Form 4 - 2007 - Module - Terengganu - Additional Mathematics - 03

8/13/2019 Form 4 - 2007 - Module - Terengganu - Additional Mathematics - 03

1/10

ADDITIONAL MATHEMATICS

FORM 4

MODULE 3

INDICES AND LOGARITHMS

COORDINATE GEOMETRY

PANEL

EN. KA MARUL ZA MAN BI N LONG SMK SULTAN SULAIMAN, K. TRG.

EN. MOHD. ZULKIFLI BIN IBRAHIM SMK KOMPLEKS MENGABANG TELIPOT, K. TRG

EN. OBAI DILLAH BI N ABDULLAH SM TEKNIK TERENGGANU, K. TRGPUAN NORUL HUDA BT. SULAIMAN SM SAINS KUALA TERENGGANU, K. TRG.

PUAN CHE ZAINON BT. CHE AWANG SBP INTEGRASI BATU RAKIT, K. TRG.

MODUL KECEMERLANGAN AKADEMIK

TERENGGANU TERBILANG 2007

P R O G R A M P R A P E P E R I K S A A N S P M


2/10

5 INDICESAND LOGARITHMS

PAPER 1

1 Simplify3

32

27

93

x

xx

.

Answer :

2 Express )5(1555 12212 xxx to its simplest form.

Answer :

3 Show that 7

x

+ 7

x + 1

21(7

x 1

) is divisible by 5 for all positive integers ofn .

Answer :

4 Find the value ofa if log a 8 = 3.

Answer : a= ..

5 Evaluate 55log5 .


3/10


4/10

Answer :

10 Solve the equation log 3 (2x + 1) = 2 + log 3(3x 2).

Answer :

PAPER 2

11 The temperature of an object decreases from 80C to TC aftertminutes.Given T= 80(08)t. Find(a) the temperature of the object after 3 minutes,

(b) the time taken for the object to cool down from 80C to 25C.

12 (a) (i) Prove that 9log ab = 3 31

log log )2

( b .

(ii) Find the values ofa and bgiven that 3log 4 ab and 2

1

log

log

4

4 b

a.

(b) Evaluate

1

1

5

3(5 )

n

n

.

13 The total amount of money deposited in a fixed deposit account in a finance company after a period

ofnyears is given by RM20 000(104)n .Calculate the minimum number of years needed for theamount of money to exceed RM45 000.

14 (a) Solve the equation 5log

644 x

.


5/10

(b) Find the value of xgiven that og 5 log 135x x

= 3.

(c) Given2

5loglog 42 ba . Expressain terms ofb.

15 (a) Solve the equation 3 16og log (2 1) log 4x .

(b) Given that 3log 5 a and 3log 7 , find the value ofp if2

3log 3

bap

.


6/10

6 COORDINATE GEOMETRY

PAPER 1

1 Given the distance between two pointsA(1, 3) andB(7, m) is 10 units. Find the value ofm.

Answer : m=

2 Given pointsP(2, 12),Q(2,a) andR(4, 3) are collinear. Find the value ofa.

Answer : a =

3 Find the equation of a straight line that passes throughB(3,1) and parallel to 5x 3y= 8.

Answer :


7/10

4 Find the equation of the perpendicular bisector of pointsA(1, 6) andB(3,0).

Answer :

5 GivenA(p, 3),B(3, 7),C(5,q) andD(3, 4) are vertices of a parallelogram. Find(a) the values ofpandq,

(b) the area ofABCD.

Answer: (a) p =

q =

(b) .

6 The pointsA(h, 2h),B(m,n) and C(3m, 2n) are collinear.B dividesACinternally in the ratio of

3 : 2. Express m in terms ofn.

Answer :


8/10

7 The equations of the straight linesABandCD are as follows:

AB : y= hx+ k

CD: 36

hx

ky

Given that the lines AB andCD are perpendicular to each other, expresshin terms ofk.

Answer :

8 Given pointA is the point of intersection between the straight lines 32

1 xy andx+ y = 9.

Find the coordinates ofA.

Answer :

9 Find the equation of the locus of a moving pointPsuch that its distance from pointR(3, 6) is5 units.

Answer :


9/10

10 Given pointsK(2, 0) and pointL (2, 3). PointPmoves such thatPK: PL = 3 : 2.Find the equation ofthe locus ofP.

Answer :

PAPER 2

11 Given C(5,2) andD(2, 1) are two fixed points. PointPmoves such that the ratio ofCPto PD is2 : 1.

(a) Show that the equation of the locus of pointPis 034222 yxyx .

(b) Show that pointE(1, 0) lies on the locus of point P.(c) Find the equation of the straight lineCE.

(d) Given the straight lineCEintersects the locus of pointPagain at pointF, find the coordinates

of pointF.

12 Given pointsP(

2,

3),Q(0, 3) andR(6, 1).(a) Prove that anglePQRis a right angle.

(b) Find the area of trianglePQR.

(c) Find the equation of the straight line that is parallel toPRand passing through point Q.

13 The diagram above shows a quadrilateralKLMNwith verticesM(3, 4) andN(2,4).Given theequation ofKL is 5y = 9x 20. Find

(a) the equation ofML,

(b) coordinates of L,(c) the coordinates ofK,

(d) the area of the quadrilateralKLMN.

x

M(3, 4)

N(2,4) K

L

0

y


10/10

14 In the above diagram,PQRSis a trapezium.QRis parallel toPSand QRS= PSR = 90.(a) Find

(i) the equation of the straight lineRS,(ii) the coordinates ofS.

(b) The linePQproduced meets the line SR produced atT.Find(i) the coordinates ofT,

(ii) the ratio ofPQ : QT.

15 The above diagram shows a rectangleABCDwith verticesB(3, 3),A andCare points On thex-axis

andy-axis respectively. Given that the equation of the straight line AB is 2y =x + 3, find(a) the coordinates ofA,

(b) the equation ofBC,

(c) the coordinates ofC,(d) the area of triangleABC,

(e) the area of rectangleABCD.

C

B(3,3)

A

D

0 x

y

Q(2, 7)

P(0, 1)

R(10, 11)

S

0 x

y

Documents

Form 4 - 2007 - Module - Terengganu - Additional Mathematics - 03