add math mid year form 5 paper 1 2015
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Peperiksaan Pertengahan tahun Matematik tambahanTRANSCRIPT
1. Diagram 1 shows the relation between set P and Set Q in the arrow diagram form. State
a. the relation in the form of ordered pairs.b. the type of relation.c. the range of the relation.
[ 3 marks ]
Answer;
2. Diagram 2 shows the function , where m is a constant.Find the value of m.
[ 2 marks ]
Answer;
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Set Q –3 –1 0
41Set P
2
Diagram 1 1
fx
52m
3x – m
Diagram 2
3. Diagram 3 shows the function f maps set A to set B and function g maps set B to set A.Find
a. the function g in similar form.b. g(–5)
[ 3 marks ]
Answer;
4. The Diagram 4 shows a trapezium ABCD in which AB = x cm, AD = (x + 2) cm and BC = (2x + 5) cm.
a. Given that the area of the trapezium is 24 cm2 , show that 3x2 + 7x = 48.
b. Hence, find the value of x.
[ 3 marks ]Answer;
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f
yx 3x,
x3x2
A B
BA
g
Diagram 3
B
x
x + 2
2x +5 C
A D
Diagram 4
5. Find the range of values of m such that the roots of the equation mx2 – x(x + 4) + 2 = 0 are not real.
[ 3 marks ]
Answer;
6. Diagram 5 shows the graph of a quadratic function f(x) = –2(x – p)2 + 18, where p
is constant, intersects the x-axis at –1 and 5. The curve y = f(x) has the maximum point (2, 3k). State
a. the value of p, b. the value of k,
c. the values of x when f(x) = 0[ 3 marks ]
Answer;
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y = f(x)
(2, 3k)
–1 50
y
x
Diagram 5
7. Diagram 6 shows the graph of quadratic function y = f(x).
i. Express the quadratic function in the form of f(x) = ax2 + bx + c, where a, b and c are constants
ii. Find the range of values of x when f(x) ≤ 0
[ 3 marks ]Answer;
8. a. Simplify the expression 3p + 3p + 1 + 3p + 2 + 3p + 3.
b. Hence, show that 3p + 3p + 1 + 3p + 2 + 3p + 3 is divisible by 5 for all positive integers
of p.[ 3 marks ]
Answer;
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–5 20
f(x)
x
Diagram 6
9. Given that p = 2m and q = 2n, express the following in term of m and n
a.
b. log16 p – log4 q[ 4 marks ]
Answer;
10. a. Given log9 n = , find the value of n
b. Solve the equation . [ 3 marks]
Answer;
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11. A graduate is required to service his interest-free education loan in 36 monthly
instalments, with the first instalment being RM 100. Subsequent instalments are increased by RM 20 each month. Find
a. the amount of the 10th instalment.b. the total sum of his education loan instalment.
[ 3 marks ]
Answer;
12. It is given the sum of the first n terms of a geometric progression is .Find
a. the first term of the progressionb. the common ratio of the progression.
[ 4 marks ]Answer;
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13. The Diagram 7 shows the graph xy against x is a straight line passing though the point P(5, 3) and Q(0, –3).
a. Find the gradient of the straight line PQ.
b. Show that
[3 marks]
Answer;
14. Diagram 8 shows the straight line PQ with equation intersects the
straight line AB at point P.
a. State the y-intercept of PQb. Find the coordinate of B if 2BP = 3PA
[3 marks]Answer;
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0 xP(5, 0)
y
Q
A(3, –4)
B
0
P
xy
x
Q
Diagram 7
Diagram 8
15. Given and . Find
a. in term of h and k.b. the numerical value of h and of k if is zero vector.
[3 marks]
Answer;
16. In Diagram 9, O is the origin and A, B and C are three points on a horizontal plane. Given the vector OA = –a + b, OB = a + 5b and OC = 4a + 11b.
a. Find AB and BC in terms of a and bb. Show that A, B and C are collinear and hence find the ratio AB : BC
[4 marks] Answer;
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Diagram 9
A
x0
yC
B
17. Solve the equations for
a. tan (2x + 500) = 0.8b. 3sin x cos x = cos x
[4 marks]Answer
18. The Diagram 10 shows a circle PAQ with centre O, of radius 8 cm. SR is an arc of
a circle with centre O. The reflex angle POQ is radians. Given that P and Q are midpoints of OS and OR respectively, find the area of shaded region, giving your answer in terms of .
[ 3 marks ]
Answer:
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P
QR
S
OA 1.6 rad
8 cm
Diagram 10
19. Diagram 11 shows a cylindrical jar contains water to a depth of h cm. The
volume v cm2 of water given by . If h is increasing at the rate of
0.25 cm s–1, find the rate of increase of volume when the depth of water is 2 cm.
[3 marks]
Answer;
20. Given , find
a. , if h is a constant
b. , if r is a constant
[3 marks]
Answer;
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h cm
Diagram 11
21. A set of numbers 3, k, 2k, 10, 12 and 17 arranged in ascending order has a mean of m.
a. Find k in term of mb. If each number in the set is decreased by 2, the median of the new
set of data is m – 2. Calculate the values of m and k.[4 marks]
Answer;
22. A set of data consists of twelve positive numbers. It is given that
.
Finda. the varianceb. the mean
[4 marks}
Answer;
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23. Of the 80 boy students, 26 students play football, 20 students play football and hockey, and 42 students play football or hockey.
a. Find the number of students who play hockey.b. Hence, calculate the probability that a students, chosen at
random, plays hockey.
(Hint: Use formula)
[3 marks]Answer;
24. a. Find the number of code words, with their consonants placed side by side that
can be formed from the letters of word RANDOM
b. Diagram 12 shows a piece of broken business-card. The last three digits of the hand phone numbers could not be made out. Find the number of ways to fill the last three digits if the number forms an odd number.
[3 marks]Answer;
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Dr. Hjh. Balqis Binti Medical Consultant UIAM
H/Phone.: 019–5874
Diagram 12
25. Diagram 13 shows two parallel lines, L1 and L2. Three points are marked on L1 and five points are marked on the L2. A triangle will be formed by chosen any three points. Determine the number of different triangles that can be formed by connecting
a. only a point from L1.b. any points.
[ 3 marks]
Answers;
END OF QUESTION PAPER
Prepared byHj. Busrah bin Md. Seh / SMKJ 2015
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L1
L2
Diagram 13
JADUAL SPESIFIKASI UJIAN (JSU) MATEMATIK TAMBAHAN
(KERTAS 1)
Bidang
TOPIK
Tin
gkata
n
Jum
lah
soala
n
KERTAS 1
No
Soala
n
Ara
s
KB
AT
Mark
ah
Alg
eb
raic
Functions 4 3
1 R 3
2 R 2
3 T / 3
Quadratic Equations4
24 S 3
5 S 3
Quadratic Functions4
26 S 3
7 T / 3
Indices and Logarithms 4 3
8 T / 3
9 T 4
10 S 3
Progressions5
211 T / 3
12 T 4
Linear Law 5 1 13 S 3
Geom
etr
y
Coordinate Geometry 4 1 14 S 3
Vectors5
215 R 3
16 T / 4
Sta
tisti
cs Statistics4
221 T / 4
22 T / 4
Probability 5 1 23 T / 3
Permutations/Combinations5
224 T / 3
25 T / 3
Tri
gon
om
etr
y Circular Measure 4 1 18 T 3
Trigonometric Functions 5 1 17 T / 4
Calc
ulu
s Differentiation 4 2
19 S 3
20 T /3
TOTAL 25 12 80
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