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Higher Mathematics Objective Questions

This collection features a set of objective questions designed for higher mathematics, aimed at students and educators. It covers key topics, including trigonometric functions, their properties, domain, and graphical representations. Each question is methodically crafted to challenge understanding and application of mathematical concepts, providing exact values for trigonometric functions and determining the period of functions. Ideal for exam preparation, this resource enhances comprehension through practical problem-solving.

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Higher Mathematics Objective Questions

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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

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