assignment pelajar add math f4

LATIHAN TOPIK 1 : FUNGSI

1. The function f and g are defined by and

respectively. If the composite function fg is given by ,

find (a) the value of b and of c.

(b) the value of .

2.(a) The function f is defined by . Find

(i)

(ii)

(b) Given the functions and , find the

value of p and of q.

3.

The above arrow diagram represents a function , Find

(a) the value of h and of k,(b) the value of x such that the function f is undefined.(c) the image of 10(d) the object that has the image -10.

4. Given the functions and , find

(a) (a) ,

(b) the value of

5. Given the function and , find the value of k for each

of the following cases:

(a) (a)

(b) (b)

LATIHAN TOPIK 2 & 3 : PERSAMAAN & FUNGSI KUADRATIK

x f h

x k7

-5

5

-1

6. Express 2x2 – 5x – 2 = 0 in the form of a(x – p)2 + q = 0. Hence,

solve the quadratic equation .

7.(a) Given that α and β are the roots of the quadratic x2 + 4x + 7 = 0. Form a quadratic equation with roots α – 1 and β – 1 .

(b) Given that α and β are the roots of the quadratic 2x2 + 5x + 10 = 0. Form a quadratic equation with roots α + 1 and β + 1 .

(c ) Given that α and β are the roots of the quadratic 3x2 - 6x + 1 = 0.

Form a quadratic equation with roots and .

8.(a) Given the quadratic equation 2x2 – 6x = 3px2 + p . Find the range of values of p if the quadratic equation has two distinct roots.

(b) Given the quadratic equation 4x2 + p = 3(2x – 1). Find the range of values of p if the quadratic equation has no roots.

(c) Given the quadratic equation x2 = 2(2-m)x + 4 - m2. Find the range of values of p if the quadratic equation has two different roots.

9.Find the values of k if the quadratic equation has

two equal roots.

10.(a)

Given that 5 and are the roots of the quadratic equation

. Find the value of m and n.

(b)Given that 3 and are the roots of the quadratic equation

. Find the value of m and n.

(c) Given that -2 and 6 are the roots of the quadratic equation . Find the value of k and n.

11. One of the roots of quadratic equation is

reciprocal of the other root. Find the values of k and the roots of the quadratic equation.

12. Form the quadratic function in the form of

, hence, find the minimum or maximum point.

13. Find the minimum or maximum point of the graph of quadratic

function .

14.(a)

14(b)

The diagram shows a graph of quadratic function

, where p and q are constant. Find the value of

p, q and k. Hence, state the equation of the axis of symmetry of the graph.

The diagram shows a graph of quadratic function

, where p and q are constant. Find the value of p,

q and n.

15. Find the range of x in each of the following (a)

(b)

(c) and f(x) is always positive.

(d)

16. Find the range of x if the quadratic function

never touches the x-axis.

17. y

x

0 A(3,m)

B

Diagram 1 shows the curve of a quadratic function f(x) = -x2 – nx +4.

The curve has a maximum point at A(3,m) and intersects that f(x)-

axis at point B.

(a) State the coordinates of point B.

(b) By using the method of completing the square , find the

value of m and n.

2. y

x

0

Q(k, m)

Diagram 2 shows the curve of a quadratic function f(x) = x2 + 5x - 3.

The curve has a minimum point at Q(k, m). By using the method of

completing the square , find the value of k and m.

LATIHAN TOPIK 4 : PERSAMAAN SERENTAK

1. Solve the simultaneous equations and




5.Solve the simultaneous equations and

6.Solve the simultaneous equations and

7.Solve the simultaneous equations

8. Solve the simultaneous equations



.Give your answer correct to three significant

figures11.

Solve the simultaneous equations and


.

Give your answer correct to two decimal places.13. Given that (-1, ) are the solutions to the simultaneous

equations

,find the values of and .

14. Find the coordinates of the points of intersection between the

line and the curve

assignment pelajar add math f4

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