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]