Year End Revision Exercise AddMaths Form 4

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Name of student: ________________________________ Class: Saturday
Date: 19.11.2016
Week: 46
Time: 10.30 pm ~ 2.00 pm
Kipli Yassin Resources, Heritage Garden, Kuching
Subject: Additional Mathematics Form 4
Revision Exercise
1. A function f is defined by kx
x
xf 

 ,
1
6
3: . Find
(a) the value of k,
(b) the value of )1(1

f .
2. Given that k and 2k are the roots of the quadratic equation 092
 mxx , find the value of k and of
m.
3. Diagram 3 shows the movement of a ball that was thrown by Azizah.
Diagram 3
The ball is thrown at the height of 3.5 m from the ground. The ball achieved its maximum height of 8 m
at a horizontal distance of 3 m from point A. Write a quadratic function which represents the movement
of the ball.

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4. It is given that the curve of the quadratic function prxxxg  2
)( intersects the x-axis at the points
)0,4( and (1, 0). Find the value of r and of p.
5. Find the range of values of x for which 2
)5( x > 17 – x.
6. Solve the equation  41
10
100
1
)5(2 
 xxx
.
7. Given that rqp
1553  , express r in terms of p and q. [SPM 2016, P1]
8. Solve the equation )7(log13log2 55 aa  .

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9. Diagram 9 shows a circle with centre P(4, 4). A rope is marked at P and Q where R divides the line
segment PQ in the ratio of PR = 0.4RQ.
Diagram 9
Find the radius of the new circle PQ.
10. Diagram 10 shows a straight line that passes through point P, Q and R.
Diagram 10
Show that 2523  sr .
11. Diagram 19 shows the straight line passes through the point M(–2, 7) which makes an angle α from the
x-axis.
Diagram 19
Given that
5
4
cos  , find the equation of the straight line MN.

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12. Set Q is a set of six numbers x, 5, 7, 10, 3x and 16 with mean µ. When 3 is added to each number, the
mean is 
3
4
. Find the mean, value of x and variance of the six numbers in set Q.
13. Diagram 13 shows the cross-section of a cylinder block floating in water.
Diagram 13
The water surface is 16 cm above the water level at point Q. Find
(a) POQ in radians,
(b) the percentage of the volume of cylinder above the water surface.
14. Nadhirah wishes to cut out a circle of radius 5 cm from a piece of manila card. Due to her carelessness,
a circle with radius 5.2 was cut.
Actual Mistake
Diagram 14
Find the extra area, in terms of π, that has been cut out of the card.

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15. Diagram 15 shows the growth of a pearl that is cultured in an oyster, which has radius of r mm.
1st month 2nd month
3rd month 4th month
Diagram 15
Given that the radius increases at a constant rate 0.2 mm, find the rate of change of the surface area of
the pearl when r = 8 mm.
16. A curve has the equation 2
)21( x
c
y

 , where c is a constant. When x increases from 1 to 1 + h, where
h is very small, the appproximate change in y is
9
7h
 , find the value of c.
17. Adam planted vegetables on a piece of land. The shape of the land is right angled triangle. Given the
longest side of length is y metre. The other two sides of the land are x metre and (2x – 1) respectively.
He fenced the land with 40 metre of barbed wire.
Find the length, in metre, of each side of the land. [SPM 2016, P2]

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18. If  and  are the roots of the quadratic equation 0432 2
 xx , find the value of
(a) 22
  ,
(b)

11
 ,
(c) Hence, form a quadratic equation whose roots are


12
 and


12
 .
Ans: (a)
4
7
 (b)
4
3
(c) 06
2
 xx
19. The curve of a quadratic function khxxf 2)(2)( 2
 intersects the x-axis at points (1, 0) and (5, 0).
The straight line y = –8 touches the minimum point of the curve. [SPM 2016, P2]
(a) Find the value of h and of k.
(b) Hence, sketch the graph of )(xf for 60  x .
(c) If the graph is reflected about the x-axis, write the equation of the curve.

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20. Diagram 20 shows the curves of 832
 qxxxy and pxy  2
)3(3 that intersect at two points
A and B on the x-axis.
Diagram 20
Find
(a) the value of p and of q,
(b) the minimum points of each curve.
[7 marks]
21. Table 13 shows the frequency distribution of the mass of watermelons at a fruit stall. [SPM 2016, P2]
Mass (kg) Number of watermelons
1.0 – 1.4 6
1.5 – 1.9 10
2.0 – 2.4 n
2.5 – 2.9 14
3.0 – 3.4 8
Table 13
It is given that the mean mass of the watermelons is 2.28 kg.
(a) Find the value of n.
(b) Hence, without using an ogive, calculate the median mass of the watermelons.

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22. Solution by scale drawing is not accepted.
Diagram 22 shows the location of a wrecked ship R at the ocean using coordinate system with respect
to a control tower O.
Diagram 22
Given that the OR has equation xy
3
2
 and is perpendicular to line PR.
(a) Find the equation for the line PR.
(b) Hence, find the coordinates of the wrecked ship R.
As a safety precaution, floating barriers are set at 100 m around the wrecked ship R.
(c) Find the equation of the floating barriers.
Ans: (a) 26
2
3
 xy (b) )8,12(R (c) 097921624
22
 yxyx

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23. Ahmad who works as an engineer plants a pipe which has a diameter of 50 cm.
Diagram 23
Given OQ is a straight line which is parallel to the pole OB. MN is the sandy level and PQ = 10 cm.
(a) Calculate
(i) angle  in radian,
(ii) the length of the pipe which is above the surface of the sand,
(iii) the area of segment which lies below the ground level.
(b) If a cockroach moves along the visible pipe ring, calculate the difference between the length of
the pipe ring and the movement of the cockroach along the sandy surface.
Ans: (a)(i) 1.855 rad. (ii) 110.725 cm (iii) 279.7 cm2
(b) 70.725 cm

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24. The straight line mxy 2 is a normal to the curve 524 2
 xxy at the point P. Find
(a) the coordinates of P,
(b) the value of m,
(c) the turning point of the curve and show that it is a minimum point.
Ans: (a) )5( ,2
1
(b) 2
21
(c) )( 4
19
4
1
,
25. Diagram 25 shows a conical container of radius 3 cm and height 7 cm.
Diagram 25
The container is filled up with water until x cm height.
(a) Show that the volume of the water, V cm3, is given by
49
3 3
x
.
(b) If the rate of change in the level of the water is 0.4 cm s–1,calculate the rate of change in the volume
of the water when x = 3 cm.

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26. Sands are poured at the rate of 24π cm3 s–1 to form a vertical cone shape as shown in Diagram 26.
Diagram 26
Given that hr
4
3
 and the volume of the cone is hrV 2
3
1
 .
(a) Write an expression for
dr
dV
in terms of r.
(b) Hence, calculate
(i) the small change in V when r increases from 9 cm to 9.03 cm,
(ii) the rate of change of r when h = 12 cm.
Ans: (a)
2
3
4
r (b) (i) 3.24 π (ii)
1
9
2 
cms

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27. Diagram 27 shows a cyclic quadrilateral ABCD. [SPM 2016, P2]
Diagram 27
(a) Calculate
(i) the length, in cm, of AC,
(ii) ACD .
(b) Find
(i) the area, in cm2, of ABC ,
(ii) the shortest distance, in cm, from point B to AC.
cm8
cm7
cm3
A
B
C
D
o
80