CSEC Mathematics Paper 2 May/June 2011 - Free CXC Past Paper with Answers

Write as a single fraction in its lowest terms $\frac{x-2}{3} + \frac{x+1}{4}$.

The binary operation $*$ is defined by $a * b = (a+b)^2 - 2ab$. Calculate the value of $3 * 4$.

Factorise completely

$xy^3 + x^2y$

$2mh - 2nh - 3mk + 3nk$.

The table below shows corresponding values of the variables $x$ and $y$, where $y$ varies directly as $x$.

The Venn diagram below shows the number of students who study Music and Art in a class of 35 students.

$U = \{\text{students in the class}\}$ $M = \{\text{students who study Music}\}$ $A = \{\text{students who study Art}\}$

How many students study neither Art nor Music?

Calculate the value of $x$.

Hence, state the number of students who study Music only.

Using a ruler, pencil, a pair of compasses and a protractor, draw accurately a quadrilateral $EFGH$ using the following measurements: $EF = 8 \text{ cm}$ $\angle EFG = 125^\circ$

Measure and state in centimetres, the length of $GH$.

Solve the inequality: $5 - 2x < 9$

If $x$ is an integer, determine the SMALLEST value of $x$ that satisfies the inequality in (a) (i) above.

In this question, use $\pi = \frac{22}{7}$.

A piece of wire is bent to form a square of area $121 \text{ cm}^2$. Calculate: a) The length of each side of the square b) The perimeter of the square

The same piece of wire is bent to form a circle. Calculate: a) The radius of the circle b) The area of the circle

The diagram below, not drawn to scale, shows $\triangle OMN$, and its image, $\triangle O'M'N'$ under an enlargement with centre, , and scale factor, . Angle .

the value of $k$, the scale factor of the enlargement

the length of $OM$.

the length of $OM'$.

The diagram below, not drawn to scale, shows $\triangle PQR$, which represents the cross section of a roof. $QS$ is perpendicular to $PSR$. $PQ = 12.6 \text{ metres}$ $Q$

the length of $QS$

the measure of $\angle RQS$

the area of $\triangle PQR$.

The functions $f$ and $g$ are defined by $f(x) = 6x + 8$ ; $g(x) = \frac{x-2}{3}$.

Calculate the value of $g\left(\frac{1}{2}\right)$.

Write an expression for $gf(x)$ in its simplest form.

Find the inverse function $f^{-1}(x)$.

The diagram below shows the line segment which passes through the points $A$ and $B$.

Determine

the coordinates of $A$ and $B$

the gradient of the line segment $AB$

the equation of the line which passes through $A$ and $B$.

Copy and complete the table to show the cumulative frequency for the distribution.

Using a scale of 2 cm to represent 10 kg on the $x$-axis and 1 cm to represent 10 packages on the $y$-axis, draw the cumulative frequency curve for the data.

Estimate from the graph

the median mass of the packages

the probability that a package, chosen at random, has a mass which is LESS than 35 kg.

Draw the FOURTH diagram in the sequence.

How many sticks are in the SIXTH diagram?

How many thumb tacks are in the SEVENTH diagram?

Complete the table by inserting the missing values at the rows marked (i) and (ii).

Row (i) in the table.

Row (ii) in the table.

Write the rule, in terms of $s$ and $t$, to show how $t$ is related to $s$.

Solve the pair of simultaneous equations $y = x^2 - x + 3$ $y = 6 - 3x$.

Express the function $f(x) = 4x^2 - 8x - 2$ in the form $a(x + h)^2 + k$, where , and are constants.

State the minimum value of $f(x)$

the value of $x$ for which $f(x)$ is a minimum.

The speed-time graph below, not drawn to scale, shows the three-stage journey of a racing car over a period of 60 seconds.

During the FIRST stage of the journey, the car increased its speed from 0 m/s to 12 m/s in $x$ seconds accelerating at $0.6 \text{ m/s}^2$.

Calculate the value of $x$.

What is the gradient of the graph during the SECOND stage? Explain, in one sentence, what the car is doing during this stage.

Calculate the distance travelled by the car on the THIRD stage of the journey.

In the diagram below, not drawn to scale, $W, X, Y$ and $Z$ are points on the circumference of a circle, centre $O$. $TPV$ is a tangent to the circle at $Y$. $\angle XWZ = 64^\circ$ and $\angle ZYV = 23^\circ$.

Calculate, giving reasons for your answer, the measure of angle

$XYZ$

$YXZ$

$OXZ$.

The diagram below, not drawn to scale, shows the route of an aeroplane flying from Porticity ($P$) to Queenstown ($Q$) and then to Riversdale ($R$). The bearing of $Q$ from $P$ is $132^\circ$ and the angle is .

Calculate the value of $x$, as shown in the diagram.

The distance from Porticity ($P$) to Queenstown ($Q$) is 220 kilometres and the distance from Queenstown to Riversdale ($R$) is 360 kilometres. Calculate the distance $RP$.

Determine the bearing of $R$ from $P$.