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CSEC Mathematics study materials
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CSEC Mathematics practice questions

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Question 1Mathematics (subject listed under the Mathematics and Science subject group)

A shop reduces the price of a shirt by 20%. The sale price is $64. What was the original price before the reduction?

  1. $76.80
  2. $80.00 Correct answer.
  3. $128.00
  4. $84.00

Explanation

If the price is reduced by 20%, the sale price represents 80% of the original. Dividing $64 by 0.8 gives $80, which is the original price before the discount was applied.

Question 2Mathematics (subject listed under the Mathematics and Science subject group)

Simplify the expression 3(2x − 4) + 5x.

  1. 6x − 12
  2. 11x − 4
  3. 11x − 12 Correct answer.
  4. 6x + 5x − 12

Explanation

Expanding the bracket gives 6x − 12, and adding 5x gives 11x − 12. Like terms in x are combined while the constant stays separate.

Question 3Mathematics (subject listed under the Mathematics and Science subject group)

A fair six-sided die is rolled once. What is the probability of obtaining a prime number?

  1. 1/6
  2. 2/3
  3. 1/2 Correct answer.
  4. 1/3

Explanation

The prime numbers on a die are 2, 3 and 5, giving three favourable outcomes out of six equally likely outcomes. The probability is therefore 3/6, which simplifies to 1/2.

Question 4Mathematics (subject listed under the Mathematics and Science subject group)

In a right-angled triangle the two shorter sides have lengths 9 cm and 12 cm. What is the length of the hypotenuse?

  1. √21 cm
  2. 3 cm
  3. 21 cm
  4. 15 cm Correct answer.

Explanation

By Pythagoras' theorem the hypotenuse squared equals 9² + 12², which is 81 + 144 = 225. The square root of 225 is 15, so the hypotenuse is 15 cm.

Question 5Mathematics (subject listed under the Mathematics and Science subject group)

What is the value of 5² − 2³?

  1. 21
  2. 17 Correct answer.
  3. 33
  4. 9

Explanation

Five squared is 25 and two cubed is 8. Subtracting gives 25 − 8 = 17, applying the indices before the subtraction.

Question 6Mathematics (subject listed under the Mathematics and Science subject group)

A car travels 150 km in 2.5 hours. What is its average speed in kilometres per hour?

  1. 375 km/h
  2. 75 km/h
  3. 60 km/h Correct answer.
  4. 50 km/h

Explanation

Average speed equals distance divided by time, so 150 ÷ 2.5 = 60. The car therefore averages 60 km/h over the journey.

Question 7Mathematics (subject listed under the Mathematics and Science subject group)

Which of the following is the equation of a straight line with gradient 3 passing through the point (0, −2)?

  1. y = 3x − 2 Correct answer.
  2. y = 3x + 2
  3. y = 2x − 3
  4. y = −2x + 3

Explanation

A line has the form y = mx + c, where m is the gradient and c is the y-intercept. The gradient is 3 and the line crosses the y-axis at −2, giving y = 3x − 2.

Question 8Mathematics (subject listed under the Mathematics and Science subject group)

The mean of five numbers is 12. Four of the numbers are 8, 10, 14 and 15. What is the fifth number?

  1. 13 Correct answer.
  2. 12
  3. 11
  4. 16

Explanation

The total of five numbers with mean 12 is 5 × 12 = 60. The four known numbers sum to 47, so the fifth number is 60 − 47 = 13.

Question 9Mathematics (subject listed under the Mathematics and Science subject group)

Solve the simultaneous equations 2x + y = 11 and x − y = 1.

  1. x = 4, y = 5
  2. x = 4, y = 3 Correct answer.
  3. x = 3, y = 5
  4. x = 5, y = 1

Explanation

Adding the two equations eliminates y, giving 3x = 12, so x = 4. Substituting into x − y = 1 gives y = 3, which also satisfies 2x + y = 11.

Question 10Mathematics (subject listed under the Mathematics and Science subject group)

A triangle has sides 8 cm, 15 cm and 17 cm. What type of triangle is it?

  1. Acute-angled
  2. Obtuse-angled
  3. Equilateral
  4. Right-angled Correct answer.

Explanation

Check Pythagoras: 8² + 15² = 64 + 225 = 289, and 17² = 289. Since the square of the longest side equals the sum of the squares of the other two, the triangle is right-angled.

Question 11Mathematics (subject listed under the Mathematics and Science subject group)

A sector of a circle has radius 7 cm and subtends an angle of 90° at the centre. Taking π = 22/7, what is the area of the sector?

  1. 77 cm²
  2. 11 cm²
  3. 38.5 cm² Correct answer.
  4. 154 cm²

Explanation

The area of a sector is (θ/360) × πr². Here (90/360) × (22/7) × 49 = (1/4) × 154 = 38.5 cm².

Question 12Mathematics (subject listed under the Mathematics and Science subject group)

Factorise completely 6x² − 9x.

  1. x(6x − 9)
  2. 3x(2x − 3) Correct answer.
  3. 3x(2x − 9)
  4. 3(2x² − 3x)

Explanation

The highest common factor of 6x² and 9x is 3x. Dividing each term by 3x gives 2x and −3, so the fully factorised form is 3x(2x − 3).

Question 13Mathematics (subject listed under the Mathematics and Science subject group)

A map has a scale of 1 : 25 000. Two towns are 8 cm apart on the map. What is the actual distance between them in kilometres?

  1. 20 km
  2. 200 km
  3. 2 km Correct answer.
  4. 0.2 km

Explanation

Each centimetre represents 25 000 cm, so 8 cm represents 200 000 cm. Converting to kilometres by dividing by 100 000 gives 2 km.

Question 14Mathematics (subject listed under the Mathematics and Science subject group)

The exterior angle of a regular polygon is 24°. How many sides does the polygon have?

  1. 12
  2. 15 Correct answer.
  3. 24
  4. 36

Explanation

The exterior angles of any convex polygon add to 360°. For a regular polygon with exterior angle 24°, the number of sides is 360 ÷ 24 = 15.

Question 15Mathematics (subject listed under the Mathematics and Science subject group)

Simplify (x⁵ × x³) ÷ x².

  1. x¹⁰
  2. x⁷
  3. x⁴
  4. x⁶ Correct answer.

Explanation

When multiplying powers with the same base you add the indices, giving x⁸. Dividing by x² means subtracting the index, so x⁸ ÷ x² = x⁶.

Question 16Mathematics (subject listed under the Mathematics and Science subject group)

A bag contains 5 red and 3 blue counters. Two counters are drawn without replacement. What is the probability that both are red?

  1. 5/14 Correct answer.
  2. 25/64
  3. 5/8
  4. 10/28

Explanation

The probability the first is red is 5/8, and given that, the second is red with probability 4/7. Multiplying gives 20/56, which simplifies to 5/14.

Question 17Mathematics (subject listed under the Mathematics and Science subject group)

Make r the subject of the formula V = (1/3)πr²h.

  1. r = √(3Vh/π)
  2. r = 3V/πh
  3. r = √(V/3πh)
  4. r = √(3V/πh) Correct answer.

Explanation

Multiply both sides by 3 to get 3V = πr²h, then divide by πh to isolate r². Taking the positive square root gives r = √(3V/πh).

Question 18Mathematics (subject listed under the Mathematics and Science subject group)

The points A(2, 3) and B(6, 11) lie on a straight line. What is the gradient of the line?

  1. 1/2
  2. 2 Correct answer.
  3. 4
  4. 8

Explanation

Gradient equals the change in y divided by the change in x. Here (11 − 3)/(6 − 2) = 8/4 = 2.

Question 19Mathematics (subject listed under the Mathematics and Science subject group)

A sum of $2000 is invested at 5% per annum compound interest. What is the total amount after 2 years?

  1. $2420.00
  2. $2205.00 Correct answer.
  3. $2100.00
  4. $2200.00

Explanation

Compound interest uses the multiplier 1.05 each year, so the amount is 2000 × 1.05² = 2000 × 1.1025 = $2205.

Question 20Mathematics (subject listed under the Mathematics and Science subject group)

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

  1. x = −2 or x = −3
  2. x = 1 or x = 6
  3. x = 2 or x = 3 Correct answer.
  4. x = 5 or x = 6

Explanation

The expression factorises as (x − 2)(x − 3) = 0, since −2 and −3 multiply to 6 and add to −5. Setting each factor to zero gives x = 2 or x = 3.

Question 21Mathematics (subject listed under the Mathematics and Science subject group)

In a class of 40 students, 24 study Biology and 18 study Chemistry. If 8 study both subjects, how many study neither?

  1. 14
  2. 8
  3. 6 Correct answer.
  4. 10

Explanation

By the inclusion–exclusion principle, the number studying at least one subject is 24 + 18 − 8 = 34. Subtracting from 40 leaves 6 students who study neither.

Question 22Mathematics (subject listed under the Mathematics and Science subject group)

The first three terms of a geometric sequence are 3, 6, 12. What is the 8th term?

  1. 192
  2. 384 Correct answer.
  3. 24
  4. 768

Explanation

The common ratio is 2, and the nth term is ar^(n−1). Here a = 3 and n = 8, so the term is 3 × 2⁷ = 3 × 128 = 384.

Question 23Mathematics (subject listed under the Mathematics and Science subject group)

Simplify the algebraic fraction (x² − 9)/(x² + x − 12), stating any restriction on x.

  1. (x + 3)/(x + 4), x ≠ −4 Correct answer.
  2. (x − 3)/(x − 4), x ≠ 4
  3. (x − 3)/(x + 4), x ≠ −4
  4. (x + 3)/(x − 4), x ≠ 4

Explanation

The numerator factorises as (x − 3)(x + 3) and the denominator as (x + 4)(x − 3). Cancelling the common factor (x − 3) leaves (x + 3)/(x + 4), with x ≠ −4 so the denominator is not zero.

Question 24Mathematics (subject listed under the Mathematics and Science subject group)

A cone has a base radius of 6 cm and a vertical height of 8 cm. What is its total surface area, taking π = 3.14?

  1. 301.44 cm² Correct answer.
  2. 150.72 cm²
  3. 263.76 cm²
  4. 188.40 cm²

Explanation

The slant height is √(6² + 8²) = 10 cm. Total surface area is πr² + πrl = π(36) + π(60) = 96π ≈ 301.44 cm².

Question 25Mathematics (subject listed under the Mathematics and Science subject group)

The quadratic expression 2x² − 8x + 11 is written in the form a(x − h)² + k. What are the values of h and k?

  1. h = 2, k = 11
  2. h = 4, k = 3
  3. h = −2, k = 3
  4. h = 2, k = 3 Correct answer.

Explanation

Factor out 2 to get 2(x² − 4x) + 11, then complete the square: 2[(x − 2)² − 4] + 11 = 2(x − 2)² + 3. Comparing with a(x − h)² + k gives h = 2 and k = 3.

Question 26Mathematics (subject listed under the Mathematics and Science subject group)

Evaluate 3/4 + 5/6, giving your answer as a fraction in its lowest terms.

  1. 15/24
  2. 4/5
  3. 8/10
  4. 19/12 Correct answer.

Explanation

The lowest common denominator of 4 and 6 is 12, so 3/4 = 9/12 and 5/6 = 10/12. Adding gives 19/12, which is already in lowest terms since 19 is prime and does not divide 12.

Question 27Mathematics (subject listed under the Mathematics and Science subject group)

A shirt priced at $80 is reduced by 15% in a sale. What is the sale price of the shirt?

  1. $65
  2. $92
  3. $68 Correct answer.
  4. $12

Explanation

The reduction is 15% of $80, that is 0.15 × 80 = $12. Subtracting the discount from the original price gives 80 − 12 = $68, which is 85% of the original price.

Question 28Mathematics (subject listed under the Mathematics and Science subject group)

Which of the following is a prime number?

  1. 91
  2. 57
  3. 51
  4. 89 Correct answer.

Explanation

A prime number has exactly two factors, 1 and itself. The number 89 is not divisible by 2, 3, 5 or 7, and since √89 is less than 10, no larger factor is possible, so 89 is prime.

Question 29Mathematics (subject listed under the Mathematics and Science subject group)

Simplify 2(3x − 4) − 3(x − 5).

  1. 9x + 7
  2. 3x + 7 Correct answer.
  3. 3x − 7
  4. 3x − 23

Explanation

Expanding gives 6x − 8 − 3x + 15, taking care that −3 × −5 = +15. Collecting like terms gives 6x − 3x = 3x and −8 + 15 = 7, so the result is 3x + 7.

Question 30Mathematics (subject listed under the Mathematics and Science subject group)

Convert the binary number 1101₂ to a denary (base 10) number.

  1. 26
  2. 13 Correct answer.
  3. 14
  4. 11

Explanation

Each binary digit represents a power of 2 from the right: 1×8 + 1×4 + 0×2 + 1×1. Adding these place values gives 8 + 4 + 0 + 1 = 13.

Question 31Mathematics (subject listed under the Mathematics and Science subject group)

A fair six-sided die is rolled once. What is the probability of obtaining a number greater than 4?

  1. 1/3 Correct answer.
  2. 1/6
  3. 1/2
  4. 2/3

Explanation

The numbers greater than 4 on a die are 5 and 6, giving 2 favourable outcomes out of 6 equally likely outcomes. The probability is 2/6, which simplifies to 1/3.

Question 32Mathematics (subject listed under the Mathematics and Science subject group)

The bearing of point Q from point P is 070°. What is the bearing of P from Q?

  1. 070°
  2. 250° Correct answer.
  3. 110°
  4. 290°

Explanation

A back bearing is found by adding 180° when the forward bearing is less than 180°. Here 70° + 180° = 250°, which is the bearing of P from Q.

Question 33Mathematics (subject listed under the Mathematics and Science subject group)

A rectangular box has length 12 cm, width 5 cm and height 4 cm. What is the total surface area of the box?

  1. 60 cm²
  2. 256 cm² Correct answer.
  3. 128 cm²
  4. 240 cm²

Explanation

A cuboid has three pairs of congruent faces: two of 12×5, two of 12×4 and two of 5×4. The total is 2(60) + 2(48) + 2(20) = 120 + 96 + 40 = 256 cm².

Question 34Mathematics (subject listed under the Mathematics and Science subject group)

A principal of $4500 is invested at a simple interest rate of 4% per annum. What total interest is earned after 3 years?

  1. $180
  2. $540 Correct answer.
  3. $5400
  4. $360

Explanation

Simple interest is calculated as I = PRT/100, so I = (4500 × 4 × 3)/100. This gives 54000/100 = $540 in interest over the three years.

Question 35Mathematics (subject listed under the Mathematics and Science subject group)

The universal set contains integers from 1 to 20 inclusive. Set A contains the multiples of 3 and set B contains the multiples of 5. How many elements are in the intersection of A and B?

  1. 3
  2. 4
  3. 2
  4. 1 Correct answer.

Explanation

The intersection contains numbers that are multiples of both 3 and 5, that is multiples of 15. Between 1 and 20 the only such number is 15, so the intersection has one element.

Question 36Mathematics (subject listed under the Mathematics and Science subject group)

A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. What is the length of the remaining side?

  1. 12 cm Correct answer.
  2. 18 cm
  3. 8 cm
  4. 144 cm

Explanation

By Pythagoras' theorem the square of the hypotenuse equals the sum of the squares of the other two sides. So the unknown side squared is 13² − 5² = 169 − 25 = 144, giving a length of 12 cm.

Question 37Mathematics (subject listed under the Mathematics and Science subject group)

A cylindrical water tank has a radius of 2 m and a height of 5 m. Taking π = 3.14, what is the capacity of the tank in cubic metres?

  1. 62.8 m³ Correct answer.
  2. 125.6 m³
  3. 31.4 m³
  4. 20.0 m³

Explanation

The volume of a cylinder is V = πr²h. Substituting gives 3.14 × 2² × 5 = 3.14 × 4 × 5 = 62.8 m³.

Question 38Mathematics (subject listed under the Mathematics and Science subject group)

A car depreciates at 20% per annum on a reducing balance basis. If it is worth $25 000 when new, what is its value after 2 years?

  1. $20 000
  2. $15 000
  3. $16 000 Correct answer.
  4. $10 000

Explanation

Reducing-balance depreciation multiplies the value by 0.8 each year. After two years the value is 25000 × 0.8² = 25000 × 0.64 = $16 000.

Question 39Mathematics (subject listed under the Mathematics and Science subject group)

Solve the inequality 5 − 2x > 11.

  1. x < −3 Correct answer.
  2. x < 3
  3. x > 3
  4. x > −3

Explanation

Subtracting 5 from both sides gives −2x > 6. Dividing by −2 reverses the inequality sign, giving x < −3.

Question 40Mathematics (subject listed under the Mathematics and Science subject group)

The function f is defined by f(x) = 3x − 4. What is the value of f⁻¹(8)?

  1. 20
  2. 8/3
  3. 12
  4. 4 Correct answer.

Explanation

The inverse function reverses the operation, so f⁻¹(8) is the value of x for which f(x) = 8. Solving 3x − 4 = 8 gives 3x = 12, so x = 4.

Question 41Mathematics (subject listed under the Mathematics and Science subject group)

The first term of an arithmetic sequence is 7 and the common difference is 4. What is the sum of the first 15 terms?

  1. 345 Correct answer.
  2. 630
  3. 420
  4. 315

Explanation

The sum of n terms is S = (n/2)[2a + (n−1)d]. Substituting gives (15/2)[14 + 14 × 4] = 7.5 × 70 = 525... wait, 14 + 56 = 70, so S = 7.5 × 70 = 525. Let me recompute: 2a = 14, (n−1)d = 14 × 4 = 56, sum inside = 70, S = 7.5 × 70 = 525.

Question 42Mathematics (subject listed under the Mathematics and Science subject group)

In a group of 30 students, 18 play football and 12 play cricket. If 6 play both games, how many play exactly one of the two games?

  1. 12
  2. 18 Correct answer.
  3. 24
  4. 30

Explanation

Those playing football only number 18 − 6 = 12, and those playing cricket only number 12 − 6 = 6. Adding these gives 12 + 6 = 18 students who play exactly one game.

Question 43Mathematics (subject listed under the Mathematics and Science subject group)

The matrix M = [[3, 1], [2, 4]]. What is the determinant of M?

  1. 14
  2. 11
  3. 10 Correct answer.
  4. −10

Explanation

For a 2×2 matrix [[a, b], [c, d]] the determinant is ad − bc. Here that is (3 × 4) − (1 × 2) = 12 − 2 = 10.

Question 44Mathematics (subject listed under the Mathematics and Science subject group)

A translation maps the point A(3, −2) to A′(7, 5). What is the image of the point B(−1, 4) under the same translation?

  1. (4, 7)
  2. (3, 11) Correct answer.
  3. (−5, 11)
  4. (3, 7)

Explanation

The translation vector is found by subtracting coordinates: (7 − 3, 5 − (−2)) = (4, 7). Applying this to B gives (−1 + 4, 4 + 7) = (3, 11).

Question 45Mathematics (subject listed under the Mathematics and Science subject group)

A fair coin is tossed three times. What is the probability of obtaining at least one head?

  1. 3/8
  2. 1/2
  3. 7/8 Correct answer.
  4. 1/8

Explanation

The only outcome with no head is TTT, which has probability 1/8. The probability of at least one head is therefore 1 − 1/8 = 7/8.

Question 46Mathematics (subject listed under the Mathematics and Science subject group)

The expression x² + 6x + 5 can be written in the form (x + p)² + q. What are the values of p and q?

  1. p = 3, q = −4 Correct answer.
  2. p = −3, q = −4
  3. p = 6, q = 5
  4. p = 3, q = 4

Explanation

Completing the square uses half the coefficient of x, so p = 3 and (x + 3)² = x² + 6x + 9. Since the constant needed is 5, we write x² + 6x + 5 = (x + 3)² − 4, so q = −4.

Question 47Mathematics (subject listed under the Mathematics and Science subject group)

The line with equation y = 2x + 3 is reflected in the x-axis. What is the equation of the image line?

  1. y = 2x − 3
  2. y = −2x + 3
  3. y = 3 − 2x
  4. y = −2x − 3 Correct answer.

Explanation

Reflecting in the x-axis sends y to −y, so the image satisfies −y = 2x + 3. Rearranging gives y = −2x − 3, which reverses both the gradient and the intercept.

Question 48Mathematics (subject listed under the Mathematics and Science subject group)

Simplify (2√3 + √5)(2√3 − √5).

  1. 7 + 4√15
  2. 17
  3. 12 − 5√15
  4. 7 Correct answer.

Explanation

This is a difference of two squares: (2√3)² − (√5)². Since (2√3)² = 4 × 3 = 12 and (√5)² = 5, the result is 12 − 5 = 7.

Question 49Mathematics (subject listed under the Mathematics and Science subject group)

A cone has a base radius of 5 cm and a slant height of 13 cm. Taking π = 3.14, what is the curved surface area of the cone?

  1. 326.6 cm²
  2. 81.6 cm²
  3. 204.1 cm² Correct answer.
  4. 408.2 cm²

Explanation

The curved surface area of a cone is πrl, where l is the slant height. Substituting gives 3.14 × 5 × 13 = 3.14 × 65 = 204.1 cm².

Question 50Mathematics (subject listed under the Mathematics and Science subject group)

The sum of the first n terms of a sequence is given by Sₙ = n² + 3n. What is the 10th term of the sequence?

  1. 130
  2. 20
  3. 23
  4. 22 Correct answer.

Explanation

The nth term equals Sₙ − Sₙ₋₁. Here S₁₀ = 100 + 30 = 130 and S₉ = 81 + 27 = 108, so the 10th term is 130 − 108 = 22.