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# Soalan kuiz matematik tambahan ting empat 2006

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### Soalan kuiz matematik tambahan ting empat 2006

1. 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. 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. 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. 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. 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. 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. 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