CSEC Mathematics Paper 2 May/June 2024 - Free CXC Past Paper with Answers

Using the information given above, derive a simplified expression for $y$ in terms of $x$.

The area of the rectangular seedbed is equal to the area of the square seedbed.

Use this information and your answer in (a) to write down a quadratic equation, in terms of $x$, and show that it simplifies to $x^2 - 60x + 225 = 0$.

Solve the equation $x^2 - 60x + 225 = 0$ using the quadratic formula.

Calculate the TOTAL area of the two seedbeds.

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 $FGP = 38^\circ$.

Calculate the height of the flagpole, $FP$.

Find $PR$, the length of one of the pieces of rope used to hold the flagpole.

In the diagram below, $PQ$ is parallel to $MN$, $LRT$ is an isosceles triangle and $SLT$ is a straight line.

Find the value of $x$.

The diagram below shows a shape, $T$, and its image, $Q$, after a transformation.

(i) Describe fully the single transformation that maps Shape $T$ onto Shape $Q$.

On the diagram above, draw the image of Shape $T$ after it undergoes a translation by the vector $\begin{pmatrix} -1 \\ 6 \end{pmatrix}$. Label this image $M$.

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 $PR$.

Determine the equation of the line $PR$.

Two functions, $f$ and $g$, are defined as follows.

$f(x) = 3x + 1$ and $g(x) = x^2$.

$g(3x+2) + 10$.

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.

(i) For the data set shown above, state the a) mode b) median.

(ii) Calculate the mean number of words spelt correctly.

For the data set shown above, state the a) mode b) median.

Calculate the mean number of words spelt correctly.

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 students who took at MOST 32 minutes to travel to school (ii) the inter-quartile range.

the number students who took at MOST 32 minutes to travel to school

the inter-quartile range.

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".

The diagram below shows a gold bar in the shape of a trapezoidal prism. Its volume is $2 \ 886 \text{ cm}^3$. The length and height of the prism are indicated on the diagram.

Calculate the area of the shaded cross-section of the trapezoidal prism.

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.

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

radius [The volume, $V$, of a sphere with radius, $r$ is $V = \frac{4}{3}\pi r^3$.]

surface area [The surface area, $A$, of a sphere with radius $r$, $A = 4\pi r^2$.]

mass, to the nearest kilogram, given that the density of gold is $19.3 \text{ g/cm}^3$. [Density = $\frac{\text{mass}}{\text{volume}}$]

Complete the diagram below to represent Diagram 5 in the sequence of regular hexagons.

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.

Row (i) for Diagram Number 5.

Row (ii) where the Number of Sticks ($S$) is 191.

Row (iii) for Diagram Number $n$.

Skyla says that she can make one of these figures with a perimeter of EXACTLY 1 005. Explain why she is incorrect.

Determine the value of a) $g(2)$

Derive an expression, in its simplest form, for $f g(x)$.

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.

The graph below shows a quadratic function.

(i) On the grid above, draw the tangent to the curve at $x = 1$. (ii) Use the tangent drawn to estimate the gradient of the curve at $x = 1$.

On the grid above, draw the tangent to the curve at $x = 1$.

Use the tangent drawn to estimate the gradient of the curve at $x = 1$.

Write down the equation of the tangent in the form $y = mx + c$.

State a theorem that justifies EACH of the following angles.

Angle $b = 62^\circ$

Angle $c = 124^\circ$

Angle $OVW = 90^\circ$

Find the values of Angles $a$, $d$ and $e$. Show ALL working where appropriate. $a =$

$d =$

$e =$

The diagram below shows a quadrilateral PQRS formed by joining two triangles, PQS and QRS.

Calculate the length of QR.

The bearing of P from S is $205^\circ$. Determine the bearing of a) R from S b) S from P.

The determinant of the matrix $\begin{pmatrix} 6 & 2v \\ -5 & -v \end{pmatrix}$ is 24. Calculate the value of $v$.

The matrices L and M are defined as follows. $L = \begin{pmatrix} 9 & 5 \\ 3 & 2 \end{pmatrix}$, . Evaluate EACH of the following. (i) The matrix product

$L^{-1}$, the inverse of $L$

$P\vec{Q} = \begin{pmatrix} 5 \\ -4 \end{pmatrix}$. If is the point , determine the coordinates of .

In the pentagon $OABCD$, $OA$ is parallel to $DC$ and $AB$ is parallel to $OD$. and and .

$A\vec{D}$.

$B\vec{C}$.

State the conclusion about $A\vec{D}$ and $B\vec{C}$ that can be drawn from your responses in (i) and (ii).