Intensive Rev 4 2009

Intensive Revision Set 4 P2 Additional Mathematics SPM 2009

SBTC@biid

SULIT

3472/2

1.

Solve the simultaneous equations x − 3 y = 4 and

2.

Given that f −1 ( x) = (a) (b)

3 2 + = 1. x y

8    x = 12, y = 3 ; x = 1, y = −1

5 − hx and g ( x) = 5 − 3 x 2 . Find 3 f (x) in terms of h, the value of h if f ( x 2 ) = 4 g (− x) .

5 − 3x 1  (a ) f ( x ) = h , ( b) h = 4 

3.

In a geometric progression, the sum of the first 5 terms is 248 and the sum of the next 5 3 terms is 7 . Find 4 (a) the common ratio and the first term, (b) the nth term of the progression, (c) the 11th term of the progression. 1 1  8− n (a ) r = 2 , a = 128, ( b)Tn = 2 , ( c)T11 = 8 

4.

Table 1 shows the costs of producing a particular type of paper in the years 2005 and 2007.

Item Material A Material B Material C Labour

Cost per unit in 2005 (RM) 0.80 0.50 1.60 0.30

Cost per unit in 2007 (RM) 1.00 0.80 2.40 0.40

Table 1

(a) (b)

Calculate the price index of each of the items used for the year 2007 based on the year 2005. Given that the weightages for material A, B, C and labour are 2, 3, 1 and m respectively. Find (i) the value of m if the composite index for producing this paper in the year 2007 based on the year 2005 is 140.6, (ii) the total cost of producing the paper for the year 2005 if the total cost of producing the paper for the year 2007 is RM8.50.

[(a) 125, 160, 150, 133.33,

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]

(b)(i ) m = 5, (ii ) RM 6.05

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Intensive Revision Set 4 P2 Additional Mathematics SPM 2009

SBTC@biid

SULIT

3472/2

5.

P

R

8.2 cm

5.6 cm

S

11.5 cm 12.4 cm

Q

Diagram 1

In diagram 1, RSQ is a straight line. Given that PQ = 11.5 cm, PR = 8.2 cm, PS = 5.6 cm and QS = 12.4 cm. Calculate (a) ∠PQR , (b) ∠PRS if ∠PRS is an acute angle, (c) two possible angles of ∠PSR and the area of ∠PSR if ∠PSR is an obtuse angle.

[(a) 26 46 o

6.

'

o

(b) 39 10

'

o

o

(c) 67 38' ,112 22' ,10.94cm

2

]

Given that cos θ = − q and θ is a reflex angle. State each of the following in terms of q. (a) cos ecθ (b) tan 2θ π  (c) sin  − θ  2  2   2q 1 − q 1 (b ) (c ) − q  ( a ) − 2 2 2q − 1 1− q  

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