Senior Class WAEC/NECO/UTME Mock Exams(Further Maths) : GATE Academy

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NAME

E,MAIL

PHONE NUMBER

1. Find the value of cos (-45)°

0.8712

-0.7071

0.4335

0.7071

2. Solve for x
log_x 0.0001 = 4

1/5

1/2

-1

1/10

3. Using the product rule differentiate wrt x
(3x + 4)(x - 3)

6x²

6x-5

x²+12

9x-12

Solve the equation:

4^{(w - 1)} × 5^{(2w - 2)}× 10^w= 1

2/3

5/4

4/3

3/4

5. Find the fourth term in the expansion of (1+x)¹⁵

13x³

455x³

6. A wooden block of weight 16N is placed on a rough surface. If the co-efficient of friction between both surfaces is 0.25, the least horizontal force required to move the block is

6.4N

4.0N

64.0N

0.4N

7. Solve for y if

5 log (y+3) = log 32

-1

8. The gradient of a curve which passes through the point ( 1, 2) is given by x². Determine the equation of the curve.

y = 3x³ + 3/5

y = 1/3 x³ + 5/3

y = x³ + 2x

y = 1/3 x³ - 5/3

9. Given that

Find the values of x for which |A| is zero.

-4, 4

4, -2(twice)

2, 3(twice)

-2, 3

10. Find the coordinate of the point which will divide the line joining the point (2, 4) and (7,9) internally in the ratio 1:2?

(8/3 11/3)

(11/3, 17/3)

(5/3, 1/3)

(3/8, 3/11)

11. If
y + 1/y = 4, find y² + 1/y²

12. The gradient of a curve at any point (x, y) is given by dy/dx = 2(x - 3) and the point(3, -12) lies on the curve. Find the equation of the curve.

y = x² - 6x - 3

y = x - 18

y = x² - 6x

y = x² - 6x - 5

13. Which of the following is a root of the equation
y² + 6y = 0 ?

14. A figure is selected randomly from a group of figures consisting of a square, a triangle, a rectangle, a trapezium and a rhombus.
The probability that the figure selected is a parallelogram is

2/5

1/5

3/5

4/5

15. The figure below shows four forces 3N, 10N, 3√3N and 6N acting on a particle P. The resultant of the four forces is

10√3N

5√3N

10N

16. During the same interval, it is observed that a train travels the same distance as does a lorry. The two vehicles therefore have the same

average velocity

average speed

uniform acceleration

instantaneous velocity

initial velocity

17. Tara pushes a 500kg box along a floor with a force of 2000N. If the velocity of the box is uniform, the coefficient of friction between the box and the floor is.
(g = 10m/s²)

0.65

1.0

0.8

0.4

0.5

18. Given that y and x are two variables such that dy/dx = 2x - 6, and y = -1 when x = 3, express y in terms of x.

y = x - 3

y = x² - 6x + 8

y = x² + 6

y = x² + 6x + 8

19. The gradient of a curve is given by
x² - 4x + 3
If the curve passes through the point (3, 1).
Find the area of the finite region enclosed by the curve,
the lines x = 1, x = 3 and y = 0

10/3

5/9

8/7

6/7

20. Find angle a°

40.3°

27°

72°

50.1°

21. The radius r of a circular disc is increasing at the rate of 0.5 cm/s. At what rate is the area of the disc increasing when its radius is 6 cm?

6π cm²/s

3π cm²/s

36π cm²/s

18π cm²/s

22. Find the value of x for which
3^2x + 6(3^x) = 27

-1

-3

23. The line y =3x + 1 intersects the
curve y = x² -2x + 7 at the points

(2, 7) and (3, 10)

(-1, -2) and (3, 10)

(-2, -5) and (1, 4)

(1, 4) and (2, 7)

24. Find a positive angle between 0° and 360° that is equivalent to -315°

421°

45°

124°

105°

25. Write the value of the angle in surd form sin 300°

√2

√3/2

-√2

-√3/2

26. The speed s of a particle after t seconds is given by v = 7 + 25t -4t² . Find the acceleration of the particle after 2 seconds.

28 m/s²

25 m/s²

41 m/s²

9 m/s²

27. Tireni stands on a spring scale placed in a lift. The lift descends at constant velocity. As a result, the scale reads a weight

greater than the weight of Tireni

the same as the weight of Tireni

of zero

less than the weight of Tireni

greater than the weight of Tireni by 1kg

28. If (x-3) and (x+5) are factors of the expression x³ + mx² - nx - 45, what is the product of m and n

29. Determine the order of the matrix:

1x2

2x3

2x2

1x1

30. cos 65° is equal to

sin 115°

cos 295°

cos 115°

cos 245°

31. Solve the equation
8 sin x = 3 for 0° ≤x≤ 360°

98°

17°

22°

100°

32. The velocity of a particle is given by v =3t² + 8t. Find the acceleration when t = 8s

56 m/s²

23 m/s²

8 m/s²

18 m/s²

33. Find the angles between 0° and 360° whose sine is -0.9781

23°

235°

443°

258°

34. Two forces of magnitude 7N & 3N act at right angles to each other. The angle θ between resultant and the 7N force is given by

sinθ = 3/7

cosθ = 3/7

cotθ = 3/7

tanθ = 3/7

35. The sine, cosine and tangent of 240° are, respectively

-0.866, 1/2, -1.732

-0.866, -1/2, 1.732

0.866, -1/2, 1.732

0.866, 1/2, 1.732

36. Resolve

into partial fractions.

2/(x-1) - 3/(x+1) + 2/(x+3)

2/(x-1) - 1/(x+1) + 1/(x+3)

2/(x-1) + 3/(x+1) + 1/(x+3)

2/(x-1) - 3/(x+1) + 1/(x+3)

37. Multiply (x + 3y + 5) by (2x² + 5y + 2)

x²+31y+18x+2x+9

2x³+6yx²+5xy+15y²+31y+10x²+2x+10

2x²+6y²x+4xy+12x²+31y+18x+2x+9

2x³+6yx²+5xy+15y

38. Using the binomial theorem in the expansion of (x + 3/x)⁴,

find the term which is independent of x.

39. The gradient of a curve is given by dy/dx = 10x - 3x². If the curve passes through the point (-1, 10), find the equation of the curve

y = 5x³ - x² + 8

y = x² -4

y = 5x² - x³ + 4

y = 5x² - x³

40. Solve for x
2^2x - 6(2^x) = - 8

-1

41. If x + 1 is a factor of x³ + 3x² + kx + 4, find the value of k

42. The 1st and the 11th terms of an A.P. are -5 and 20 respectively.
The common difference is

5/2

43. A ball is thrown vertically upwards and its height s metres after t seconds is given by s = 16t - 4t². Find the time when the velocity is 8 m/s.

44. A triangle has sides of lengths y cm, (y-4) cm and (y+4) cm.
If the largest angle of the triangle is cos^-1 (1/5),
find the value of y

24 cm

20 cm

28 cm

90/7 cm

45. Find, from the first principles, the derivative with respect to x of the function

y = 2x² - x + 3

4x - 1

4x - 4

4x - 2

46. If y = 2xcos2x - sin2x, find dy/dx when x = π/4

π/2

-π

π/4

47. Given that dv/dt = -64t and v = 10 when t = 0, find v when t = 2.

v = 118

v = -118

v = -64

v = 64

48. Given that
log_b2 = 0.693 and
log_b5 = 1.609,

evaluate: log_b62.5

1.016

5.520

4.134

2.202

49. The marks scored by students in a test are recorded in the table below

Calculate the median

50. Differentiate, with the respect to x:

cosx - x sinx

2sinx -xcosx

-2sinx - xcosx

xcosx

-2sinx + xcosx

51. Given that

tanx = 5/12,

what is the value of sinx + cosx?

13/17

17/13

52. Find the value of x if

log₄x = 3.5

256

128

53. The standard deviation of the set of numbers

-3, -2, -1, 0, 1, 2, 3, is

4√2

2√2

54.

The polynomial f(x) = 3 x⁴ + 5 x³ - 17 x² - 25 x + 10

has irrational zeros at + √(5) and - √(5). Find the other zeros

-2, 1/3

2, 2/3

2/3, 1/2

1, 4

55. Which of the following pairs of graphs cannot be used to find the solution to the cubic equation x³ -3x² + 3x - 9 = 0 ?

y = x³ and y = 3x² - 3x + 9

y = x³ -3x² and y = 3x - 9

y = x³ -3x² + 3x and y = 9

y = x² - 3x + 3and y = 9/x

56.

Line M has a y-intercept of –4, and its slope must be an integer-multiple of 1/7.

Given that Line M passes below (4, –1) and above (5, –6), how many possible slopes could Line M have?

57. Evaluate the determinant

-14

58. Find
∫x tan²x dx

Incos x+C

x(tanx- x) +In cosx + C

x(tanx -x) + C

x(tanx- x) +In cosx + x²/2 + C

59. Find the value of x if

1/2 log₁₀x = 1

100

√10

0.01

1/√10

60. If cos θ > 0 and sin θ < 0, then

270°< θ < 360°

90° < θ < 180°

180° < θ < 270°

0° < θ < 90°

61 out of 60

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