80 Marks
Open Rubric
1
Question 1
The functions f , g and h are defined by
f pxq “
2
,
|x ` 3|
and
c
gpxq “ x ´
5´x
´ 4,
2
respectively. If the set Df and Dg represents the domains of f and g respectively. Then Df and Dg
are given by
1.
„
˙
1
,8 ,
3
`
˘ `
˘
Dg “ ´ 8, 5 Y 5, 8 ,
Df “
2.
`
˘ `
˘
Df “ ´ 8, 3 Y 3, 8 ,
`
˘ `
˘
Dg “ ´ 8, 5 Y 5, 8 ,
3.
`
˘ `
˘
Df “ ´ 8, ´3 Y ´ 3, 8 ,
„
˙
Dg “ 5, 8 ,
4.
`
˘ `
˘
Df “ ´ 8, ´3 Y ´ 3, 8 ,
ˆ
ȷ
Dg “ ´ 8, 5 ,
2
Question 2
The function f is defined by
f pxq “ 2x `
?
5x ´ 6 ´ 3,
which of the the following represents the solutions for the equation f pxq “ 0.
2
1.
x“´
5
4
or
x “ ´3
2.
x“
5
4
3.
x“
5
4
or
x“3
4.
x“3
3
Question 3
The function gpxq is defined by
hpxq “ log2 px ` 2q ` log2 px ` 4q ` 1
for x P Dh , where Dh is the domain of h. The solution of the inequality hpxq ă 4 is
1.
´6 ă x ă 0
2.
´2 ă x ă 0
3.
x ą ´2
4.
x“3
3
4
Question 4
The solution of the equation
ex ` 12e´x ´ 7 “ 0
is
1.
ex “ ´3
or ex “ ´4
2.
x “ ln 2
3.
x “ ln 4
4.
?
x “ 2 ln 3
5
or x “ 2 ln 2
Question 5
The straight line EB cuts the parabola y “ 2x2 ´ 3x ´ 2 at E and B and is parallel to y ` x “ 0
Find the coordinates of A and B.
4
1.
ˆ
A is
1
´ ,0
6
˙
1
´ ,0
4
˙
ˆ
˙
3, 0
ˆ
˙
4, 0
and B is
2.
ˆ
A is
and B is
3.
ˆ
˙
ˆ ˙
´ 1, 0 and B is 5, 0
ˆ
1
´ ,0
2
A is
4.
A is
6
˙
ˆ
and B is
˙
2, 0
Question 6
The straight line EB cuts the parabola y “ 2x2 ´ 3x ´ 2 at E and B and is parallel to y ` x “ 0
Find the coordinates of C.
1.
C is
5
ˆ
˙
1
0, ´
2
2.
ˆ
˙
0, ´2
ˆ
C is
˙
0, ´3
C is
ˆ ˙
0, 2
C is
3.
4.
7
Question 7
The straight line EB cuts the parabola y “ 2x2 ´ 3x ´ 2 at E and B and is parallel to y ` x “ 0
Find the coordinates of D.
1.
ˆ
D is
7 25
,´
4
2
˙
25
8
˙
2.
ˆ
D is
6
2, ´
3.
ˆ
3
1
, ´3
4
8
˙
ˆ
1 43
,´
4
8
˙
D is
4.
D is
8
Question 8
The straight line EB cuts the parabola y “ 2x2 ´ 3x ´ 2 at E and B and is parallel to y ` x “ 0
If H is the point pk, 3q. Find k
1.
k“
5
2
k“
7
2
2.
3.
k“3
4.
k“
7
9
4
9
Question 9
The straight line EB cuts the parabola y “ 2x2 ´ 3x ´ 2 at E and B and is parallel to y ` x “ 0
Find the coordinates of E.
1.
ˆ
E is
3 1
´ ,
2 2
˙
2.
ˆ
E is
˙
´ 1, 3
3.
ˆ
˙
7
, ´3
3
ˆ
˙
E is
4.
E is
8
´ 2, 3
10
Question 10
The area covered by water weed on a dam increases exponentially according to the formula
Aptq “ Ap0qekt ,
where Aptq is the area of the water weed in square metres after t days. The initial area of water weed
was 120 m2 . After 5 weeks the area was 280 m2 . Find the value of k in the above formula.
1.
ˆ ˙
7
ln
3
k“
5
2.
ln
k“
ˆ ˙
7
3
35
3.
ˆ ˙
9
ln
4
k“
5
4.
ln
k“
11
ˆ ˙
3
2
10
Question 11
Supposed that
ˆ ˙
ln 1.5
Aptq “ 100e
10
,
represents the area of the water weed in square metres after t days. The area of the water weed after
480 hours is given by
1.
Ap 480hours q “ 450 hours
2.
Ap 480hours q “ 225 hours
3.
Ap 480hours q “ 300 hours
4.
Ap 480hours q “ 450 hours
9
12
Question 12
Find the period of the function defined by the following equation,
ˆ
π
y “ 2 ´ 4 cos 2x ´
3
˙
1.
period “ 2π
2.
π
4
period “
3.
period “ π
4.
period “
13
3π
2
Question 13
Find an appropriate interval on which to graph one complete period of the function defined by the
following equation,
˙
ˆ
π
y “ 2 ´ 2 sin 2x `
4
1.
„
´
π 7π
,
8 8
ȷ
2.
„
π π
´ ,
8 8
ȷ
„
π π
´ ,
8 4
ȷ
3.
4.
„
π 7π
´ ,
8 4
10
ȷ
14
Question 14
Find the horizontal shift of the function defined by the following equation,
ˆ
π
y “ 2 ´ 4 cos 2x ´
3
˙
1.
Horizontal shift “ ´
π
6
2.
Horizontal shift “
π
6
Horizontal shift “
π
3
3.
4.
Horizontal shift “ ´
15
π
3
Question 15
Find the range of the function defined by the following equation,
´
π¯
y “ 5 ´ 2 sin 2x ´
3
1.
´1 ď y ď 1
2.
´6 ď y ď 3
3.
´3 ď y ď 7
4.
3ďyď7
16
Question 16
Find the amplitude of the function defined by the following equation,
´
π¯
y “ 2 ´ 2 sin x `
4
11
1.
Amplitude “ 2
2.
Amplitude “ 1
3.
Amplitude “ 4
4.
Amplitude “ 3
17
Question 17
In the following sketch C ÂB “ 18˝ , C ÂD “ 38˝ and AC represents a distance of 100 metres.
What is the measure of the angle of elevation from A and C?
12
18
Question 18
In the following sketch C ÂB “ 15˝ , C ÂD “ 45˝ and AC represents a distance of 100 metres.
What is the measure of the angle of depression from D and A?
19
Question 19
In the following sketch C ÂB “ 15˝ , C ÂD “ 45˝ and AC represents a distance of 100 metres.
Use the Law is Sines to determine the distance by DC. Leave your answer in surd form.
13
1.
DC “
?
40000 m
2.
DC “
?
20000 m
3.
DC “
?
18000 m
4.
DC “
20
?
25000 m
Question 20
Two cars leave from the same place and travel along two straight roads. The two roads make an angle
of 60˝ with each other at the point from which
? the cars begin their journey. The one car travels 60
km/h and the other at x km/h. If the cars are 1300 km apart after an hour, what is the speed of the
other car?
Apply the Law of Cosines to solve for x.
1.
The speed of the other car is 20 km/h.
2.
The speed of the other car is 75 km/h.
3.
The speed of the other car is 80 km/h.
4.
The speed of the other car is 120 km/h.
21
Question 21
A soft drink vendor at a popular beach analyzes his sales records and finds that if he sells r cans of
soda pop in one day, his profit is given by
P prq “ ´0.001r2 ` 5r ` 20,
What is his maximum profit per day?
1.
The maximum profit per day is 6270.
2.
The maximum profit per day is 8200.
3.
The maximum profit per day is 7220.
4.
The maximum profit per day is 1230.
14
22
Question 22
Which of the following is the set of solutions for
2 tan2 x cos x ´ 6 cos x ´ 4 tan2 x ` 12 “ 0
for x P r0, 2πq
1.
"
S“
π 2π 4π 5π
,
,
,
3 3 3 3
*
2.
"
*
π 2π 4π 5π
S “ 0, ,
,
,
3 3 3 3
3.
"
S“
π 2π 5π 7π
,
,
,
3 3 3 3
*
4.
"
*
π 2π 4π 5π 7π
S “ 0, ,
,
,
,
3 3 3 3 3
23
Question 23
The circle with equation
x2 ` y 2 ` 2x ` 4y ´ 31 “ 0
has center C and radius r units, where
1.
C “ p´1, ´2q; r “ 6
2.
C “ p´1, ´2q; r “ 6
3.
C “ p´1, 2q; r “ 6
4.
C “ p1, 2q; r “ 6
15
RESULTS
Total = 80 / 80 (100%)
Finalize