perfect score add maths f5 2010 set 4

8/8/2019 Perfect Score Add Maths F5 2010 Set 4

1/13

Perfect Score 2010

Section A

[40 markah]

Answerall

questions.Jawab semua soalan.

1 Solve the simultaneous equation:

Selesaikan persamaan serentak:

2 3 1

1 42

3

h k

h k

.

Give your answers correct to three decimal places.[5 marks]

Berikan jawapan anda betul kepada tiga tempat perpuluhan. [5 markah]

2 (a) Given 3log x p and 9log y q , show that23p qxy and 23p q

x

y

.

[4 marks]

Diberi3

log x p dan9

log y q , tunjukkan bahawa 23p qxy dan 23p qx

y

.

[4 markah]

(b) Hence, if xy = 1 and1

3

x

y , find the value of p and of q . [3 marks]

Seterusnya, jika xy = 1 dan

1

3

x

y , cari nilai bagi p dan q . [3 marks]

3 A curve has a gradient function3

5

h x

x

, where h is a constant. The tangent to the

curve at the point Q(-1, 2) is perpendicular to the straight line passing through points

(2, 4) and (6, -2).

Suatu lengkung mempunyai fungsi kecerunan3

5

h x

x

, dengan keadaan h adalah

pemalar. Tangent kepada lengkung itu di titik Q(-1, 2) adalah berserenjang kepada

garis lurus yang melalui titik-titik (2, 4) dan (6, -2).

FindCari

(a) the value of h. [5 marks]

nilai bagi h. [5 markah]

(b) the equation of the curve at point Q . [2 marks]

persamaan lengkung itu di titik Q. [2 markah]


2/13

4 Diagram 4 shows a few semicircles such that the diameters of the semicircles increaseby 3 cm, in sequence.

Rajah 4 menunjukkan beberapa semibulatan dengan keadaan diameter bagi semibulatan itu

bertambah sebanyak 3cm, secara berturutan.

Diagram 4

Rajah 4

(a) Show that the perimeters of the semicircles form an arithmetic progression and

state its common difference, in terms of . [4 marks]

Tunjukkan bahawa perimeter bagi semibulatan itu membentuksuatu janjang aritmetik

dan nyatakan beza sepunya dalam sebutan . [4 markah]

(b) Given that p = 7 cm and use 3.142 , find the value of n if the nth semicircle is thesmallest semicircle whose perimeter exceeds 100 cm. [4 marks]

Diberi bahawa p = 7 cm dan guna 3.142

, cari nilai bagi n jika semibulatan ke-nadalah semibulatan yang terkecil di mana perimeternya melebihi 100 cm. [4 markah]

5 (a) Sketch the graph of 2sin2y x for3

02

x .

[4 marks]

Lakar graf 2sin2y x untuk3

02

x .

[4 markah]

(b) Hence, by using the same axes, draw a suitable straight line to find the number of

solutions to the equation

1

sin2 2 2

x

x

for

3

0 2x

.State the number of solutions [3 marks]

Seterusnya, dengan menggunakan paksi yang sama, lukis satu garis lurus yang

sesuai untuk mencari bilangan penyelesaian bagi persamaan1

sin22 2

xx

p cm (p + 3) cm (p +6) cm


3/13

untuk3

02

x . Nyatakan bilangan penyelesaian. [3 markah]

6 Diagram 6 shows a parallelogram PQRS.

Rajah 6 menunjukkan suatu segiempat selari PQRS.

Diagram 6Rajah 6

It is given that SQ = 5 ST, SR = 4 SU, 10PQ u

and PS

= 8 v

.

Diberi bahawa SQ = 5 ST, SR = 4 SU, 10PQ u

dan PS

= 8 v

.

(a) Express in terms of u

and v

:

Ungkapkan dalam sebutan u

dan v

:

(i) PT

(ii) TU

[4marks]

[4 markah](b) Hence, determine whether the points P, T and Uare collinear. [2 marks]

Seterusnya, tentukan sama ada titik-titik P, T dan U segaris. [2 markah]

S R

P

Q

T

U

10u

8v


4/13

SECTION B

7. Use graph paper to answer this question.Table 7 shows the values of two variables, x and y, obtained from an experiment. Variables x

and y are related by an equation = + , where m and kare constants.

x 0.5 1.0 1.5 2.0 2.5 3.0 3.5

y 5.1 6.1 6.9 7.6 8.3 8.9 9.5

Table 7

(a) Plot against x , using a scale of 2 cm to 0.5 units on the x axis and 2 cm to 10 unitson the y axis. Hence, draw the line of best fit.

[5 marks]

(b) Use your graph in 7(a) to find the value of(i) m

(ii) k(iii) x when y = 8.0

[5 marks]

8. Diagram 8 shows a straight line = 8 which intersects a curve = at point P.

Diagram 8

(a) State the value ofh . [1 mark]

(b) Find the coordinates of P . [2 marks]

(c) (i) Find the area of the shaded region. [3 marks]

(ii) The region enclosed by the curve, the straight line = 8 andthe y axis is revolved through 360

oabout the y axis .

9P

Qx

y y = 8x

=


5/13

Find the volume of revolution, in terms of .[4 marks]

9. Solution by scale drawing is not accepted.

Diagram 9 shows a triangle ABC. The straight line BC passing through point D.

Diagram 9

(a) A point E moves such that its distance is always 5 units from point D. Find the equation

of the locus of E.

[3 marks]

(b) It is given that point B and C lie on the locus of E. Calculate

(i) the value ofh

(ii) the coordinates of C [4 marks]

(c) The straight line AD is extended to point F(8, - 5). Find the ratio of AD : DF .

[3 marks]

x

y

A(0.3)

B(- 2, h)

C

D(2.1)

O


6/13

10. In Diagram 10, EAC is a sector of a circle with centre A and radius 10 cm. EBD is aquadrant of a circle with centre B.

Diagram 10

It is given that the length of BC = 2 cm.

Use = 3.142 and give the answer correct to two decimal places.Calculate

(a) < , in radian [2 marks]

(b) the perimeter, in cm, of shaded region [4 marks]

(c) the area, in cm2, of the shaded region. [4 marks]

11. (a) A Geography test paper consist of 60 multiple choice questions. Each question have

four choices of answer, where only one is correct.Razak answers 50 questions correctly and randomly choosing an answer for the

remaining 10 questions.Find the probability that he answers

(i) 55 questions correctly,

(ii) at the most 8 questions wrongly.

[5 marks]

(b) The weight of the chocolate cake produced by a bakery is normally distributed with a

mean of 450 g and a standard deviation of 5 g.

(i) Find the probability that the weight of the chocolate cake selected at random is

less than 453 g.

(ii) If 500 chocolate cakes are sold in one week, estimate the number of chocolate

cake which weight more than 445 g.

[5 marks]

AC DB

E

10 cm


7/13

SECTION C

12 Diagram 12 shows two points , A and B , on a straight line, where AB = 4 m.

Diagram 12

A particle P moves along the line so that its velocity , v ms-1, is given by

v = t2

4t 5 , where tis the time in seconds after leaving B. Initially, particle P isat B, moving towards A.

(a) Find an expression , in terms of t, for

(i) the acceleration of P,

(ii) the distance of P from A. [4 marks](b) Find the distance , from A, when particle P comes instantaneously

to rest. [3 marks](c) Find the total distance traveled by P in the time interval of t = 0 to t = 10.[3 marks]

13 A certain type of cake is made by using four ingredients A, B C and D. Table 12shows the prices and price indices of the ingredients used and their weightages.

IngredientsPrice per kilogram (RM) Price Index in 2009

based on 2006Weightage

Year 2006 Year 2009

A 1.20 x 125 4

B 0.60 0.90 150 7

C y z 120 6D 2.00 2.60 130 m

Table 13(a) Find the value ofx. [2 marks]

(b) The price for ingredient C in the year 2009 is RM0.30 more than its

corresponding price in the year 2006.Calculate the value of y and ofz.[3 marks]

(c) The composite index for the cost of making the cake in the year 2009 based on

the year 2006 is 133.

Calculate(i) the price of a cake in the year 2009 if its corresponding price in the year 2006 is

RM10,(ii) the value ofm. [5 marks]

4 m

A B


8/13

14 Use a graph paper to answer this question.

An Art Institution offers two art courses A and B. The number of students for course

A and B is x and y respectively. The enrolment for the classes is based on thefollowing constraints:

I The number of students does not exceed 140.II The number of students for course B is not more than 3 times the number of

students for course A.

III The number of students for course A must exceed the number of students forcourse B by at most 40.

(a) Write down three inequalities other than x 0 and y 0 that define theconstraints above. [3 marks]

(b) By using a scale of 2 cm to 20 students on both axes, construct and shade the

region R that satisfies all the above constraints. [3 marks](d) By using the graph from 13(b), find

(i) the range of the number of students of course A if the number of studentsfor course B is 60.

(ii) the maximum fees collected per month if the fees for course A and B are

RM60 and RM40 respectively and the number of course A students islimited to 50 only. [4 marks]

15 Diagram 15 shows a quadrilateral DEFG.

Diagram 15

Given thatDFDE

= 11 cm,FG

7 cm,

EDF= 50

0

,

FDG = 25

0

.Calculate

(a) EF . [2 marks]

(b) DGF. [2 marks](c) the shortest distance from Eto DG. [2 marks]

(d) the area of quadrilateral DEFG. [4 marks]

D

G

F

E

11 cm

7 cm

250

500


9/13

ANSWER for Section A

1. h = 1.866 , 0.134 ; k = -0.911 , 0.199

2. b) 1 1,4 8

p q

34

5 5 1 31( ) (b)

3 12 12a h y

x x

4. (b) n = 10

5.

Straight line : 1x

y

No. Of solutions = 3

6 (a)32 1 8

( ) 2 (ii)5 2 5

i u v u v

(b) 4PT TU collinear

Answers. For Section B

7. (a) = +

x 0.5 1.0 1.5 2.0 2.5 3.0 3.5y2

26.01 37.21 47.61 57.76 68.89 79.21 90.25

(b) (i) m = 4.608

(ii) k= 0.7537

(iii) x = 2.28

y

-1

-2

2

1

x 3

2


10/13

8. (a) h = 9

(b) P(1, 8)

(c) (i) Area =

(ii) Volume =

9. (a) + 4 2 20 = 0

(b) (i) h = - 2 (ii) C(6,4)

(c) AD : DF = 1 : 3

10. (a) 0.9274 rad

(b) BE = 6 cm , CD = 4 cm

Perimeter shaded = 22.70 cm

(c) Area shaded = 5.91 cm2

11. (a) (i) P(x = 5) = 0.05840

(ii) P( 2) = 0.6621

(b) (i) P( < 453) = 0.7257

(ii) P( > 445) = 0.8413

Number of cakes = 420 or 421

No. Solutions Marks Total marks

12 (a) (i) a = 2t 4

(ii) s =3

t 3

2t2 5t + c

t = 0, s = 4

s =3

t 3

2t2

5t + 4

(b) v = 0

P1

K1

K1

N1


11/13


t2

4t 5 = 0(t + 1) (t 5) = 0

t = 5

s =3)5( 3 -2(5)2- 5(5) + 4

= -293

1

Distance from A = 293

1m

(c) t = 10 , s =3

)10( 3

2(10)2

5(10) + 4

= 87 3

1

Total distance = 4 + 293

1+ 29

3

1+ 87

3

1

= 150 m.

K1

K1

N1

K1

K1

N1 10

13(a)

(b)

(c)(i)

125=10020.1

x

x = 1.50

120=100y

30.0+y

0.2y = 0.3

y = 1.50

z = 1.80

K1

N1

K1

N1

N1

293

1

873

129

3

1

4


12/13


(ii)

133=10010

P09

P09 = RM13.30

133=17+m

m130+)120(6+)150(7+)125(4

m = 3

K1

N1

K1 K1

N1 10

15(a)

(b)

(c)

(d)

0222 50cos111121111 EF

= 86.45

EF= 9.30 cm

025sin7

sin11

DGF

7

25sin11sin

0

DGF

DGF= '37410

Shortest distance = EN

075sin11

EN

EN= 10.625 cm

Area of quadrilateral DEF,D1 =050sin1111

2

1

= 46.35 cm2

Area of quadrilateral DEF,D2 =

000

62.4125180sin7112

1

= 35.34 cm2

Area of quadrilateral DEFG = 46.35 + 35.34

= 81.69 cm2

K1

N1

K1

N1

K1

N1

K1

K1

K1

N110


13/13

0

0

0

160

R

0

0

0

0

0

20 40 60 80 100 120 140

c (i) 20 x 80 N1

(ii) ( 50, 90) N1

K = 60(50) + 40(90) K1

= RM 6600 N1

Correct axes , uniform scaleAnd one line drawn correctly K1

(equation involves x and y)

All lines drawn correctly N1

correct Region N1

I x + y 140 N1

II : y 3x N1

III: x y 40 N1

Q 14

perfect score add maths f5 2010 set 4

Documents