This document contains 30 multiple choice mathematics questions related to quadratic equations, functions, and their inverses. The questions cover topics such as finding the inverse of a function, determining the roots of a quadratic equation, finding the range of values for variables in equations, and relating the roots and coefficients of related quadratic equations.

1. 1. Given that f:(x) → 2x + 3, find f –1(x).
[2 marks]
2. If function g : x → 6 x + 4, find the object which is mapped onto itself.
[2 marks]
3. Given that function g ( x) = 5 − 4 x. Find g 2 ( x) .
[2 marks]
4. Cari julat nilai-nilai x dengan keadaan 2x2 - 4x + 3 ≤ 3x – 2
[2 marks]
5. Diberi α dan β adalah punca-punca untuk persamaan 5 + 4x – x2 = 0. Tentukan
nilai bagi α+β dan αβ.
[2 marks]
1

2. 6. Diberi f:x 3x – 4. Cari ff(x)
[3 marks]
7. Determine the roots of the following quadratic equation:
3 x 2 + 14 − 9 = 0
[3 marks]
8. Form the quadratic equations from its roots:
2 2
and
3 5
[3 marks]
9. Find the range of values of p if the quadratic equation below has no real roots.
−3 x − p + 3 x 2 = 0
[3 marks]
2

3. 10. If p and q are the roots of equation 3 x 2 − 4 x + 1 = 0 , form an equation with roots
4 p − 1 and 4q-1.
[3 marks]
11. Find the range of values of x if 6x2 + x ≤ 2.
[3 marks]
12. If m+1 and n-2 are the roots of the equation x(x+3)=10, find the possible values of
m and n.
[3 marks]
13. The function f ( x) = a − ( x − b) 2 has a maximum point of (2,-1). State the values
of a and b.
[3 marks]
14. Find the range of values of x if 3(2 x 2 + x) ≥ 6 − 2 x
[3 marks]
3

4. 15. Find the range of values of m if x 2 + mx − m + 3 = 0 .
[3 marks]
16. Given that 2 is a root of the quadratic equation x − kx − 10 = 0 ,
2
find the value of k.
[3 marks]
x+2
17. Given that f ( x) = , find f −1 (3)
x −1
[3 marks]
18. Given that f ( x) = 4 x − 9 and g ( x) = 3x + 5 , find the value of x such that
gf(-x) = -34.
[3 marks]
2
−1
19. Given that g ( x ) = , x ≠ −m and f ( x) = 4 + 2 x . Find the value of m if
m+ x
g −1 (3m) = f (m 2 − 3)
[3 marks]
4

5. x
20. Solve the equation x + 2 = .
x−4
[3 marks]
21. Given that the quadratic equation (a + 2)x2 – 6ax + 9 = 0 has two equal and real
roots, find the possible values of a.
[4 marks]
22. Find the range of values of k such that the quadratic equation x2 + 3x = 1 – k has
no real roots.
[4 marks]
23. Find the range of values of p if the quadratic equation 3x2 + 5x + p = 0 has two
distinct and real roots.
[4 marks]
5

6. 24. Given the functions f ( x) = px + q , g ( x) = ( x − 1) 2 + 5 and fg ( x) = 3( x − 1) 2 − 2 ,
find the values of p and q.
[4 marks]
25. Given that g(x) = 3x – 2 and h(x) = 4x + 1, find g-1h.
[4 marks]
26. A function is defined by f(x) = a + bx. Given that f(-1) = 7 and f(3) = -13, find the
values of a and b.
[4 marks]
27. Given that α and β are the roots of the quadratic equation 2x2 + 4x + p = 0 and
α-3β = 0, find the values of α, β and p.
[4 marks]
28. If α and β are the roots of the quadratic equation 3x2 – 4x + 6 = 0, form the
3 3
quadratic equation whose roots are + .
α β
[4 marks]
6

7. 29. Find the range of values of m if the straight line y = mx – 4 does not intersect the
curve y = -4x2- 5.
[4 marks]
−3
30. Show that the quadratic equation kx2 + (2k + 3)x + k = 0 has real roots if k ≥ .
4
[4 marks]
END OF QUIZ
7