NSC Mathematics AI Practice

Question 1

What is the value of x if 3x + 5 = 20?

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Question 2

Which function represents a quadratic function?

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Question 3

What is the derivative of f(x) = 3x^3 - 2x + 7?

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Question 4

In triangle ABC, if angle A = 90°, and side a = 5, side b = 12, what is the length of side c?

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Question 5

Calculate the area of a circle with radius 7 cm.

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Question 6

If events A and B are independent, and P(A) = 0.4, P(B) = 0.5, what is P(A and B)?

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Question 7

Find the median of the data set: 3, 7, 9, 15, 21.

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Question 8

Solve for x: 2^(x) = 16.

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Question 9

If f(x) = 2x + 3 and g(x) = x^2, what is (f ∘ g)(2)?

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Question 10

Differentiate y = sin(3x).

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Question 11

In triangle PQR, if sides p=7, q=24, r=25, what type of triangle is it?

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Question 12

Calculate the volume of a cylinder with radius 3 cm and height 10 cm.

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Question 13

A bag contains 5 red, 3 blue, and 2 green marbles. What is the probability of picking a blue marble?

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Question 14

The function f(x) = x^3 - 3x^2 + 4 has a turning point at x = ?

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Question 15

Prove that triangle with vertices A(1,2), B(4,6), C(1,6) is right angled.

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Question 16

Calculate the integral ∫(2x + 3) dx.

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Question 17

A data set has mean 20 and standard deviation 4. What is the z-score of a value 28?

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Question 18

Solve for x: log₂(x) = 5.

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Question 19

If the probability of rain tomorrow is 0.7, what is the probability it will not rain?

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Question 20

Evaluate sin 60°.

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Question 21

If f(x) = 2x + 3, what is f(4)?

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Question 22

Solve for x in the equation 3x - 7 = 11.

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Question 23

What is the derivative of f(x) = x²?

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Question 24

In a right triangle, if one acute angle is 30°, what is the sine of this angle?

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Question 25

Calculate the area of a triangle with base 10 cm and height 6 cm.

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Question 26

If P(A) = 0.3 and P(B) = 0.5, what is the maximum possible value of P(A ∩ B)?

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Question 27

Find the mean of the data set: 2, 4, 6, 8, 10.

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Question 28

Solve the quadratic equation x² - 5x + 6 = 0.

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Question 29

Determine the domain of f(x) = 1/(x - 4).

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Question 30

Evaluate the integral ∫2x dx.

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Question 31

If sin θ = 3/5 in a right triangle, what is cos θ?

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Question 32

Calculate the volume of a cylinder with radius 3 cm and height 7 cm.

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Question 33

A bag contains 4 red and 6 blue balls. What is the probability of drawing a red ball?

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Question 34

The median of the data set 1, 3, 3, 6, 7, 8, 9 is:

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Question 35

Differentiate f(x) = 3x³ - 5x + 2.

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Question 36

If tan θ = 1, what is θ in degrees (0° < θ < 90°)?

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Question 37

The slope of the line passing through points (2, 3) and (5, 15) is:

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Question 38

Evaluate the limit: lim(x→2) (x² - 4)/(x - 2).

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Question 39

Prove that the sum of interior angles of a triangle is 180° using parallel lines.

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Question 40

A fair die is rolled twice. What is the probability of getting two sixes?

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Question 41

Solve for x: 3x - 7 = 11.

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Question 42

What is the derivative of f(x) = x^3?

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Question 43

If sin θ = 0.5, what is θ in degrees (0° ≤ θ ≤ 90°)?

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Question 44

Find the length of the hypotenuse of a right triangle with legs 6 cm and 8 cm.

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Question 45

If the probability of event A is 0.3, what is the probability of not A?

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Question 46

Calculate the mean of the data set: 4, 7, 9, 10, 5.

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Question 47

Simplify: (2x^3)(3x^2).

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Question 48

If f(x) = x^2 - 4x + 3, find f(3).

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Question 49

Solve for x: x^2 - 5x + 6 = 0.

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Question 50

If f(x) = 3x + 1, find f^{-1}(x), the inverse function.

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Question 51

Differentiate y = 5x^4 - 3x + 2.

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Question 52

In triangle ABC, angle A = 90°, side AB = 5 cm, side AC = 12 cm. Find BC.

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Question 53

Find the range of f(x) = 2x - 5 for all real x.

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Question 54

If sin A = 0.6 and triangle ABC is right angled at C, find cos A.

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Question 55

A box contains 3 red, 4 blue, and 5 green balls. What is the probability of picking a blue ball?

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Question 56

Calculate the median of the data set: 3, 8, 7, 5, 12.

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Question 57

Differentiate y = sin x * cos x.

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Question 58

Find the exact value of tan(45°).

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Question 59

If f(x) = x^2 and g(x) = 3x + 1, find (f ◦ g)(2).

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Question 60

If f(x) = 3x - 7, what is f(4)?

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Question 61

Solve for x: 2x + 5 = 17.

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Question 62

Determine the derivative of y = 5x^3.

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Question 63

What is the value of sin 30°?

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Question 64

Find the length of the hypotenuse in a right triangle with legs of length 6 cm and 8 cm.

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Question 65

If the probability of event A occurring is 0.3, what is the probability of event A not occurring?

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Question 66

Calculate the mean of the data set: 4, 8, 6, 5, 3.

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Question 67

Factorize completely: x^2 - 16.

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Question 68

What is the domain of the function f(x) = 1/(x - 3)?

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Question 69

Differentiate y = sin x.

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Question 70

In triangle ABC, angle A = 90°, AB = 3 cm, AC = 4 cm. Find BC.

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Question 71

If cos θ = 0.6 and θ is acute, find sin θ.

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Question 72

The function f(x) = x^2 - 4x + 3 has roots at:

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Question 73

In a probability experiment, the chance of event B is 0.4. What is the probability of event B occurring twice in two independent trials?

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Question 74

Find the equation of the line passing through (2,3) with slope 4.

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Question 75

Find the area of a sector of a circle with radius 10 cm and angle 60°.

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Question 76

If f(x) = 2x^3 - 5x + 1, find f'(x).

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Question 77

Given that tan θ = 3/4, find sin θ.

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Question 78

Calculate the variance of the data set: 2, 4, 4, 4, 5, 5, 7, 9.

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Question 79

Simplify the expression: 3x - 2 + 5x + 7.

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Question 80

Given the function f(x) = 2x^2 - 3x + 1, find f(2).

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Question 81

Calculate the derivative of f(x) = 5x^3 - 4x + 7.

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Question 82

Find the exact value of sin 60°.

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Question 83

In triangle ABC, angle A = 90°, side AB = 6 cm, side AC = 8 cm. Find the length of side BC.

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Question 84

If the probability of event A occurring is 0.4 and event B is 0.5, assuming A and B are independent, what is the probability that both A and B occur?

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Question 85

The mean of five numbers is 12. If one number is removed, the mean of the remaining four numbers is 11. Find the number removed.

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