line, <
/p>
x
?
4
y
?
8
?
0
is:
a)
-4
b)
4
c)
1
d)
-1
18. The
shortest
distance
from the point (2, -3) to the
line
x
?
?
4
is:
a)
5
b)
3
c)
2
d)
6
}
19.
The
value
of the polynomial
4
a
2
?
5
a
?
8
when
a
?
?
3
is:
a)
59
b)
44
c)
13
d)
29
20. Which of the following is
not a function
:
a)
?
?
2
,
3
?
,
?
4
,
5
?
,
?
6
,
7
< br>?
?
b)
< br>y
?
2
x
2
c)
x
?
2
y
2
d)
?
?
6
,
2
?
,
?
7
,
3
?
,
?
8
,
3
?
?
< br>
21. The
range
of the relation whose
equation is
y
?
?
x
2
?
5
is:
`
a)
y
?
?
5
b)
y
?
5
c)
y
?
?
5
d)
y
?
5
2
22. The
vertex
of the parabola
y
?
?
x
?
4
?
?
6
is:
a)
?
?
4
,
6
?
b)
?
4
,
?
6
?
c)
?
?
6
,
4
?
d)
?
6
,
?
4
?
< br>
2
23. The
equation
of the
axis of symmetry
of the
parabola
y
?
?
4
?
x
?
2
?
?
5
is:
a)
x
?
5
b)
x
?
?
5
c)
x
?
2
d)
x
?
?
2
；
1
24. A parabola with a
vertex of
?
2
,
3
?
and a
stretch factor of
?
(
relative
to
y
?
x
2
)
would
4
have an equation
of:
1
1
1
1
2
2<
/p>
2
2
a) <
/p>
y
?
?
?
x
?
2
?
?
3
b)
y
?
?
?
x
?
2
?
?
3
c)
y
?
?
?
x
?
3
?
?
2
d)
y
?
?
?
x
?
3
?
?
2
4
4
< br>4
4
25
The
parabola
y
?
?
4
x
2
?
k
passes
through the point
?
?
< br>2
,
3
?
.
T
he value of
k
is:
a)
-19
b)
11
c)
13
d)
19
A/C
~
Part B
–
Short
Answers
For each of the
questions in this section,
write your
answers in the spaces provided
.
Use the foolscap provided for any rough
work.
Show details of calculations
wherever
requested.
1
.
In
the accompanying diagram, state each of the
following:
(4 Marks)
a)
domain:
__________ (
1 Mark)
b)
range: __________ (
1
Mark)
c)
`
[K]
[K]
[C]
、
Is the
relation a function Justify
your
answer.
(2 marks)
-4
-2
2
4
[A]
%
2.
The
x-intercepts
of the parabola
y
?
x
2
?
289
are:
__________ and __________.
(Show your work)
(2
Marks)
[A]
3.
The
roots
of the quadratic
equation
3
x
2
?
17
x
?
10
?
0
are:
__________ and __________.
(Show your work)
(3
Marks)
[A]
/
4.
Write the
equation of the parabola
with a vertex of (4, 23) if it passes through the
point (-1, -2): (Show your work)
(3 Marks)
____________________
[T]
[K]
.
5.
A line passes through 2 points (1, 4)
and (2,-4).
Calculate the slope of the
line
.
Also show
the equation of the line in the form
Ax
?
By
?
C
?
0
.
(Show your work)
(4
Marks)
____________________
Slope
____________________
Equation
6.
The Tangent of
45
?
is:
__________
(1 Mark)
[A]
[T]
,
7.
a) In the
accompanying diagram,
the two triangles
are similar
.
What is the
value of
x
(Show your work)
(2 Marks)
18
x
27
^
12
x
?
__________
b) If the area
of the smaller triangle is 8
cm
2
, what is the area of the
larger triangle
(Show your work)
( 2
Marks)
1
2
Area = __________
[K]
8
Given that sin A =
, find
?
A
(to the
nearest degree) __________
(1
Mark)