Modul Cuti pt3

PFS/MATHEMATICS/PT3/2015

ANSWER ALL QUESTIONS

1 State each of the following numbers correct to the nearest ten thousand.

(a) 12 345

(b) 27 536

(c) 65 000

(d) 343 629

2 Find all the factors of the following numbers.

(a) 18

(b) 25

(c) 40

(d) 63

3 Find the highest common factor of the following numbers.

(a) 15 and 21

(b) 12 and 30

(c) 18, 24 and 54

(d) 45, 75 and 105

4 Calculate each of the following.

(a)(1 14−12 )× 8

15

(b)( 58 + 1

6 )÷(3 14−2 23 )

(c)214−11128

× 613

(d)512+1 23÷ 310

−4 59

1


4 (a) Jasmin bought a skirt at a discount of 15% of the original price. If the original price is

RM78, calculate the discount offered.

(b) The total price of a gold chain and a ring is RM1 350. If the price of the gold ring is

20% less than that of the gold chain, calculate the price of the gold ring.

6 In the following diagrams, HK and MN are two straight lines. Find the values of x and y.

(a) (b)

(c) (d)

7

In the diagram, PQR is an equilateral triangle. HRK and PQT are straight lines. Determine the values of x and y.

2

x

y


8

In the diagram, AEPT is a rhombus. EHLP and PMRT are squares with sides of length 5 cm

each. Calculate

(a) the perimeter of the whole figure,

(b) the area of the whole figure.

9 Calculate each of the following:

(a) [(–

23 ) + (–

49 )] × (–

34 ) (b) (–

910 ) × (

56 – 1

19 )

(c) [(–3

23 ) ÷ (–1

47 )] –

19 (d) (

13 – 1

25 ) ÷ [

25 – (–

815 )]

10 Calculate the value of each of the following:

(a) (–15.2) × [2.83 + (–0.13)] ÷ (–2.4)

(b) [5.18 – (–26.8)] ÷ 15 – 1.67

(c) [49.16 – (–5.78)] ÷ 4 + (–2.12)

(d) [(–4.07) × (–8) + (–2.8)] ÷ 6

12 Calculate the value of the following:

(a) √0 .0016

(b) (√0 .81 + 3√0 .125 )2

3


(c) (√225 – 33)2

(d) (3√8 ÷

√2536 )

13 Solve each of the following linear equations.

(a) 3x + 2 = 2x + 3 (b) 7y – 5 = 4y + 7

(c) 5m + 6 = m + 4 (d) 4n – 9 = 6 – n

(e)

5t6 – 6 =

7 t12 – 10 (f)

3u5 + 3 = –9 +

u3

(g)

7v4 + 15 = 5 +

4 v3 (h)

6w7 – 4 =

3w14 – 10

14 Calculate the values of x and y in the following cases.

(a) x : y = 2 : 5 and x + y = 42

(b) x : y = 8 : 15 and x + y = 115

(c) x : y = 20 : 11 and x + y = 279

(d) x : y = 33 : 16 and x + y = 539

15 In a study, the colour of cars owned by workers of a firm shows that the number of white

cars, red cars and blue cars are in the ratio 10 : 4 : 3. Given that the number of white cars

exceeds the number of red cars by 42. Calculate

(a) the number of white cars,

(b) the total number of cars owed by the workers.

16

Based on the diagram, find the coordinates of the midpoint of the straight line joining points

4


(a) P and Q

(b) R and S

(c) T and U

(d) V and W

17

In the diagram, the midpoint of EF lies on the x-axis. Calculate(a) the value of t,

(b) the distance between point E and point N.

18 Calculate the perimeter of the following shaded regions.

(a) (b)

(c) (d)

19 Copy and complete the table below.

Radius Diameter Circumference Area of circle

5


(a) 14 cm

(b) 11.2 m

(c) 484 mm

(d) 1 207.36 cm2

20 For each of the following shaded regions, calculate its

(i) area (ii) perimeter

(a) (b)

(c) (d)

21 The diagram shows a triangle EFG drawn on a Cartesian plane. If triangle E'F'G' is the image of

the triangle EFG under the translation

(4 ¿ ) ¿¿

¿¿, write down the coordinates of E', F' and G'.

22

6


In the diagram, the surface area of the prism is 648 cm2. Calculate the

value of x.

23

The diagram shows a solid consisting of two cylinders X and Y. The axes of the cylinders are

the same. The curved surface areas of both the cylinders are also the same.Calculate

(a) the height of cylinder X.

(b) the total surface area of the solid.

(Use π =

227 )

24

In the diagram, PMU is a straight line. Calculate the values of f and h.

7


25

In the diagram, FJK is a straight line. Find the values of x and y.

26

In the diagram, EF is parallel to GH. Find the value of x.

27

The diagram shows a square KLMN and a regular hexagon KPQNRS. KPF and LFN are straight

8


lines. Calculate the values of x, y and z.

28 In the following diagrams, O is the centre of the circle. Find the size of the angles that are

represented by the letters.

(a) (b)

(c) (d)

29

In the diagram, the length of the minor arc LQ is four times the length of the minor arc FH.

FJW, FMNQ, HJML, LNS and WSK are straight lines. Find the values of x, y and z.

9

z


30 The table below shows the number of new teachers who are placed in a school.

(a) Copy and complete the table below.

(b) Construct a pie chart to represent the data.

31

The pictogram shows the number of oranges sold by Chuen Thau in a day.

(a) One grade A, grade B and grade C orange is sold at 80 sen, 70 sen and 55 sen

respectively. Calculate the amount of money received by selling all the oranges in that

day.

(b) If the information given in the pictogram is represented by a pie chart, calculate the

angle of sector representing the total number of grade B oranges sold on that day.

32

The number of letters delivered to each of the 50 houses in a residential area is shown in the

table above.

Determine the

(a) mode (b) median (c) mean

10

Grade A

Grade B

Grade C

represents 40 oranges

Subject Frequency Angle of sector

Malay 2

English 3

Mathematics 5

Geography 1

Science 4

Number of letters 0 1 2 3 4 5

Number of houses 4 13 16 8 5 4


33

(a) Calculate the value of ( 925 )−

12

.

(b) Simplify 3h7k–3 ÷ 6h4k3.

(c) Find the value of

(d) Simplify (9m–2p)2 ÷ (3m4p–5)3.

(e) Calculate the value of 0.00823

.

(f) Simplify (3k5w–4)3 ÷ k–3w6.

34 Simplify each of the following:

a) (3x – 7)(y + 2) – 4y(x – 3)

b) 2(p2 + 4q2) – 5(p – 2q)2

c)

12 [(h + 2)2 + (8 – h)2]

d) 9a(a – 2b) – (4a – b)2

35 Factorise completely.

a) 3ac – 2ab

b) 3m2n2 – 9mn3 + 15n4

c) 9h2 – k2

d) 169m2 – 100n2

e) 2ab + bc – 2cd – 4ad

f) 2hk – 8km – hn + 4mn

36 Copy and complete the table below.

11

Formula Subject

s = px – q p =

m =

7 xyz + 4

y =

p = 3√r + 3 r =

w= t2 xy

t =


37

It is given that

1p =

4m –

1n .

a) Express

(i) p in terms of m and n.

(ii) m in terms of n and p.

b) Find

(i) the value of p when m = 8 and n = 3.

(ii) the value of m when n = 10 and p = 6.

38

Given that

14 g =√2− 3y , find y in terms of g.

39 Given that 4e(t + 3e) = 3f(t – 2e), express t in terms of e and f.

40

The diagram shows an oil tank consisting of a cylinder and a hemisphere. The radius and

height of the tank are 7 m and 14 m respectively. By taking π =

227 , calculate the volume of

the oil tank.

41

The diagram shows a solid cylinder with radius 7 cm and height 12 cm. A circular cone with

radius 3 cm and height 7 cm is removed from the solid. By using π =

227 , calculate the volume

12


of the remaining solid.

42

The diagram shows a scale drawing of a tower with a height of 225 m. Find the scale of the

drawing.

43

In the diagram, the regular hexagon FGHSTE is the image of the regular hexagon PQRSTU

under a reflection. The regular hexagon PJKLMN is the image of the regular hexagon PQRSTU

under an enlargement with a scale factor 3.

(a) State the axis of the reflection.

(b) Given that the area of the regular hexagon PQRSTU is 13 cm2. Calculate the area of the

shaded region.

44 Solve the following simultaneous linear equation

(a) 3m + n = 2

5m −3n = −20

(b) 4p + t = −14

p −

15 t = 1

(c) 2h + 3j = 5

3h – 4j = 33

(d) x – 2y = 13

2x − y = 11

13


45 List all the integer values of f that satisfy both the inequalities 3f + 4 < 5 (4 − f) and

4f − 7 ≥ 2f − 13.

46 Given that y is an integer that satisfies the inequalities 17 − 5y ≥ 2 and 4 − 7(y + 2) < 11. Find

all the values of y.

47

The diagram shows the graph of a function. Find

(a) the value of y when

(i) x = 3, (ii) x = −2.

(b) the value of x when

(i) y = 10, (ii) y = −20.

14


48 Copy and complete the table of values for the function y = x2 − 4x + 3.

By choosing suitable scales, draw the graph of the function y = x2 − 4x + 3 for 0 ≤ x ≤ 5.

From the graph, find

(a) the value of y when x = 3.5,

(b) the value of x when y = 6.

49

The diagram shows the positions of three towns which are connected by a straight road. At

0830 hours, a bus departed from G to N via L. The average speeds of the bus for the journey

from G to L and from L to N are 60 km/h and 80 km/h respectively. Calculate

(a) the average speed of the bus for the entire journey from G to N,

(b) the time, in the 24-hour system, when the bus arrives at N.

50 An aircraft travels at a speed of 800 km/h from Kuala Lumpur to Manila.

(a) The distance between Kuala Lumpur and Manila by air is 2 500 km. Calculate the time, in

hour and minute, taken by the aircraft to travel from Kuala Lumpur to Manila.

(b) From Manila, the aircraft departed for Taipei at the same speed. If the time of flight from

Manila to Taipei is 4 hours, calculate the distance between Manila and Taipei by air.

“IT’S YOUR ROAD…..AND YOURS ALONE…..

OTHERS MAY WALK IT WITH YOU, BUT NO ONE CAN WALK IT FOR YOU……”

15

x 0 1 2 3 4 5

y 0 8

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Modul Cuti pt3