CSEC Mathematics Paper 2 January 2026 - Free CXC Past Paper with Answers

Factorize the expression $1 - p$.

Expand and simplify the following expression. $(4r - 5q)(3r + q) + 3qr$

Solve the inequality $-4p + 3 \ge 19 + 2p$.

Determine the LARGEST integer value of $p$ that satisfies the inequality in (c) (i).

The diagram below shows a right-angled triangle with its dimensions given in terms of $x$.

For the right-angled triangle, show that $x^2 + 4x - 45 = 0$.

$ABCDEFGH$ is a regular octagon, with one of its internal angles marked $g$, as shown in the diagram below.

Complete the statement below in relation to the diagram shown above. The regular octagon has .................................... lines of symmetry and rotational symmetry of order ....................................

Calculate the value of Angle $g$.

The diagram below shows two similar, right-angled triangles drawn from a common vertex, $V$. The lines $ZY$ and $WX$ are parallel. Also, the lines $VY = 5$ cm, $ZY = 7$ cm and cm.

Calculate the length of $VX$.

Determine the magnitude of Angle $VWX$.

Show that the value of $c$ is 10.

Determine the gradient of $L$.

The line with equation $3x + 4y = 8$ intersects the line $L$ at the point $T$. Determine the coordinates of the point $T$.

The diagram below shows the graph of $L$ and two other lines, $x = -1$ and $y = 5$.

On the graph above, draw the line $y = x - 1$ and shade the region that satisfies the inequalities listed below.

Some Grade 11 students were surveyed to determine the job sector in which they are most likely to seek employment after graduating. Their choices are represented on the pie chart shown below.

Calculate the (i) percentage of students who are likely to seek employment within the agriculture and ICT sectors (ii) value of $p$.

percentage of students who are likely to seek employment within the agriculture and ICT sectors

value of $p$.

Liz has a set of red, yellow, and white buttons in a sack. She chooses a button at random.

The probability that she chooses a yellow button is 0.3.

The probability that she chooses a white button is 0.1.

Determine the probability that Liz chooses a red button.

If there were 80 buttons in the sack originally, determine the number of buttons that were red or yellow.

A map is drawn to a scale of $1 : 20 \ 000$. On the map, 1 cm represents $n$ km.

Determine the (i) value of $n$ (ii) distance on the map, in cm, which corresponds to an actual distance of 4.8 km (iii) actual area, in square kilometres, of a lake which has an area of 12 cm$^2$ on the map.

value of $n$

distance on the map, in cm, which corresponds to an actual distance of 4.8 km

actual area, in square kilometres, of a lake which has an area of 12 cm$^2$ on the map.

The diagram below shows a running belt, $EFGHIJE$, that revolves around a running board on a treadmill. In the diagram, $EJI$ and $HGF$ are semicircles with a diameter of 0.7 m and $EFHI$ is a rectangle.

Calculate the length of the belt.

Glenda uses the equipment to exercise 4 times a week and runs at 9 km/h for 20 minutes each time.

Calculate the number of complete revolutions the running belt makes in one week during Glenda's exercise routine. [Assume that the running belt moves at the same speed as Glenda.]

Complete the diagram below to show Figure 5.

The number of squares, $Q$, the number of sticks, $S$, and the perimeter, $P$, of each figure, follow a pattern. The values for $Q$, $S$ and $P$ for the first 4 figures 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.

Complete the row for Figure Number (D) = 5.

Complete the row for Number of Squares (Q) = 47.

Complete the row for Figure Number (D) = $n$.

Mala says that she can make one of the figures with EXACTLY 502 squares. Explain why she is incorrect.

The functions $f$ and $g$ are defined as follows.

$f: x \to x^2 + 3, x \ge 0$ $g: x \to 2x + 2, x \in R$

Calculate the value of $g(-1)$.

Write down an expression for $f^{-1}(x)$.

Derive a simplified expression for $gf(x)$.

Given that $fg(x) = 4x^2 + 8x + 7$, solve the following equation.

$fg(x) = 2gf(x) + 15$

On the grid provided in the answer booklet, plot the graph of the functions $f$ and $g$, for $x \ge 0$.

The diagram below shows quadrilaterals $O$, $M$ and $N$. Quadrilaterals $M$ and $N$ are the images of Quadrilateral $O$ after it has undergone 2 different transformations.

Describe fully the single transformation that maps Quadrilateral $O$ onto Quadrilateral $M$.

Describe fully the single transformation that maps Quadrilateral $O$ onto Quadrilateral $N$.

On the diagram on page 24, draw the image of Quadrilateral $O$ after it undergoes the following transformations. a) Translation by the vector $\begin{pmatrix} -5 \\ 2 \end{pmatrix}$. Label this image $L$. b) Reflection in the line . Label this image .

A buoy ($B$) and a lighthouse ($L$) are 95 km apart. The bearing of $B$ from $L$ is $230^\circ$.

Using a scale of 1 cm : 10 km and the space provided below, complete the diagram to show the buoy () relative to the lighthouse (). Indicate the given bearing on your drawing.

The diagram below shows Triangle $OPR$. The point $M$ is the midpoint of $OP$ and the point $N$ is the midpoint of $OR$. In the diagram, $\vec{OM} = \mathbf{u}$ and $\vec{ON} = \mathbf{v}$.

Find in terms of $\mathbf{u}$ and $\mathbf{v}$, simplified expressions for a) $\vec{MN}$

Find in terms of $\mathbf{u}$ and $\mathbf{v}$, simplified expressions for b) $\vec{NP}$

Show that $MN$ is parallel to $PR$.

The matrix $P$, written in terms of $a$ where $a$ is a real constant, is as follows.

$P = \begin{pmatrix} 3a & 4 \\ 6 & 2a \end{pmatrix}$

Calculate the determinant of $P$, in terms of $a$.

Determine the values of $a$ for which Matrix $P$ is singular.

Determine $P^{-1}$, the inverse of $P$, for which $P$ is non-singular.

Write down the $2 \times 2$ matrix that represents a

counterclockwise rotation of $90^\circ$ about the origin. Label this matrix $X$.

counterclockwise rotation of $90^\circ$ about the origin followed by a reflection in the $y$-axis, given that $Q = \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}$ represents a reflection in the -axis. Label this matrix .