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TUISYEN KITA | cgnash
PENCETUS BIJAK MATEMATIK
Latih Tubi Mat Tam T5 set 8
demo suka matematik, kawe suka matematik, kita suka matematik
1. Table 5 shows the price indices and the weightages of
Luqman’s monthly expenses in the year 2009 based in the
year 2008.
(a) If the expenses for miscellaneous in the year 2009
was RM 1 456 , find the miscellaneous expenses in the year
2008.
(b) If the rental increases by 10% from the year 2009 to
the year 2010,find the price index for the rental in
the year 2010 based on the year 2008.
(c) Calculate the composite index for the expenses in
the year 2009 based on the year 2008.
(d) The price index for food in the year 2010 based on
the year 2009 is 105. If the expenses on food in the
year 2010 were RM3150, find the expenses on food
in the year 2008.
[a) 1300 b) 118.8 c) 112 d) 2500]
2. Diagram 2 shows a triangle ABC such that ADC and
AEB are straight lines.
It is given that AB = 15 cm, AD = 8 cm, DC = 16 cm, BC =
18 cm and 120CDE .
Calculate
a) BAC
b) the length, in cm, of DE,
c) the area , in cm2, of triangle ABC.
(a) '3148 (b) 6.3204 cm (c) 134.8467 cm2
3. The table shows the values of two variables, x and y ,
obtained from an experiment. The variables x and y
, are related by the equation 1 xpky where p
and k are constants.
(a) Plot a graph of y10log against )1( x , using a scale
of 2 cm to 1 unit on the )1( x -axis and 2 cm to 0.2 unit on
the ( y10log )-axis.Hence, draw the line of best fit.
(b) Use your graph from (a) to find the value of
(i) p
(ii) k
(iii) x when 22y
[ 6.5,766.1,585.1 xkp ]
4. (a) Sketch the graph of y = 2cos 2x + 1 for 0 x 2.
(b) Hence, using the same axes, sketch a suitable
straight line to find the number of solutions for the equation
2cos 2x = 2x for 0 x 2. State the number of
solutions.
5. Diagram 6 shows the points A and B such that OA a
and OB b .
Line OA is extended to P such that
OP = 4OA and line OB is extended to
Q such that OQ = 3OB.
(a) Express the following in
terms of a and b .
(i) AQ
(ii) BP
(b) Given AS mAQ and
BS nBP , express OS
(i) in terms of m, a and b ,
(ii) in terms of n, a and b .
(c) Find the value of m and of n.
[(a) (i) 3a b (ii) 4a b
(b) (i) (1 – m) a + 3mb (ii) 4n a + (1 – n) b
(c) m = 3
11, n =
2
11]
6. Diagram 10 shows triangle ABC. The line BC is
perpendicular to the line AB and intersects the x-axis at the
point C.
(a) Find
(i) the equation
of the line BC,
(ii) the
coordinates of
point C,
(iii) the area of
triangle ABC.
(b) Point P divides AC in the ratio m : n. Find the
ratio m : n.
(c) A point W moves such that it is equidistant from
A and C. Find the locus of point W.
[(a) (i) y = 3
5x + 6 (ii) (10, 0) (iii) 34 unit
2
(b) 3 : 10 (c) 13x + y + 45 = 0]
7. Diagram 9 shows two circle
with centres P and Q. The circles
intersect each other at points R
and S. The radias of both circles
are 10 cm. [Use = 3.142]
Find
(a) RPS in radian,
(b) the perimeter of the shaded region,
(c) the length of chord RS,
(d) the area of the shaded region.
[(a) 2.094 rad (b) 41.88 cm (c) 17.32 cm (d) 118.3 cm2]
TUISYEN KITA | cgnash
PENCETUS BIJAK MATEMATIK
Latih Tubi Mat Tam T5 set 8
demo suka matematik, kawe suka matematik, kita suka matematik
8. Diagram 7 shows a shaded region which is bounded by
the curve y = x2 + 1 and the straight
line y = k.
Given the volume generated when the
shaded region is revolved 180o about
the y-axis is 2 unit3. Find
(a) the value of k,
(b) the coordinates of P and Q,
(c) the area of the shaded
region.
[(a) 3 (b) P( 2 , 0), Q( 2 , 0) (c) 3.771 unit2]
9. Diagram 7 shows a shaded region bounded by the curve 24 xy , the y-axis and
the line y=k. Given that the
volume of the solid
generated when the shaded
region is revolved 360o
about the y-axis is 2 unit3
, find the value of k.
(b) A curve with minimum point ( )4
14,
6
5 has a
gradient function mx – 5.
Find
(i) the value of m,
(ii) the equation of the curve
[ kk (2 <4) ; m = 6 ]
10. Given
2
0
( )f x dx = 17, where f(x) is a linear function.
(a) Find the value of k when
0
2
[ ( ) ]f x k dx = 1.
(b)
Diagram 4 shows the graph of the straight line y =
f(x) which intersects the curve y = (x – 5)2 at the
point P(2, 9).
(i) Find the area of the shaded region.
(ii) Calculate the volume generated, in terms of
, when the area bounded by the straight line
OP, the curve and the x-axis is revolved
through 360o about the x-axis.
11. Table 1 shows the frequency distribution of the scores
of a group of 40 pupils in a quiz.
Score
Number of
pupils
10 – 19
20 – 29
30 – 39
40 – 49
50 – 59
60 – 69
1
2
h
12
4
k
(a) It is given that the median
score of the distribution is 42, find the value of h
and of k.
(b) State the modal class of the distribution.
[(a) h = 14, k = 7 (b) 30 – 39]
12. Diagram 2 shows a frequency polygon which
represents the distribution of the scores of 80 pupils in a
test.
(a) Complete the frequency distribution table below.
(b) Calculate the median score.
(c) Calculate the variance of the distribution.
[(b) 22 (c) 29.568]
13. Table 6 shows the marks obtained by a group of
students in a class.
(a) Given that the median mark of a student is
,
find the value of k
(b) Calculate the standard deviation of the distribution.
(c) If each marks of the students in the class is
multiplied by 2 and then subtracted by 3. For the
new set of marks, find the standard deviation.
[a) k=13 b) =18.79 c) 37.58]
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