Past Paper Question Bank
500 questions from real CXC past papers
500 questions found
MAY/JUNE 2025 · Paper 2
Section I
- (a) Using a calculator, or otherwise, evaluate EACH of the following, giving your answers in EXACT form. (i) (3/2)² − 1 + 6 (ii) (2.1 × 10/7) + 12 ÷ 1 3/5. (b) Maranda earns $8 316 per month. She spends 4/7 of her earnings on utility bills, food and personal items, and saves the remainder. (i) What percentage of her monthly salary does she save? (ii) The portion of her earnings spent on utility bills, food and personal items is divided in the ratio 5:3:4 respectively. Calculate the amount of money she spends on personal items. (iii) Maranda saves the same amount of money each month. Show that her annual savings from her earnings is $42 768. (iv) She invests the $42 768 in her credit union which pays compound interest of 5% per annum. What is the TOTAL interest earned after 2 years? The final amount, A, when principal, P, is invested compound interest at rate, r, for n number of years is given by A = P(1 + r/100)ⁿ.
Objective 1.19— Solve problems involving number theory and computation
MAY/JUNE 2025 · Paper 2
Section I
- (a) Factorize, completely, EACH of the following expressions. (i) xy² − x²y (ii) 3x² + x − 10. (b) Solve for n. 4ⁿ ÷ 4³ = 1/4. (c) The lengths of three sides of a trapezium are shown on the diagram below. The area of the trapezium is 750 square units. The diagram shows the parallel sides labelled 4p and 3q and the perpendicular height labelled 6p. (i) Write down an expression in terms of p and q for the area of the trapezium. (ii) Given that q = 2p, determine the value of p.
Objective 2.1— Factorise algebraic expressions, including difference of squares, grou
MAY/JUNE 2025 · Paper 2
Section I
- (a) Using a ruler, a pencil and a pair of compasses, construct the triangle PQR, such that PQ = 9 cm, ∠QPR = 60° and PR = 12 cm. (b) The diagram below shows two quadrilaterals, R and S, where S is the image of R under a transformation. (i) Describe, fully, the single transformation that maps Quadrilateral R onto Quadrilateral S. (ii) On the grid on page 12, draw the image of Quadrilateral R when it is translated by the vector [−4; 5]. Name the image T. (iii) On the grid on page 12, draw the image of Quadrilateral R when it is rotated 180° about the origin. Name the image M.
Objective 4.4— Construct lines, angles and polygons using appropriate instruments
MAY/JUNE 2025 · Paper 2
Section I
- (a) The graph below shows the straight line PQ. (i) Find the gradient of the line PQ. (ii) Write down the equation of the line through PQ in the form y = mx + c. (b) Two functions, f and g, are defined as f(x) = x² − 1 and g(x) = 3x + 2. Find (i) g(−6) (ii) the inverse function, g⁻¹(x). (iii) a) Show that fg(x) = 3(3x + 1)(x + 1). b) Hence, solve the equation fg(x) = 0.
Objective 3.14— Evaluate functions, inverse functions and composite functions
MAY/JUNE 2025 · Paper 2
Section I
Thirty students took a Mathematics test. The marks they scored are shown in the table below. The table has the columns Mark, Tally, Frequency and Cumulative Frequency, with rows: Mark 1, Frequency 3, Cumulative Frequency 3; Mark 2, Frequency 4, Cumulative Frequency 7; Mark 3, Frequency 8; Mark 5, Frequency 3, Cumulative Frequency 18; Mark 7, Frequency 1, Cumulative Frequency 19; Mark 8, Frequency 6; Mark 10, Frequency 5, Cumulative Frequency 30. (a) Complete the Cumulative Frequency column in the table above. (b) Using the information in the table above, determine the (i) range (ii) modal mark (iii) median mark (iv) mean mark. (c) The following two-way table shows the gender distribution of the students’ performance on the Mathematics test. The columns are Male, Female and Total. Pass: Male 4, Female 8, Total 12. Fail: Male 5, Female 13, Total 18. Total: Male 9, Female 21, Total 30. (i) A student is chosen at random. Find the probability that the student is a female who failed the test. (ii) A male student is chosen at random. What is the probability that he passed the test?
Objective 1.4— Determine mean, median and mode for raw ungrouped data
MAY/JUNE 2025 · Paper 2
Section I
PMQROS is the cross-section of a play area in a park. PQRS is a rectangle and PMQ is a semi-circle. O is the mid-point of RS. OP = OQ = 15 m and Angle POQ = 40°. Use π = 22/7. (a) (i) Determine the value of Angle OPQ. (ii) Calculate the length of OR. (b) Calculate the area of the shaded portion of the diagram. (c) Find the perimeter of the cross-section PMQROS. The diagram includes the labels 15 m, 14.1 m and 40°.
Objective 4.13— Solve problems involving measurement, including compound shapes and so
MAY/JUNE 2025 · Paper 2
Section I
A sequence of figures is made up of regular pentagons, using sticks of unit length. The first three figures in the sequence are shown below. The vertices in each figure are marked with dots. (a) An incomplete diagram of Figure 4 of the sequence is shown below. Complete Figure 4 by adding more sticks and dots. (b) Study the pattern of numbers in each row of the table below. Each row relates to one of the figures in the sequence of figures shown on page 22. Some rows have not been included in the table. Complete the rows corresponding to (i), (ii) and (iii) in the table below. The table has the columns Figure, Number of Sticks (S) and Number of Dots (D), with rows: Figure 1, S = 5, D = 5; Figure 2, S = 9, D = 8; Figure 3, S = 13, D = 11; ⋮, ⋮, ⋮; (i) Figure 20, S blank, D blank; (ii) Figure blank, S = 169, D blank; (iii) Figure n, S blank, D blank. (c) Write an equation in S, D and n to show the relationship between the number of sticks, S, and the number of dots, D, for Figure n.
MAY/JUNE 2025 · Paper 2
Section II
- (a) The following diagram shows the graph of the function y = x² + x − 2. (i) From the graph, state the (a) roots of the function (b) coordinates of the y-intercept of the function (c) minimum value of the function (d) equation of the axis of symmetry of the function. (b) (i) On the same pair of axes on page 24, draw and label the line y = 2x + 4. (ii) Using your graphs, determine the solutions to the following pair of simultaneous equations: y = x² + x − 2; y = 2x + 4. (c) The following diagram shows the velocity–time graph of a car’s journey from Town R to Town Q. The car accelerates for two minutes, travels at a constant maximum speed, then slows to a stop. (i) Determine the initial acceleration of the car. (ii) Calculate the distance between the two towns.
Objective 2.5— Interpret graphs of functions, including distance-time and speed-time
MAY/JUNE 2025 · Paper 2
Section II
- (a) A ship sails from Point A to Point B, which is 15 km from A on a bearing of 042°. The ship then sails to Point C, which is 19 km from B on a bearing of 130°. The following diagram shows a sketch of the ship’s journey. (i) On the diagram, insert the bearings 042° and 130°. (ii) Calculate the distance between Town A and Town C. (iii) Determine the bearing of Town A from Town C. (b) The points L, M and P lie on the circumference of a circle whose centre is O. The line NP is a tangent to the circle at P and OMN is a straight line. The line PL is a diameter and Angle ONP = 24°. Calculate the value of EACH of the following angles. Show detailed working where necessary and give a reason to support your answers. (i) Angle PON (ii) Angle PLM (iii) Angle PMN.
Objective 3.1— Solve geometric problems using properties of circles and circle theore
MAY/JUNE 2025 · Paper 2
Section II
- (a) In the diagram below OPQL is a parallelogram. OP⃗ = r and OL⃗ = s. T is the point such that PQ⃗ = QT⃗. The point M divides PL in the ratio 2:1. (i) Find, in terms of r and s, (a) PL⃗ (b) OM⃗. (ii) Prove that the points O, M and T are collinear. (b) Three matrices, A, B and C, are such that A = [[3, 2], [5, 4]], B = [[4, 0, 2], [3, −1, 7]] and C = [[4, −1, 2], [7, 3, −5]]. (i) Find the matrix AB + C. (ii) Find A⁻¹, the inverse of A. (iii) Write down the 2 × 2 matrix that represents the matrix product AA⁻¹.
Objective 4.9— Use matrices to solve simple problems in Arithmetic, Algebra and Geome
MAY/JUNE 2024 · Paper 2
Section I
- (a) (i) Calculate the value of √((7.1)² + (2.9)²), giving your answer correct to a) 2 significant figures b) 2 decimal places. (ii) Write the following quantities in ascending order: 12/25, 0.46, 47%. (b) Mahendra and Jaya shared $7 224 in the ratio 7:5. How much MORE money does Mahendra receive than Jaya? (c) The present population of Portsmouth is 550 000. It is expected that this population will increase by 42% by the year 2030. (i) Write the number 550 000 in standard form. (ii) Calculate the expected population of Portsmouth in 2030. (d) The graph below can be used to convert between United States dollars (US$) and Eastern Caribbean dollars (EC$). Using the graph, (i) convert US$2 to EC$. (ii) convert EC$70 to US$.
Objective 1.19— Solve problems involving number theory and computation
MAY/JUNE 2024 · Paper 2
Section I
Laura needs to put mesh around two seedbeds to protect her seedlings. Altogether, she uses 60 m of mesh. One of the seedbeds is a rectangle and the other is a square, as shown in the diagram below. The width of the rectangular seedbed is x metres. The length of the rectangular seedbed is 3 times its width. The length of a side of the square seedbed is y metres. (a) Using the information given above, derive a simplified expression for y in terms of x. (b) The area of the rectangular seedbed is equal to the area of the square seedbed. (i) Use this information and your answer in (a) to write down a quadratic equation, in terms of x, and show that it simplifies to x² − 60x + 225 = 0. (ii) Solve the equation x² − 60x + 225 = 0 using the quadratic formula. (iii) Calculate the TOTAL area of the two seedbeds.
Objective 2.8— Represent direct and inverse variation symbolically
MAY/JUNE 2024 · Paper 2
Section I
- (a) A vertical flagpole, FP, stands on horizontal ground and is held by two ropes, PG and PR, as shown in the diagram below. PG = 18 m, FR = 9.7 m and angle FGP = 38°. (i) Calculate the height of the flagpole, FP. (ii) Find PR, the length of one of the pieces of rope used to hold the flagpole. (b) In the diagram below, PQ is parallel to MN, LRT is an isosceles triangle and SLT is a straight line. Find the value of x.
Objective 4.10— Apply trigonometric ratios to solve problems
MAY/JUNE 2024 · Paper 2
Section I
- (a) A rectangle, PQRS, has a diagonal, PR, where P is the point (−3, 10) and R is the point (4, −4). (i) Calculate the length of the line PR. (ii) Determine the equation of the line PR. (b) Two functions, f and g, are defined as follows. f(x) = 3x + 1 and g(x) = x². Find, in its simplest form, an expression for (i) f(x − 2) (ii) g(3x + 2) + 10.
Objective 3.14— Evaluate functions, inverse functions and composite functions
MAY/JUNE 2024 · Paper 2
Section I
- (a) Mr Morgan administered a spelling test to his class. The table below shows the number of words out of 10 that each student spelt correctly. Number of Words: 5, 6, 7, 8, 9, 10. Frequency: 8, 4, 2, 2, 3, 4. (i) For the data set shown above, state the a) mode b) median. (ii) Calculate the mean number of words spelt correctly. (b) The attendance officer at a particular school recorded the time, t, in minutes, taken by each student in a group to travel to school. The data collected is shown on the cumulative frequency curve below. Using the cumulative frequency curve, find an estimate of (i) the number of students who took at MOST 32 minutes to travel to school (ii) the inter-quartile range. (c) The letters in the word “POSITIVITY” are each written on separate cards and placed in a bag. Dacia picks 2 of these cards, at random, with replacement. Find the probability that she picks the letter “I” then the letter “V”.
Objective 1.4— Determine mean, median and mode for raw ungrouped data
MAY/JUNE 2024 · Paper 2
Section I
[In this question, take π = 22/7.] (a) The diagram below shows a gold bar in the shape of a trapezoidal prism. Its volume is 2 886 cm³. The length and height of the prism are indicated on the diagram. (i) Calculate the area of the shaded cross-section of the trapezoidal prism. (ii) The cuboid-shaped gold bar shown below has the same volume as the trapezoidal prism-shaped gold bar displayed at (a). Calculate the height, h, of the cuboid-shaped gold bar. (b) The trapezoidal gold bar is melted down and all the gold is used to make SIX identical spheres. Calculate, for EACH sphere of gold, its (i) radius [The volume, V, of a sphere with radius, r, is V = 4/3πr³.] (ii) surface area [The surface area, A, of a sphere with radius r, A = 4πr².] (iii) mass, to the nearest kilogram, given that the density of gold is 19.3 g/cm³. [Density = mass/volume]
Objective 4.13— Solve problems involving measurement, including compound shapes and so
MAY/JUNE 2024 · Paper 2
Section I
The diagram below shows the first four diagrams in a sequence of regular hexagons. Each regular hexagon is made using sticks of unit length. (a) Complete the diagram below to represent Diagram 5 in the sequence of regular hexagons. (b) The number of regular hexagons, H, the number of sticks, S, and the perimeter of each figure, P, follow a pattern. The values for H, S and P, for the first 4 diagrams are shown in the table below. Study the pattern of numbers in each row of the table and answer the questions that follow. Complete the rows marked (i), (ii) and (iii) in the table below. Table: Diagram Number (D), Number of Hexagons (H), Number of Sticks (S), Perimeter (P): 1, 3, 15, 12; 2, 5, 23, 16; 3, 7, 31, 20; 4, 9, 39, 24; (i) 5, ..., ..., 28; (ii) ..., 47, 191, ...; (iii) n, ..., ..., .... (c) Skyla says that she can make one of these figures with a perimeter of EXACTLY 1 005. Explain why she is incorrect.
MAY/JUNE 2024 · Paper 2
Section II
- (a) The functions f and g are defined as follows. f(x) = (2x − 1)/3 and g(x) = 5 − x². (i) Determine the value of a) g(2) b) f⁻¹(3). (ii) Derive an expression, in its simplest form, for fg(x). (iii) Sketch the graph of the function g(x) in the space provided below. On your sketch, indicate the maximum/minimum point and the roots of the function.
Objective 3.14— Evaluate functions, inverse functions and composite functions
MAY/JUNE 2024 · Paper 2
Section II
- (a) V, X, Y and Z lie on the circumference of the circle shown below, centre O, with diameter VY. UW is a tangent to the circle at V. Angle VXZ = 62° and Angle XYV = 18°. (i) State a theorem that justifies the values of EACH of the following angles. a) Angle b = 62° b) Angle c = 124° c) Angle OVW = 90°. (ii) Find the values of Angles a, d and e. Show ALL working where appropriate. (b) The diagram below shows a quadrilateral PQRS formed by joining two triangles, PQS and QRS. In the diagram, PQ = 21 m, SQ = 18 m, SR = 16 m, ∠PSQ = 72°, ∠QSR = 25° and ∠SQR = 43°. (i) Calculate the length of QR. (ii) The bearing of P from S is 205°. Determine the bearing of a) R from S b) S from P.
Objective 3.1— Solve geometric problems using properties of circles and circle theore
MAY/JUNE 2024 · Paper 2
Section II
- (a) The determinant of the matrix [[6, 2v], [−5, −v]] is 24. Calculate the value of v. (b) The matrices L and M are defined as follows. L = [[9, 5], [3, 2]], M = [[2], [−4]]. Evaluate EACH of the following. (i) The matrix product LM (ii) L⁻¹, the inverse of L. (c) PQ⃗ = [5, −4]ᵀ. If P is the point (−2, 3), determine the coordinates of Q. (d) In the pentagon OABCD, OA is parallel to DC and AB is parallel to OD. OD = 2AB and OA = 2DC. OA⃗ = a and AB⃗ = b. Find, in terms of a and b, in its simplest form, (i) AD⃗ (ii) BC⃗. (iii) State the conclusion about |AD⃗| and |BC⃗| that can be drawn from your responses in (i) and (ii).
Objective 4.9— Use matrices to solve simple problems in Arithmetic, Algebra and Geome
MAY/JUNE 2023 · Paper 2
Section I
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(a) Find the EXACT value of 5/6 + 2/3 − 12/35 × 7/9.
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(b) (i) Calculate the value of √[1 − (cos 37°)²] correct to 3 decimal places.
- (ii) Write 0.00527 in standard form.
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(c) Haresh works at a call centre for 35 hours each week. He is paid an hourly rate of $11.20.
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(i) Calculate the amount of money Haresh earns in a four-week month.
- (ii) In a certain week, Haresh works 8 hours overtime. Overtime hours are paid at 1 1/2 times the usual rate of $11.20 per hour. Find the TOTAL amount of money Haresh is paid for that week.
Objective 1.19— Solve problems involving number theory and computation
MAY/JUNE 2023 · Paper 2
Section I
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(a) Simplify 4/(5x) × 15x/16.
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(b) Solve the inequality 12 − 4m ≤ 5 − 8m.
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(c) The diagram below shows a compound shape, LMNPQR, made from two rectangles. The lengths in the diagram, which are written in terms of x, are in centimetres. The diagram gives LM = 4x − 5, MN = 3x, LR = x + 3 and PN = x + 1.
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(i) Find an expression, in terms of x, for the length
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a) PQ
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b) RQ.
- (ii) Given that the TOTAL area of the shape is 414 cm², show that x² + x − 72 = 0.
Objective 5.8— Simplify algebraic fractions
MAY/JUNE 2023 · Paper 2
Section I
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(a) The diagram below shows a semicircle with diameter AC. B is a point on the circumference and AB = BC = 8.2 cm.
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(i) State the geometrical name of the line AB.
- (ii) Find the value of the radius of the circle.
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(b) Each interior angle of a regular polygon is 160°. Calculate the number of sides of the polygon.
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(c) The diagram below shows a trapezium, A, drawn on a square grid. On the diagram above, draw the image of A after it undergoes a
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(i) reflection in the line x = −1 and label this image A′.
- (ii) translation with vector [4; −7] and label this image A″.
Objective 4.6— Solve geometric problems using properties of lines, angles, polygons,
MAY/JUNE 2023 · Paper 2
Section I
Consider the following functions.
f(x) = 3/(x + 2), g(x) = 4x − 5 and h(x) = x² + 1.
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(a) (i) For what value of x is f(x) undefined?
- (ii) Find the value of
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a) g(1/4)
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b) h(−3)
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c) ff(0).
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(b) Write an expression, in its simplest form, for gh(x).
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(c) Find g⁻¹(−2).
Objective 3.14— Evaluate functions, inverse functions and composite functions