Evaluate: lim\(_{x→-2}\) \(\frac{x^3+8}{x+2}\).
- A. 12
- B. 8
- C. 4
- D. 2
A particle is acted upon by forces F = (10N, 060º), P = (15N, 120º) and Q = (12N, 200º). Express the force that will keep the particle in equilibrium in the form xi + yj, where x and y are scalars.
- A. 17.55i + 13.78j
- B. 17.55j - 13.78i
- C. -17.55i + 13.78j
- D. -17.55i - 13.78j
If α and β are roots of x\(^2\) + mx – n = 0, where m and n are constants, form the
| equation | whose | roots | are | 1
α |
and | 1
β |
. |
- A. mnx\(^2\) - n\(^2\) x - m = 0
- B. mx\(^2\) - nx + 1 = 0
- C. nx\(^2\) - mx + 1 = 0
- D. nx\(^2\) - mx - 1 = 0
A particle of mass 3kg moving along a straight line under the action of a F N, covers a line distance, d, at time, t, such that d = t\(^2\) + 3t. Find the magnitude of F at time t.
- A. 0N
- B. 2N
- C. 3(2t + 3)N
- D. 6N
The gradient of a function at any point (x,y) 2x – 6. If the function passes through (1,2), find the function.
- A. x\(^2\) - 6x - 5
- B. x\(^2\) - 6x + 5
- C. x\(^2\) - 6x - 3
- D. x\(^2\) - 6x + 7
The equation of a circle is given as 2x\(^2\) + 2y\(^2\) – x – 3y – 41 = 0. Find the coordinates of its centre.
- A. (\(\frac{-1}{4}\), \(\frac{3}{4}\))
- B. (\(\frac{1}{4}\), \(\frac{3}{4}\))
- C. (\(\frac{-1}{2}\), \(\frac{3}{2}\))
- D. (\(\frac{-1}{2}\), \(\frac{-3}{2}\))
The probability that a student will graduate from college is 0.4. If 3 students are selected from the college, what is the probability that at least one student will graduate?
- A. 0.06
- B. 0.22
- C. 0.78
- D. 0.80
Find the range of values of x for which 2x\(^2\) + 7x – 15 ≥ 0.
- A. x ≤ -5 or x ≥ \(\frac{3}{2}\)
- B. x ≥ -5 or x ≤\(\frac{3}{2}\)
- C. -5 ≤ x ≤ \(\frac{3}{5}\)
- D. \(\frac{3}{5}\) ≤ x ≤ -5
Solve: 4sin\(^2\)θ + 1 = 2, where 0º < θ < 180º
- A. 60º 0r 120º
- B. 30º 0r 150º
- C. 30º 0r 120º
- D. 60º 0r 150º
Find correct to the nearest degree, the acute angle formed by the lines y = 2x + 5 and 2y = x – 6
- A. 76\(^∘\)
- B. 53\(^∘\)
- C. 37\(^∘\)
- D. 14\(^∘\)
The mean heights of three groups of students consisting of 20, 16 and 14 students each are 1.67m, 1.50m and 1.40m respectively. Find the mean height of all the students.
- A. 1.63m
- B. 1.54m
- C. 1.52m
- D. 1.42m
A body of mass 18kg moving with velocity 4ms-1 collides with another body of mass 6kg moving in the opposite direction with velocity 10ms-1. If they stick together after the collision, find their common velocity.
- A. \(\frac{1}{2}\) m/s
- B. \(\frac{1}{3}\) m/s
- C. 2m/s
- D. 3m/s
The first, second and third terms of an exponential sequence (G.P) are (x – 4), (x + 2), and (3x + 1) respectively. Find the values of x.
- A. \(\frac{-1}{2}, 8\)
- B. \(\frac{1}{2}, -8\)
- C. \(\frac{-1}{2}, -8\)
- D. \(\frac{1}{2}, 8\)
Find the coefficient of x\(^3\)y\(^2\) in the binomial expansion of (x-2y)\(^5\)
- A. -80
- B. 10
- C. 40
- D. 80
If g(x) = √(1-x\(^2\)), find the domain of g(x)
- A. x < -1 or x > 1
- B. x ≤ -1 or x ≥1
- C. -1 ≤ x ≤ 1
- D. -1 < x < 1
The table shows the distribution of the distance (in km) covered by 40 hunters while hunting.
What is the mode of the distribution?
| Distance(km) | 3 | 4 | 5 | 6 | 7 | 8 |
| Frequency | 5 | 4 | x | 9 | 2x | 1 |
- A. 5
- B. 6
- C. 7
- D. 8
The table shows the distribution of the distance (in km) covered by 40 hunters while hunting.
| Distance(km) | 3 | 4 | 5 | 6 | 7 | 8 |
| Frequency | 5 | 4 | x | 9 | 2x | 1 |
If a hunter is selected at random, find the probability that the hunter covered at least 6km.
- A. \(\frac{3}{5}\)
- B. \(\frac{2}{5}\)
- C. \(\frac{3}{8}\)
- D. \(\frac{9}{40}\)
If →PQ = -2i + 5j and →RQ = -i – 7j, find →PR
- A. -3i + 12j
- B. -3i - 12j
- C. -i + 12j
- D. i - 12j
Given that P = (-4, -5) and Q = (2,3), express →PQ in the form (k,θ). where k is the magnitude and θ the bearing.
- A. (10 units, 053º)
- B. (9 units, 049º)
- C. (10 units, 037º)
- D. (9 units, 027º)
Solve: \(3^{2x-2} – 28(3^{x-2}) + 3 = 0\)
- A. x = -2 or x = 1
- B. x = 0 or x = -3
- C. x = 2 or x = 1
- D. x = 0 or x = 3