2SULIT 3472/1

NAMA: KELAS: 4

SEKOLAH TUN FATIMAH, JOHOR BAHRUPEPERIKSAAN PERTENGAHAN TAHUN 2015MATEMATIK TAMBAHANTINGKATAN 4 Kertas 1 2 jam The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.

1.

2 am an = a m + n

3 am an = a m - n 4 (am) n = a nm 5 loga mn = log am + loga n

6 loga = log am - loga n7 log a mn = n log a m

8 logab =

ANSWER ALL QUESTIONS(80 marks)

1Given F(x) = 2 sin x . Determine the(i) domain and (ii) range of F(x)

F(x)= 2 sin x

F(x)

2

x

90180

(2marks)

2The arrow diagram shows the function f : x - 3 .Find the values of p and q. - 3 xf

p

1f(x)9

13q

Diagram 2

(4 marks)

3Given the function g(x) = { 2x + 1 , x 4 x 3 , x > 4 , find

(a) g(6)

(b) g(-2)

(2marks)

4Given that f:x 5x + 2 and g : x , find(a) The value of x if fg(x) = 13(b) f -1 (4)

(3 marks)

5Given that h(x) = p + q x where q < 0 , p and q are constants, and h2 (x) = 9x 10 , find

(a) the values of p and q

(b) (h-1)2 (x)

(4marks)

6

Given the functions h (x) = 4 5x and h k (x) = 2x + 3, find the function k

(3marks)

7

Sketch the graph of the function f(x) = 2x + 3 - 2, for the domain -3 x 2.f(x)

Statethe range of f(x) corresponding to the given domain

Ox

Diagram 7

(3marks)

8 Given that and - 3 are the roots of the quadratic equation h x2 + 5 x - k = 0, find the values of h and k .

(3marks)

9Given the quadratic equation 9x2 + 12x + 4 =0. Calculate

a) The discriminant

b) The type of roots of the quadratic equation.

(3marks)

10The quadratic equation 4x2 2kx + 16 = 0 has two equal roots.Find the values of k

(2marks)

11Given that and are the roots of the quadratic equation 2x2 - 5 x + h = 0 whereas 2 and 2 are the roots of another quadratic equation 4x2 + k x - 9 = 0.Find the value of h and k.

(4marks)

12A quadratic equation x2 + x = px 4 has two distinct roots. Find the range of values of p

(4marks)

13y

Diagram 11 shows the graph of a quadratic function y= (x+p)2 -1, where p and k are constants.Given (4,k) is the minimum point of the curve.(a)Find the value of p and k(b)Write the equation of the axis of symmetry of the curve

Ox

(4,k)

Diagram 14

(3marks)

14

15The quadratic function f(x) = 5n - (3m + x )2 has a maximum point (-2,10).Find(a) the value of m and n(b)the equation of the curve if it is being reflected through the x axis

.Determine the maximum area given the equation of the Area = 12 + 4x x2

(4marks)

(3marks)

16Find the range of the values of x for (x - 3) 2 3 x

(3marks)

17Given y = m x - 2 is the equation of a tangent to the curve y = x2 + 2. Find the possible values of m

(3marks)

18Diagram 18 shows the graph of y = 3k k x x2 . Find the range of values of k

y

Ox

Diagram 18

(3marks)

19Express the quadratic function g(x) = 2x2 + 8x 7 in the form of g(x) = 2(x + p)2 + q, where p and q are constants. Hence,state the values of p and q

(3 marks)

20Solve the equation 813x =

(3marks)

21

Express 42n+1 + 42n - 12 ( 42n-1) to its simplest form

(3marks)

22Solve the equation 2 + =

(3marks)

23Given that + , express t in terms of w

(4marks)

24Solve the equation 6x+2 = 7 3x+1

(4marks)

25Given that = m and = n, express in terms of m and n

(4marks)

25

(4marks)

23

(3marks)

24

(3marks)

25

(4marks)

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