Mathematics
Q. A bag contains 4 white balls and 6 black balls. If one ball is drawn at random, what is the probability that it is not black?
A.
2/5
B.
3/5
C.
4/5
D.
1/5
Show solution
Solution
Total balls = 4 + 6 = 10. Probability of not drawing a black ball = Number of white balls / Total balls = 4/10 = 2/5.
Correct Answer: C — 4/5
Learn More →
Q. A box contains 3 red, 5 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue?
A.
1/10
B.
1/5
C.
1/2
D.
1/3
Show solution
Solution
Total balls = 3 + 5 + 2 = 10. Probability of drawing a blue ball = Number of blue balls / Total balls = 5/10 = 1/2.
Correct Answer: B — 1/5
Learn More →
Q. A box contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball? (2021)
A.
3/8
B.
5/8
C.
1/2
D.
1/3
Show solution
Solution
Total balls = 5 + 3 = 8. Probability of red = 5/8.
Correct Answer: B — 5/8
Learn More →
Q. A chord of a circle is 8 cm long and is 3 cm away from the center. What is the radius of the circle? (2021)
A.
5 cm
B.
7 cm
C.
10 cm
D.
9 cm
Show solution
Solution
Using Pythagoras theorem, r² = (3)² + (4)² = 9 + 16 = 25. Thus, r = 5 cm.
Correct Answer: B — 7 cm
Learn More →
Q. A circle has a circumference of 31.4 cm. What is its radius? (2021)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Circumference = 2πr. Thus, r = Circumference/(2π) = 31.4/(2π) = 5 cm.
Correct Answer: A — 5 cm
Learn More →
Q. A class of 30 students has an average score of 75. If one student scores 90, what will be the new average? (2022)
Show solution
Solution
Total score = 75 * 30 = 2250. New total = 2250 - 75 + 90 = 2265. New average = 2265 / 30 = 75.5.
Correct Answer: B — 77
Learn More →
Q. A coin is tossed three times. What is the probability of getting at least one head?
A.
1/8
B.
1/2
C.
7/8
D.
3/8
Show solution
Solution
Probability of getting no heads (all tails) = (1/2)^3 = 1/8. Therefore, probability of at least one head = 1 - 1/8 = 7/8.
Correct Answer: C — 7/8
Learn More →
Q. A data set has values: 10, 12, 14, 16. What is the variance? (2021)
Show solution
Solution
Mean = (10 + 12 + 14 + 16) / 4 = 13. Variance = [(10-13)² + (12-13)² + (14-13)² + (16-13)²] / 4 = 2.5.
Correct Answer: B — 4
Learn More →
Q. A jar contains 5 red, 3 blue, and 2 yellow marbles. If one marble is drawn, what is the probability that it is either red or yellow?
A.
1/2
B.
2/5
C.
4/10
D.
7/10
Show solution
Solution
Total marbles = 5 + 3 + 2 = 10. Probability of red or yellow = (Number of red + Number of yellow) / Total = (5 + 2) / 10 = 7/10.
Correct Answer: D — 7/10
Learn More →
Q. A rectangle has a length of 12 cm and a width of 5 cm. What is its perimeter? (2021)
A.
34 cm
B.
30 cm
C.
24 cm
D.
40 cm
Show solution
Solution
Perimeter = 2(length + width) = 2(12 + 5) = 2 * 17 = 34 cm
Correct Answer: B — 30 cm
Learn More →
Q. A set of numbers has a mean of 20. If one number is removed, the mean becomes 18. What was the number removed? (2022)
Show solution
Solution
Let the number of elements be n. Then, 20n - x = 18(n - 1). Solving gives x = 22.
Correct Answer: A — 22
Learn More →
Q. A set of numbers has the following frequencies: 10 (1), 20 (2), 30 (3), 40 (4). What is the mode of this set? (2021)
Show solution
Solution
The number 40 appears most frequently (4 times), so the mode is 40.
Correct Answer: D — 40
Learn More →
Q. A survey of favorite fruits among 20 people resulted in the following counts: Apple (6), Banana (8), Orange (4), Grape (2). What is the mode of the favorite fruits? (2023)
A.
Apple
B.
Banana
C.
Orange
D.
Grape
Show solution
Solution
Banana has the highest count (8), so the mode is Banana.
Correct Answer: B — Banana
Learn More →
Q. Calculate the area under the curve y = 2x + 1 from x = 1 to x = 4.
Show solution
Solution
The area under the curve is given by ∫(from 1 to 4) (2x + 1) dx = [x^2 + x] from 1 to 4 = (16 + 4) - (1 + 1) = 20.
Correct Answer: A — 15
Learn More →
Q. Calculate the area under the curve y = x^3 from x = 0 to x = 2.
Show solution
Solution
The area under the curve is given by ∫(from 0 to 2) x^3 dx = [x^4/4] from 0 to 2 = (16/4) - (0) = 4.
Correct Answer: B — 8
Learn More →
Q. Calculate the determinant of the matrix J = [[1, 2, 1], [0, 1, 0], [2, 3, 1]]. (2023)
Show solution
Solution
The determinant of J is calculated as 1*(1*1 - 0*3) - 2*(0*1 - 0*2) + 1*(0*3 - 1*2) = 1 - 0 - 2 = -1.
Correct Answer: B — 1
Learn More →
Q. Calculate the distance between the points (1, 2) and (1, 5).
Show solution
Solution
Using the distance formula: d = √[(1 - 1)² + (5 - 2)²] = √[0 + 9] = √9 = 3.
Correct Answer: A — 3
Learn More →
Q. Calculate the distance between the points (6, 8) and (2, 3).
Show solution
Solution
Using the distance formula: d = √[(2 - 6)² + (3 - 8)²] = √[16 + 25] = √41.
Correct Answer: B — 6
Learn More →
Q. Calculate the limit: lim (x -> 0) (x^3)/(sin(x)) (2023)
A.
0
B.
1
C.
∞
D.
Undefined
Show solution
Solution
Using the fact that sin(x) ~ x as x approaches 0, we find that lim (x -> 0) (x^3)/(sin(x)) = 0.
Correct Answer: A — 0
Learn More →
Q. Calculate the limit: lim (x -> ∞) (3x^2 + 2)/(5x^2 - 4) (2023)
Show solution
Solution
Dividing numerator and denominator by x^2 gives lim (x -> ∞) (3 + 2/x^2)/(5 - 4/x^2) = 3/5.
Correct Answer: A — 3/5
Learn More →
Q. Determine the angle between the lines y = 2x + 1 and y = -1/2x + 3. (2021)
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
The slopes are m1 = 2 and m2 = -1/2. The angle θ = tan⁻¹(|(m1 - m2) / (1 + m1*m2)|) = tan⁻¹(5/3), which is approximately 90 degrees.
Correct Answer: A — 90 degrees
Learn More →
Q. Determine the continuity of the function f(x) = { x^2, x < 1; 2, x = 1; x + 1, x > 1 } at x = 1.
A.
Continuous
B.
Not continuous
C.
Depends on the limit
D.
Only left continuous
Show solution
Solution
The left limit as x approaches 1 is 1, the right limit is 2, and f(1) = 2. Since the left and right limits do not match, f(x) is not continuous at x = 1.
Correct Answer: B — Not continuous
Learn More →
Q. Determine the continuity of the function f(x) = { x^2, x < 1; 2x - 1, x ≥ 1 } at x = 1.
A.
Continuous
B.
Discontinuous
C.
Only left continuous
D.
Only right continuous
Show solution
Solution
At x = 1, f(1) = 2(1) - 1 = 1 and lim x→1- f(x) = 1, lim x→1+ f(x) = 1. Thus, f(x) is continuous at x = 1.
Correct Answer: A — Continuous
Learn More →
Q. Determine the distance between the points (2, 3) and (2, -1).
Show solution
Solution
Using the distance formula: d = √[(2 - 2)² + (-1 - 3)²] = √[0 + 16] = √16 = 4.
Correct Answer: A — 4
Learn More →
Q. Determine the local maxima or minima of f(x) = -x^2 + 4x. (2019)
A.
Maxima at x=2
B.
Minima at x=2
C.
Maxima at x=4
D.
Minima at x=4
Show solution
Solution
f'(x) = -2x + 4. Setting f'(x) = 0 gives x = 2. Since f''(x) = -2 < 0, it is a maxima.
Correct Answer: A — Maxima at x=2
Learn More →
Q. Determine the slope of the tangent line to f(x) = x^2 at x = 3. (2023)
Show solution
Solution
f'(x) = 2x; thus, f'(3) = 2(3) = 6.
Correct Answer: B — 6
Learn More →
Q. Determine the x-intercept of the line given by the equation 5x + 2y - 10 = 0. (2023)
Show solution
Solution
Setting y = 0 in the equation gives 5x = 10, thus x = 2. The x-intercept is 2.
Correct Answer: C — 5
Learn More →
Q. Differentiate f(x) = 4x^2 * e^x. (2022)
A.
4e^x + 4x^2e^x
B.
4x^2e^x + 4xe^x
C.
4e^x + 2x^2e^x
D.
8xe^x
Show solution
Solution
Using the product rule, f'(x) = 4e^x + 4x^2e^x.
Correct Answer: A — 4e^x + 4x^2e^x
Learn More →
Q. Differentiate f(x) = ln(x^2 + 1). (2022)
A.
2x/(x^2 + 1)
B.
1/(x^2 + 1)
C.
2x/(x^2 - 1)
D.
x/(x^2 + 1)
Show solution
Solution
Using the chain rule, f'(x) = 2x/(x^2 + 1).
Correct Answer: A — 2x/(x^2 + 1)
Learn More →
Q. Differentiate f(x) = x^2 * e^x. (2022)
A.
x^2 * e^x + 2x * e^x
B.
2x * e^x + x^2 * e^x
C.
x^2 * e^x + e^x
D.
2x * e^x
Show solution
Solution
Using the product rule, f'(x) = x^2 * e^x + 2x * e^x.
Correct Answer: A — x^2 * e^x + 2x * e^x
Learn More →
Showing 1 to 30 of 310 (11 Pages)
