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  1. Higher Mathematics Objective Questions

  2. Objective Questions

  3. y 2 1 x answer 90 180 270 360 Set 1 • The exact value of tan is: • The period of tan3xo, x є R , is: 3. This diagram is most likely to be part of the graph of:

  4. The exact value of tan is: The period of tan3xo, x є R , is: 3. This diagram is most likely to be part of the graph of: y 2 1 x 90 180 270 360 Set 1

  5. Set 2 y 2 1 answer x 90 180 270 360 • Which of the following has (have) a negative value: • The minimum value of occurs when x is: 3. Which of the following could be this graph:

  6. Which of the following has (have) a negative value: The minimum value of occurs when x is: 3. Which of the following could be this graph: Set 2 y 2 1 x 90 180 270 360

  7. y √2 x answer 360 180 270 90 -√2 Set 3 • Which of the following is/are solution(s) of sin2x = 1, x є R: • If has a maximum value when θ is: 3. The line with equation y = -1 intersects the curve y = √2sinx , at :

  8. Which of the following is/are solution(s) of sin2x = 1, x є R: If has a maximum value when θ is: 3. The line with equation y = -1 intersects the curve y = √2sinx , at : y √2 x 360 180 270 90 -√2 Set 3

  9. The exact value of cos is: The maximum value of occurs when x = t. What is the value of t? 3. This diagram is most likely to be part of the graph of: y 2 x 360 540 180 answer -2 Set 4

  10. The exact value of cos is: The maximum value of occurs when x = t. What is the value of t? 3. This diagram is most likely to be part of the graph of: y 2 x 360 540 180 -2 Set 4

  11. The exact value of sin (-120o) is: 2. If has a minimum value when θ is: 3. The line with equation y = √3 intersects the curve y = 2cosx , at : y 2 answer x 360 180 540 -2 Set 5

  12. The exact value of sin (-120o) is: 2. If has a minimum value when θ is: 3. The line with equation y = √3 intersects the curve y = 2cosx , at : y 2 x 360 180 540 -2 Set 5

  13. y 1 x 90 180 270 360 -1 answer Set 6 • The exact value of cos 135o is: 2. The largest possible domain of, is: 3. This diagram is most likely to be part of the graph of:

  14. The exact value of cos 135o is: 2. The largest possible domain of, is: 3. This diagram is most likely to be part of the graph of: y 1 x 90 180 270 360 -1 Set 6

  15. Which of the following graphs represents y = -f(x + 2): A B C D The exact value of cos is: 3. Functions f and g , are given by f(x) = 3x2 + 1 and g(x) = x2 - 4. Find an expression for f(g(x)). y y y y (1,5) (5,4) (3,2) Set 7 (3,2) (-1,3) (-3,2) (3,2) (-3,2) x x -5 1 x -5 (-1,-1) Y = f(x) (-3,-3) y x (-1,5) 3 -3 (5,-2) (-3,2) (3,2) x 5 answer

  16. Which of the following graphs represents y = -f(x + 2): A B C D The exact value of cos is: 3. Functions f and g , are given by f(x) = 3x2 + 1 and g(x) = x2 - 4. Find an expression for f(g(x)). y y y y (1,5) (5,4) (3,2) Set 7 (3,2) (-1,3) (-3,2) (3,2) (-3,2) x x -5 1 x -5 (-1,-1) Y = f(x) (-3,-3) y x (-1,5) 3 -3 (5,-2) (-3,2) (3,2) x 5

  17. For which real values of x is the function defined on the set of real numbers? The minimum value of occurs when x is: 3. The line with equation y = 2 intersects the curve y = 1 - 2sinx , at : Set 8 y 3 answer x 360 180 -1

  18. For which real values of x is the function defined on the set of real numbers? The minimum value of occurs when x is: 3. The line with equation y = 2 intersects the curve y = 1 - 2sinx , at : Set 8 y 3 x 360 180 -1

  19. Which of the following is/are solution(s) of 2sin2x = √3: Which of these would be the exact value of ? 3. Functions f and g , are given by f(x) = x2 – 2x and g(x) = -3x. Find an expression for f(g(x)). answer Set 9

  20. Which of the following is/are solution(s) of 2sin2x = √3: Which of these would be the exact value of ? 3. Functions f and g , are given by f(x) = x2 – 2x and g(x) = -3x. Find an expression for f(g(x)). Set 9

  21. y Y = f(x) (-2,3) x 1 -4 y y y y (1,1) (-4,1) (2,7) x (-3,6) (3,6) (-2,-5) (4,1) Set 10 (-1,1) x x x -5 0 0 5 answer • Which of the following graphs represents y = -2f(x) + 1: A B C D 2. Given that then g-1(x) equals: 3. Functions f and g, are given by and g(x) = x2 - 1. Find an expression for f(g(x)).

  22. y Which of the following graphs represents y = -2f(x) + 1: A B C D 2. Given that then g-1(x) equals: 3. Functions f and g, are given by and g(x) = x2 - 1. Find an expression for f(g(x)). Y = f(x) (-2,3) x 1 -4 y y y y (1,1) (-4,1) (2,7) x (-3,6) (3,6) (-2,-5) (4,1) Set 10 (-1,1) x x x -5 0 0 5

  23. 1. The largest possible domain of, is: 2. The minimum value of occurs when x = t. What is the value of t? 3. The line with equation y = 1 intersects the curve y = 4sin2x , at : answer Set 11

  24. 1. The largest possible domain of, is: 2. The minimum value of occurs when x = t. What is the value of t? 3. The line with equation y = 1 intersects the curve y = 4sin2x , at : Set 11

  25. y Which of the following functions represents the black curve: A. y = g(-x) + 2 B. y = -g(x) - 2 C. y = 2 – g(x) D. y = g(x – 2) 2. Given that then h-1(x) equals: 3. Functions f and g, are given by and g(x) = 1 + x. Find an expression for g(f(x)). (-1,5) (1,3) y = g(x) x (1,-1) (-1,-3) Set 12 answer

  26. y Which of the following functions represents the black curve: A. y = g(-x) + 2 B. y = -g(x) - 2 C. y = 2 – g(x) D. y = g(x – 2) 2. Given that then h-1(x) equals: 3. Functions f and g, are given by and g(x) = 1 + x. Find an expression for g(f(x)). (-1,5) (1,3) y = g(x) x (1,-1) (-1,-3) Set 12

  27. For which real values of x is the function defined on the set of real numbers? The equation of the straight line through the points (1 , -2) and (-3 , 4) is: A. 3x + 2y = -1 B. 3x – 2y = 7 C. 2x + 3y = -4 D. None of these 3. Which of the following is/are solution(s) of √3tan2x = -1: Set 13 answer

  28. For which real values of x is the function defined on the set of real numbers? The equation of the straight line through the points (1 , -2) and (-3 , 4) is: A. 3x + 2y = -1 B. 3x – 2y = 7 C. 2x + 3y = -4 D. None of these 3. Which of the following is/are solution(s) of √3tan2x = -1: Set 13

  29. The gradient of a straight line parallel to the line x + 3y + 7 = 0 is: 2. Functions f and g, are given by and Find an expression for f(g(x)). 3. The line with equation y = 4 intersects the curve y = 1 - 6sinx , at : answer Set 14

  30. The gradient of a straight line parallel to the line x + 3y + 7 = 0 is: 2. Functions f and g, are given by and Find an expression for f(g(x)). 3. The line with equation y = 4 intersects the curve y = 1 - 6sinx , at : Set 14

  31. The line joining the points (-2,-3) and (6, k) has gradient . The value of k is: 2. Which of the following could be this graph: 3. The minimum value of occurs when x is: answer Set 15 y 4 x 180 -2

  32. The line joining the points (-2,-3) and (6, k) has gradient . The value of k is: 2. Which of the following could be this graph: 3. The minimum value of occurs when x is: Set 15 y 4 x 180 -2

  33. For which real values of x is the function defined on the set of real numbers? Which of the following is the inverse of f(x) = x – 2 , where x є R ? If the points (p , q) , (3 , -2) and (-1 , 4) are collinear, then the relationship connecting p and q could be: A. 2p + 3q = 13 B. 3p – 2q = 5 C. 3p + 2q = 5 D. 3p – 2q = 13 Set 16 answer

  34. For which real values of x is the function defined on the set of real numbers? Which of the following is the inverse of f(x) = x – 2 , where x є R ? If the points (p , q) , (3 , -2) and (-1 , 4) are collinear, then the relationship connecting p and q could be: A. 2p + 3q = 13 B. 3p – 2q = 5 C. 3p + 2q = 5 D. 3p – 2q = 13 Set 16

  35. y Which of the following graphs represents y = f(1 - x) : A B C D 2. Which of the following is the equation of a line perpendicular to the line x - 3y + 4 = 0 A. y = -3x B. y = x C. y = -x D. y = -x 3. Functions f and g, are given by and Find an expression for f(g(x)). y = f(x) 3 (2,1) x -2 y y y y (-2,1) (1,3) (-1,3) (-1,3) 2 x (1,1) (-1,1) (-3,1) -2 x x x x -3 3 1 answer Set 17 x

  36. y Which of the following graphs represents y = f(1 - x) : A B C D 2. Which of the following is the equation of a line perpendicular to the line x - 3y + 4 = 0 A. y = -3x B. y = x C. y = -x D. y = -x 3. Functions f and g, are given by and Find an expression for f(g(x)). y = f(x) 3 (2,1) x -2 y y y y (-2,1) (1,3) (-1,3) (-1,3) 2 x (1,1) (-1,1) (-3,1) -2 x x x x -3 3 1 Set 17 x

  37. The line 2y = 3x + 6 meets the y-axis at C. The gradient of the line joining C to A (4,-3) is: 2. Which of these would be the exact value of ? 3. The line with equation y = 1 intersects the curve y = 3tan2x , at : answer Set 18

  38. The line 2y = 3x + 6 meets the y-axis at C. The gradient of the line joining C to A (4,-3) is: 2. Which of these would be the exact value of ? 3. The line with equation y = 1 intersects the curve y = 3tan2x , at : Set 18

  39. The straight lines with equations ay = 3x + 7 and y = 5x + 2 are perpendicular. The value of a is: 2. Which of the following could be this graph: 3. The maximum value of occurs when x is: y 4 2 x 720 answer Set 19

  40. The straight lines with equations ay = 3x + 7 and y = 5x + 2 are perpendicular. The value of a is: 2. Which of the following could be this graph: 3. The maximum value of occurs when x is: y 4 2 x 720 Set 19

  41. R and S have coordinates (5,-7) and (-1,-3) respectively. The perpendicular bisector of RS has a gradient of -. What is the equation of the perpendicular bisector of RS? A. 3y = 2x + 13 B. 3y = -2x + 19 C. 2y = -3x - 19 D. 2y = 3x - 13 2. Find the gradient of the line AB: A. m = 1 B. m = -√2 C. m = -1 D. m = - 3. What is the solution of the equation 2cosx - √3 = 0 where ? y A 45o x B answer Set 20

  42. R and S have coordinates (5,-7) and (-1,-3) respectively. The perpendicular bisector of RS has a gradient of -. What is the equation of the perpendicular bisector of RS? A. 3y = 2x + 13 B. 3y = -2x + 19 C. 2y = -3x - 19 D. 2y = 3x - 13 2. Find the gradient of the line AB: A. m = 1 B. m = -√2 C. m = -1 D. m = - 3. What is the solution of the equation 2cosx - √3 = 0 where ? y A 45o x B Set 20

  43. The side of a triangle has equation y = -x – 3. Which of these could be the equation of an altitude passing through this side? A. 2y + x – 3 = 0 B. 2y – 3x + 3 = 0 C. 2y + 3x – 1 = 0 D. 3y – 2x + 1 = 0 The vertices of triangle STV are S(-4,10) , T(10,3) and V(0,-10). Which of the following is the equation of the median TM? A. 4y = x + 2 B. y = 4x + 2 C. y = -2x + 23 D. y = 2x - 2 3. Functions f and g, are given by and Find an expression for f(g(x)). answer Set 21

  44. The side of a triangle has equation y = -x – 3. Which of these could be the equation of an altitude passing through this side? A. 2y + x – 3 = 0 B. 2y – 3x + 3 = 0 C. 2y + 3x – 1 = 0 D. 3y – 2x + 1 = 0 The vertices of triangle STV are S(-4,10) , T(10,3) and V(0,-10). Which of the following is the equation of the median TM? A. 4y = x + 2 B. y = 4x + 2 C. y = -2x + 23 D. y = 2x - 2 3. Functions f and g, are given by and Find an expression for f(g(x)). Set 21

  45. If f’(4) equals: A.  B. 2 C. 3 D. 6 2. If the line ax - 2y + 5 = 0 is parallel to the line 3x + y - 4 = 0, a is equal to: A. -6 B. - C.  D.  3. PQ, of length 2, is parallel to OY. QR, of length 4, is parallel to OX. Angle PQR = 90o. P is the point (1,2). The line PR cuts OY at: A. (0,) B. (0,) C. (0,-) D. (0,-) Set 22 y 4 Q R 2 P (1,2) x 0 answer

  46. If f’(4) equals: A.  B. 2 C. 3 D. 6 2. If the line ax - 2y + 5 = 0 is parallel to the line 3x + y - 4 = 0, a is equal to: A. -6 B. - C.  D.  3. PQ, of length 2, is parallel to OY. QR, of length 4, is parallel to OX. Angle PQR = 90o. P is the point (1,2). The line PR cuts OY at: A. (0,) B. (0,) C. (0,-) D. (0,-) Set 22 y 4 Q R 2 P (1,2) x 0

  47. 1. This diagram is most likely to be part of the graph of: 2. Find the gradient of the line ST: A. m = -1 B. m = 1 C. m = -√2 D. m = - 3. If and x ≠ 0 then f’(x) equals: y 1 x 90 -3 y S 135o x T answer Set 23

  48. If f(x) = x√x , x > 0 ; f’(x) equals: Which of the following is/are true of the line with equation 3x - 2y + 3 = 0? I. It passes through the point (-2,-3) II. It is parallel to the line 6x + 4y + 3 = 0 III. It is perpendicular to the line 2x + 3y + 3 = 0 A. I only B. I & III only C. III only D. Some other combination of responses 3. The line with equation y = √3 intersects the curve y = 2cosx, at: answer Set 24