MAT 2CD
1.
Sample Exam Questions
[4 marks]
A line has equation 2x + 4y = 10 .
State with reasons whether the following statements are true or false.
a)
The equation of the line can be written as x + 2y = 5 .
[2]
b)
The line passes through the point (2, 1).
[2]
2.
[4 marks]
Given set A = { factors of 24 } and B = { even numbers between 6 and 30 } find:
a)
b)
3.
(
n AÇB
(
P B|A
)
)
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[2]
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[2]
[5 marks]
For the points A(4, -6) and B(-2, 12):
a)
Find the distance between A and B.
[2]
b)
Find the equation of the line containing A and B, in the form y = mx + c .
[3]
4.
[3 marks]
A survey of 154 students at a particular High School resulted in the following information. 112
students enjoyed watching football on TV whilst 77 enjoyed watching netball on TV. 33 students
said they didn’t watch any sport on TV at all.
Find the probability that a student chosen at random watched both football and netball.
Football
5.
Netball
[8 marks]
Three-letter arrangements are made from the letters FOUL. These arrangements are made in
such a manner that each vowel (O or U) is followed by a consonant (F or L) and each
consonant is followed by a vowel. Letters are not repeated in each arrangement.
2
a)
MATHEMATICS 2CDMAT
Complete this tree diagram for the arrangements.
[3]
1st Letter
2nd Letter
3rd Letter
F
O
U
L
b)
Find the probability that a three-letter arrangement formed like this:
(i)
does not include an F.
[1]
(ii)
has both the consonants in it.
[1]
(iii)
ends with an F and starts with a vowel.
[1]
(iv)
starts with an F, when it is known to include an O.
[2]
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3
6.
MATHEMATICS 2CDMAT
[4 marks]
The following functions are transformations of the function with equation y = x 2 .
Match each given function with the correct description of the transformation that was applied to
it. Record your answers in the table below.
(
)
1.
y = x -1
2
2
A
y = x 2 was translated down 1 unit.
y = x2 + 1
B
y = x 2 was translated 1 unit to the right.
3
y = -x 2
C
y = x 2 was translated 1 unit to the left.
4
y = 4x 2
D
y = x 2 was reflected about the x-axis.
E
y = x 2 was dilated vertically.
F
y = x 2 was translated up 1 unit.
G
y = x 2 was reflected about the y-axis.
Equation
1
2
3
Description
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4
4
1.
MATHEMATICS 2CDMAT
[6 marks]
U = 98
A
B
18
15
27
Determine:
a)
b)
c)
( )
n B
(
n AÇB
( )
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[1]
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[1]
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[1]
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[1]
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[2]
)
()
n A +n A
If one item is randomly selected, find the following probabilities:
d)
e)
( )
P A
(
P A| AÈB
)
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5
2.
MATHEMATICS 2CDMAT
[6 marks]
There are three diagrams drawn below, labelled A to C. Choose the correct equation to match
the graphs from the list at the right:
y
A
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
(
-2
-3
-4
II
x=3
III
6x - y = -3
IV
y = - x+2 +5
V
y =3
VI
y = x - 1.5
-5
-6
2
y = - x-2 +5
x
6
)
I
(
)
2
y
6
B
5
4
3
(
)
VII y = 2 x 2 + x - 1
2
1
-6 -5 -4 -3 -2 -1
-1
1 2 3 4 5 6
x
VIII 3y = 6 - 2x
-2
-3
IX
y = x2 - 6
X
-2y = x + 3
XI
y = 2x2 - x - 6
-4
-5
-6
y
C
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
Graph A:
(
6
5
4
3
2
1
)(
XII y = x - 2 x + 2
1
2
3
4
5
6
x
Graph B:
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Graph C:
)
6
3.
[3 marks]
()
(
Given g t = - 2 - t
a)
b)
c)
)
2
- 2 find:
()
g 2
( )
Round 0.00555 to 2 significant figures.
e)
f)
g)
h)
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[1]
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[1]
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[1]
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[1]
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[1]
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[1]
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[1]
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[1]
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[1]
( )
a)
d)
[1]
g p
[8 marks]
c)
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g -2
4.
b)
MATHEMATICS 2CDMAT
Express 735 000 000 in scientific notation.
Round 66.491 to the nearest integer.
Round 0.000975 to 3 decimal places.
Express 2.475 X 10-4 as a decimal.
Find the value of x if 46 ´ 4x ¸ 43 = 49 .
Find the value of x if
(6
4
´ 62
)
3
= 6x .
What would be the gradient of any line perpendicular to the line y = -0.5x + 2 ?
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[1]
7
5.
MATHEMATICS 2CDMAT
[2 marks]
For the following Venn diagrams shade the stated region.
a)
AÇ B
A
B
[1]
b)
(AÈ B')
A
B
[1]
6.
[4 marks]
Factorise completely:
a)
a2 - 5a - 6
[2]
b)
12 - 3b2
[2]
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8
MATHEMATICS 2CDMAT
Question 1 [1, 2, 2 marks]
a) If A and B are subsets of a Universal set, U, draw a Venn diagram (in the
space below) for which A  B  .
b) Draw TWO Venn diagram below, showing P and Q as two intersecting sets, and
use it to shade the region
PQ
P Q
(i)
(ii)
(c)
Is it possible for any two sets X and Y to have elements such that
X  Y = X ? Justify your answer using diagrams.
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9
MATHEMATICS 2CDMAT
Question 2. [3, 3 marks]
a) Use set notation to describe the shaded region below.
X
Y
b) Refer to the Venn diagram below.
i)
Use set notation to describe the relationship between sets
M and N
ii) On the diagram, shade
L  M   N
U
M
L
N
Question 3. [3 marks]
Round the following to the indicated decimal place.
a)
5.0876 (3dp)
101.306429 (3dp)
b)
------------
17.89453 (2dp)
------------
c)
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Question 4. [3 marks]
Expand, and simplify each of the following:
a)
3(x - 9)
b)
2(x + 4) - 5(x + 7) c)
(x – 5)(x – 8)
Question 5. [3 marks]
Factorise each of the following:
a)
2x + 8
b)
8x2y – 16xy + 12x
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c)
x2 + 8x – 9