LIU PO SHAN MEMORIAL COLLEGE€¦  · Web view10/11/2009  · F.4D Math. M.C. Exercise (Function & Graph) 1. If g (x) =, then g (1) - g (-1) = A. -2 . D. 1 . B. -1 . E.

F.4D Math . M.C. Exercise (Function & Graph)

1. If g (x) =3x2 - 2kx + k = 0, then g (1) - g (-1) =

A. -2 . D. 1 . B. -1 . E. 2 . C. 0. 2. If g (x) = (x - 1) (1 - x) (2x - 1), then g (1 - x) = A. 0 . D. x2 (2x - 1) . B. 1 . E. x2 . C. x2 (1 - 2x).

3. If f (x) = 3x2 + 8x - 4 = 0 and f (2) = 3, then k = A. -1 . D. 2 . B. -2 . E. 3 . C. 1 .

4. If f (x) = x - 1 , then x2 - x - 3 = 0 = A. 0 . D. (x + 1)

(x2 - x + 1). B. (1 - x)3 . E. 2 x3 . C. (x - 1)3 .

5. If f (x + 2) = x2 - 2x + 4 = kx, then f (x) = A. x2 + 8x + 22. B. x2 + 3x + 8. C. x2 + 6. D. x2 + 4x + 10.

E. none of the above

6. If f (x) = x2 - 2x + 1, then f (2z) = A. (2z - 1)2 . B. 1 - 2 f (z) . C. 2 f (z) . D. 2 f (z) - 1 .

E. none of the above

7. If f (x) = 1

x + 2 , then 3x2 - x - 2 = 0 =

A. x . D. x + 2x + 3 .

B. x + 4 . E. x + 22x + 5 .

C. 1

x + 4 .

8. If f (3x) = 9x2 - (k - 1)x + 4 = 0, then f (2x) = A. 4x3 + 4x . D. 8x3 + 4x . B. 4x3 + 8x . E. 8x3 + 8x . C. 6x3 + 8x .

9. If f (y) =2y2 - 3y + 1, then f (2x) - 2 f (x) = A. 0 . D. (2x + 1) (2x - 1) . B. 3x (2x - 1) . E. none of the

above C. 3x (2x - 3) .

10. If f (x - 3) = x2 - 6x + 10, then f (x) = A. x2 - 6x + 7. B. x2 + 1. C. x2 - 6x + 13. D. x2 - 3x + 10.

E. x2 - 8 .

11. If f (x - 1) = x2 - 2x + 1, then f (x + 1) - f (x) = A. 1. D. 2x + 1. B. 3. E. x2 + 2x + 1 . C. 2x - 1. 12. If f (x) = 4x + 1, then f (x) - f (x - 1) = A. 1 . D. 5 4x-1 . B. 5 . E. 3 4x-1 . C. 4-1.

13. If f (x) = 1 - x and g (x) = x2 - 1, then g [ f (x) ] = A. x2 . D. x2 + 2x. B. 2x. E. (x - 1)2. C. x2 - 2x.

14. If f (x) = x3(x + 1) (x + 2)

, then f (n) - f (n - 1) =

A. n (n + 1) . D. 13(n + 1) (n + 2)

.

B. (n + 1) (n + 2) . E. n3(n + 1) (2n + 1)

.

C. n3 (n + 1)

.

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15. The figure below shows the graph of the function y = ax2 + bx + c. Which of the following is/are true?

(I) a > 0(II) c > 0(III) b2 - 4ac > 0

A. (I) only D. (II) and (III) B. (II) only E. All of them C. (I) and (II)

16. The figure below shows the graph of y = ax2 + bx + c. Which of the following is true?

A. a > 0, c > 0 D. a < 0, c < 0 B. a > 0, c < 0 E. a < 0, b < 0 C. a > 0, b > 0

17. For any real value of x, the maximum value of

1

x2 + 2x + 5 is

A. 1 . D. 14 .

B. 15 . E.

18 .

C. 13.

18. If the points (1 , h) and (-1 , k) lies on the graph of y = 3x2 - 5x - 7 = 0, then b = A. h + k . D. h - k .

B. 1 (h + k)2 . E.

1 (h - k)2 . C. 0 .

19. For any real value of x, the maximum value of 6x - 3x2 is A. -3 . D. 3 .

B. -1. E. 6 .C. 0 .

20. The figure below shows the graph of y = (x - 1)2 + 4. Find the coordinates of the vertex A .

A. (1 , 4) D. (2 , 1) B. (1 , 3) E. (2 , 3) C. (1 , 2)

21. The figure below shows the graph of

y =13x2

is shifted to a new position with the vertex at (2 , 1). Find the equation of the new graph .

A. x2 - 2x + 1

B. 13(x2 - 4x + 5)

C. 13(x2 - 4x + 7)

D. 13(x2 - 2x + 7)

E. 13(x2 - 2x + 5)

22. If the minimum value of x2 - 6x + k is 10, then k = A. 10 . D. 21 . B. 16 . E. 27 . C. 19 .

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y = ax2 + bx + c y

0 x

y = ax2 + bx + c y

0 x

y = (x - 1)2 + 4

x A

y

0 x

x (2,1)

y = 13x2

y

0 x

23. If P (3 , -1) is the lowest point of the graph of y = 2x2 - 5x + k = 0, find the values of a and b .

A. a = -6 , b = 10 B. a = -6 , b = 8 C. a = 6 , b = 10 D. a = 6 , b = 8 E. a = -6 , b = -10

24. The graph of y = ax2 + bx + c is given as shown. Which of the following is/are true? I. a < 0

II. b < 0III. c < 0

A. I only D. II and III B. I and II only E. I , II and III C. I and III

25. If f (x) = x - 1x , then f (x) -

f 1x

=

A. 0 . D. 2x - 1

x

.

B. 2x . E. 21x - x

.

C.

2x .

26. If f (x) =102x, then f (4y) = A. 104y . D. 40y . B. 102+4y. E. 402y . C. 108y .

27. If f (x) = x

1 - x , then f 1

x

f (-x) =

A. -12 . D.

x1 - x2 .

B. -1. E x

x2 - 1

C.

1 - x1 + x .

28. The figure below shows the graph of a quadratic function f (x). If the vertex of the graph is (1 , 3), then f (x) =

A. -3(x - 1)2 + 3 . B. -3(x + 1)2 + 3 . C. -(x - 1)2 + 3 . D. -(x + 1)2 + 3 .

E. 3(x - 1)2 - 3 .

29. If f (x) = x2 - 3x - 1, then f (a) - f (-a) = A. 2a2. D. -6a. B. 2a2 - 2. E. -2. C. 6a.

P. 3

y

x 0 x P(3,-1)

y = x2 + ax + b

x

y

0

y = ax2 + bx + c

x(1,3) y

0x

F.4 D Math . M.C. Exercise (Quadratic Equations)

1. If the equation 3x2 - 2kx + k = 0 has equal roots, where k is a constant, then k =

A. 3 . D. 0 or -3 . B. 4 . E. 0 or 3 . C. 3 or 4 . 2. If the equation (p - 1)x2 - 2x + 1 = 0 has distinct real roots, then A. p < 0 . D. p < 2 . B. p > 0 . E. p 2 . C. p > 2 .

3. If and are the roots of the equation

3x2 + 8x - 4 = 0, then

12 + 1

2 = A. 3.5 . D. 4 . B. 5.5 . E. 6 . C. 7.5 .

4. If and are the roots of the equation x2 - x - 3 = 0, find the value of 3 + 3. A. 2 . D. 8 . B. 4 . E. 10 . C. 6 .

5. For what values of k will the equation x2 - 2x + 4 = kx has real roots ? A. -6 < k < 2 B. -6 k 2 C. k 2 or k - 6 D. k > 2 or k - 6

E. k = 2 or k = -6

6. If m > 1, then the quadratic equation x2 + 2mx + m = 1 has A. two equal roots . B. two unequal real roots . C. a zero and a non-zero root D. no real root

E. a positive and a negative root .

7. If and are the roots of the equation 3x2 - x - 2 = 0, then 8 8

=

A. 2 . D. 16 . B. 4 . E. 64 . C. 8 .

8. If 23 is a root of the quadratic equation

9x2 - (k - 1)x + 4 = 0, then k = A. -13 . D. 13 .

B. -11 . E. 23 .

C. 11 .

9. The quadratic equation in x with roots 1 and (a + 1) is A. x2 - x + a + 1 = 0. B. x2 + x + a + 1 = 0. C. x2 + (a + 2)x + a + 1 = 0. D. x2 - (a + 2)x + a + 1 = 0 . E. x2 + (a + 2)x - (a + 1) = 0.

10. If and are the roots of the equation x2 - 10x + 4 = 0 and > , then - = A. 42 . D. 2 21 . B. 84 . E. 2 21 . C. 21 .

11. Find an equation whose roots are 2 + 2 and 2 - 2 . A. x2 + 4x + 2 = 0 B. x2 - 4x + 2 = 0 C. x2 + 4x - 2 = 0 D. x2 - 4x - 2 = 0 E. x2 - 2x - 4 = 0 12. If and are the roots of the equation x2 - 7x - 1 = 0, find an equation whose roots are

1 and - 13 3

. A. 9x2 - 21x + 1 = 0 B. 9x2 + 21x - 1 = 0 C. 9x2 + 21x + 1 = 0 D. 3x2 - 7x - 1 = 0 E. 3x2 + 7x - 1 = 0

P. 4

13 If the product of roots of the equation

kx2 + (k + 1)x - (k - 1) = 0 is -

45 , find the

sum of the roots .

A. -56 D.

56

B. -45 E. 5

C. -65

14. If one root of the equation x2 + 7x + c = 0 is greater than the other root by 3, find c . A. -3 D. 7 B. -10 E. 10 C. 3

15. If and are the roots of the equation x2 - 5x + k = 0 and : = 3 : 2 , then k = A. 2 . D. 6 . B. 3 . E. 8 . C. 5 .

16. Find the equation whose roots are the reciprocals of the roots of 3x2 - 5x - 7 = 0 . A. 7x2 - 5x + 3 = 0 B. 7x2 - 5x - 3 = 0 C. 7x2 + 5x - 3 = 0 D. 3x2 + 5x + 7 = 0 E. 3x2 - 5x + 7 = 0

17. If the sum of the squares of three consecutive positive integers is 110, then the greatest integer is A. 5 . D. 8 . B. 6 . E. 10 . C. 7 .

18. If and are the roots of the equation

2x2 + 4x - 3 = 0, find

+ .

A. -223 D. -

83

B. -163 E.

23

C. -143

19. For what value(s) of x does the equality

(x + 1) (x - 2)

x - 2 = x + 1 hold ?

A. -1 only B. 2 only C. Any value D. Any value except -1

E. Any value except 2

20. If and are the roots of the equation

x2 - 3x - 1 = 0, find the value of

1 1

+ .

A. -3 D. 23

B. -1 E. 3

C. -13

21. If the simultaneous equations y = x2 - k

y = x

has only one solution , find k .

A. -1 D. 14

B. -14 E. 1

C. -4

22. If

and

2 - h - b = 02 - h - b = 0

33

, then =

A. -b3 . D. -

h3 .

B. b3 . E.

h3 .

C. h .

23. Find the range of values of k such that the equation x2 + (k - 2)x + 1 = 0 has real roots . A. k = 4 B. 0 < k 4 C. 0 k 4 D. k < 0 or k 4

E. k 0 or k 4

P. 5

24. The difference of the roots of the equation

2x2 - 5x + k = 0 is

72 . Find k .

A. -6 D. 3

B. -3 E. 5116

C. -32

25. In the above figure, find the coordinates of the mid-point of AB .

A. - 72 , 35

2

B. - 52 , 25

4

C. - 52 , 37

2

D. 52 , 13

2

E. 72 , 35

2

26. If the equation x2 - 6x + k = 0 has real roots , find all possible values of k . A. k 9 B. k -9 C. k = 9 D. k 9

E. k -9

27. Solve (x - 1) (x - 3) = x - 3 . A. x = 1 B. x = 2 C. x = 0 or 3 D. x = 1 or 3

E. x = 2 or 3

28. In the figure, ABCD is a square of side 10 cm. If AE = AF and the area of △CEF is 20 cm2, which of the following equations can be used to find AF ?

A. x2 + 10(10 - x) + 20 = 100 B. x2 + 20(10 - x) + 20 = 100

C. 12x2 + 10x + 20 = 100

D. 12x2 + 10(10 - x) + 20 = 100

E.12x2 + 10(10 - x)

2 + 20 = 100

29. If (3x –1) (x – a) 3x2 + bx – 2 , then A. a = 2 , b = -1 B. a = 2 , b = -7 C. a = -2 , b = 5 D. a = -2 , b = -5 E. a = -2 , b = -7

30. If , then A. x = -1 . B. x = -1 or 5 . C. x = -2 or 1 . D. x = -5 or 1 . E. x = -5 or 8 .

31.

P. 6

y = x2 y

x 0

A

B

y =-5x + 6

A B

C D

E

F x cm

x cm

32.

P. 7

Answers to F.4D Mathematics M.C. ExercisesFunction & Graph

1. E 2. D 3. B 4. E 5. C 6. A 7. E 8. E 9. D 10. B 11. D 12. E 13. C 14. A 15. E

16. B 17. D 18. E 19. D 20. A 21. C 22. C 23. B 24. C 25. D 26. C 27. D 28. A 29. B

Qudratic Equations

1. E 2. D 3. C 4. E 5. C 6. B 7. A 8. D 9. D 10. D 11. B 12. B 13. C 14. E 15. D

16. C 17. C 18. C 19. E 20. A 21. B 22. E 23. E 24. B 25. C 26. D 27. E 28. D

29. C 30. D 31. E 32. A

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