Oxford Canotta Maths

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New Century Mathematics (Second Edition) 4B

Term Exam Paper S4

Paper 2

Multiple-choice Questions

Time allowed: 1 hour 15 minutes

INSTRUCTIONS

1. Write your Name, Class and Class Number in the spaces provided.

2. All questions carry equal marks.

3. ANSWER ALL QUESTIONS.

4. You should choose only ONE answer for each question. If you choose more than one answer, you will receive NO MARKS for that question.

5. No marks will be deducted for wrong answers.

Section A

1. Which of the following expressions give(s) the result(s) in rational number(s)?

I. p2

II.

III.

A. II only

B. III only

C. I and II only

D. II and III only

2. Which of the following numbers is a purely imaginary number?

A. -4p

C. -8i

D. 1 + i

3. The coordinates of A and B are (2 , 3) and (-2 , 5) respectively. Find the equation of the perpendicular bisector of AB.

A. 2x – y + 4 = 0

B. 2x – y + 8 = 0

C. x + 2y - 4 = 0

D. x + 2y + 8 = 0

4. In the figure, the x-intercepts of the straight lines L1 and L2 are 7 while the y-intercepts of the straight lines L1 and L4 are 4. L3 passes through the origin and the point of intersection of L2 and L4. Which of the following is/are true?

I. The equation of L1 is 4x + 7y - 28 = 0.

II. The slope of L3 is .

III. The equation of L4 is x = 7.

A. I only

B. III only

C. I and II only

D. I, II and III

5. In the figure, the equations of the straight lines L1 and L2 are ax + by = 1 and cx + dy = 1 respectively. Which of the following are true?

I. a > 0

II. d > 0

III. ad > bc

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

6. If the straight lines L1: 4x + ay + 2 = 0 and L2: bx - 3y + 1 = 0 have infinitely many points of intersection, then

A. a = 2 and b = 6.

B. a = 2 and b = -6.

C. a = -6 and b = 2.

D. a = -6 and b = -2.

7. Solve the equation (2x + 1)2 = 9.

A. x = 1

B. x = 4

C. x = -2 or x = 1

D. x = -4 or x = 2

8. Let k be a constant. Solve the equation x + 3k = (x + 3k)(x - 3k + 2).

A. x = 3k + 1

B. x = 3k - 1

C. x = 3k or x = 3k + 1

D. x = -3k or x = 3k - 1

9. Which of the following equations have real roots?

I. x2 + 3x - 1 = 0

II. x2 + 2x + 4 = 0

III. x2 - 8x + 16 = 0

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

10. Let k be a constant. If the quadratic equation 3x2 - 6x + k = 0 has no real roots, find the range of values of k.

A. k > -1

B. k < -1

C. k > 3

D. k < 3

11. Let f(x) = x2 + kx - 2k, where k is a constant. If f(-4) = 4, then k =

A. -2.

B. -1.

C. 1.

D. 2.

12. Let f(x) = x2 + 3x - 5k, where k is a constant. Find 2f(-1) - f(3).

A. -22

B. -5k - 22

C. -5k - 26

D. -15k - 26

13. In the figure, the equation of the graph of the quadratic function is

A. y = -(x - 5)(x + 4).

B. y = -(x + 5)(x - 4).

C. y = (x - 5)(x + 4).

D. y = (x + 5)(x - 4).

14. The figure shows the graph of y = ax2 - 8x + b, where a and b are constants. Which of the following are true?

I. a > 0

II. b 0

III. ab < 16

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

15. The figure shows the graph of the quadratic function y = ax2 + 4x - 16, where a is a non-zero constant. The coordinates of the vertex of the graph are

A. (-1 , -19).

B. (-2 , -20).

C. (-2 , -28).

D. (-3 , -19).

16. Let f(x) be a polynomial. When f(x) is divided by x + 5, the quotient is 2x2 – 3x + 17. If f(-5) = -88, then f(x) =

A. 2x3 + 7x2 + 2x - 3.

B. 2x3 - 3x2 + 17x - 3.

C. 2x3 + 7x2 + 2x + 173.

D. 2x3 + 13x2 + 32x + 173.

17. Let f(x) = (3x - 1)(3x - 4) + 3x + 1. Find the remainder when f(x) is divided by 3x + 1.

A. -10

B. -2

C. 2

D. 10

18. Let k be a constant. If f(x) = x3 + kx - 6 is divisible by x + 2, then k =

A. 0.

B. -1.

C. -6.

D. -7.

19. Let f(x) = x3 + ax2 + bx - 9a, where a and b are constants. If both x + 1 and x - 3 are the factors of f(x), then

A. a = 1 and b = -9.

B. a = -3 and b = 11.

C. a = -8 and b = 16.

D. a = -14 and b = 22.

20. Let f(x) be a polynomial. If f(4) = -2, which of the following must have the factor 2x + 1?

A. f(2x + 1) - 2

B. f(2x + 1) + 2

C. f(2x + 5) - 2

D. f(2x + 5) + 2

21. In the figure, O is the centre of the circle. OM ^ AB, ON ^ CD and ÐAOB = ÐCOD. If AB = 16 cm and ON = 15 cm, find the diameter of the circle.

A. 16 cm

B. 17 cm

C. 32 cm

D. 34 cm

22. In the figure, O is the centre of the circle. COD is a straight line. CD and AB intersect at P such that CD bisects AB. If ÐADC = 35°, find ÐOAB.

A. 20°

B. 35°

C. 55°

D. 70°

23. In the figure, AB and CD intersect at E. AC = BC and = . If ÐACD = 63°, find ÐBED.

A. 39°

B. 54°

C. 63°

D. 78°

24. In the figure, ABCD is a semi-circle. = 2 and ÐABD = 46°. Find ÐCAD.

A. 21°

B. 23°

C. 44°

D. 46°

25. In the figure, DCE is a straight line and DE // AB. If AB = DB and ÐABD = 42°, find ÐCBD.

A. 21°

B. 27°

C. 42°

D. 69°

26. If 135° < x < y < 180°, which of the following must be true?

I. sin x > cos y

II. cos x > cos y

III. tan x > cos y

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

27. =

A. 0

28. If tan q = a and q lies in quadrant III, then sin q × cos q =

A. .

B. .

C. .

D. .

29. Find the maximum and minimum values of y =.

Maximum value Minimum value

A. 4 1

B. 4

C. 8 1

D. 8

30. If tan q = -8, where 0° < q < 360°, then q =

A. 82.9° or 97.1° (correct to the nearest 0.1°).

B. 82.9° or 262.9° (correct to the nearest 0.1°).

C. 97.1° or 262.9° (correct to the nearest 0.1°).

D. 97.1° or 277.1° (correct to the nearest 0.1°).

Section B

31. If k is a real number, then =

A. 3 – 3ki.

B. 3 + ki.

C. –3 – 3ki.

D. –3 + 3ki.

32. The real part of (4 + i3)(i4 – 2i) is

A. –1 – 4i.

B. 2 – 9i.

C. 4 – i.

D. 6 – 7i.

33. Let k be a constant. If a and b are the roots of the equation x2 + 5x – 2k = 0, then b 2 – 5a =

A. 2k + 25.

B. 2k – 25.

C. 2k + 5.

D. 2k – 5.

34. If a ¹ b and , then a3 + b 3 =

A. 44.

B. 24.

C. –24.

D. –44.

35. The figure shows the graph of y = –x2 + ax + b, where a and b are constants. Which of the following is true?

A. a > 0 and b > 0

B. a > 0 and b < 0

C. a < 0 and b > 0

D. a < 0 and b < 0

36. Which of the following statements about the function y = –2(x + 4)2 + 8 and its graph is true?

A. The equation of the axis of symmetry of the graph is x = 4.

B. The y-intercept of the graph is 8.

C. The x-intercepts of the graph are –2 and –6.

D. The minimum value of the function is 8.

37. The figure shows the graph of y = 3–x. Which of the following is/are true?

I. The coordinates of P are (0 , 3).

II. The graph of y = 3x is the image of the graph of y = 3–x when reflected in the y-axis.

III. The graph cuts the x-axis.

A. I only

B. II only

C. I and III only

D. II and III only

38. =

A. ab

39. Let x ¹ 0. If 7x = y, then =

A. 7–y.

B. logy 7.

C. log7 y.

D. logy.

40. The graph in the figure shows the linear relation between log5 y and x. Which of the following expressions can represent the relation between x and y?

A. y = log5 (3x – 3)

B. y = log5

C. y = 53x – 3

D. y =

41. The H.C.F. of 4x3 – xy2, 4x3 – 4x2y + xy2 and 8x4 – xy3 is

A. 2x – y.

B. x(x – y).

C. x(2x – y).

D. x(2x – y)(2x + y)(4x2 + 2xy + y2).

42. In the figure, two circles with centres A and B touches each other externally at T. CD is a common tangent to the two circles, where C is the point of contact of the smaller circle and D is the point of contact of the larger circle. If the diameters of the two circles are 4 cm and 12 cm, find the length of TD.

A. 4 cm

B. 6 cm

C. 8 cm

D. 12 cm

43. In the figure, AB is the tangent to the circle at E. DE and CG intersect at F. If ÐBEF = 52° and
AB // CD, then ÐCGD =

A. 38°.

B. 52°.

C. 72°.

D. 76°.

44. In the figure, ABC is a semi-circle. O is the centre of the circle and O lies on AB. AD and BD are the tangents to the circle at A and E respectively. AB is the angle bisector of ÐCBD. If ÐAFE = 62°, then ÐBAC =

A. 28°.

B. 34°.

C. 56°.

D. 62°.

45. For 0° < q < 360°, how many distinct roots does the equation (sin q + 1)(5 cos q – 4) = 0 have?

A. 2

B. 3

C. 4

D. 5

END OF PAPER

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