CSEC Mathematics Paper 2 May/June 2003 - Free CXC Past Paper with Answers

Given $a = 2$, $b = -3$ and $c = 0$, evaluate (i) $4a - 2b + 3c$ (ii) $a^c$.

Factorize completely (i) $7mp^2 + 14m^2p$ (ii) $2y^2 - 11y + 15$.

Write as a simple fraction in its LOWEST terms $\frac{2}{a - 3} + \frac{3}{a}$.

Solve for $x$ (i) $12 \le 3x + 5$. (ii) If $x$ is a member of the set of whole numbers, state the SMALLEST value of $x$ which satisfies the inequality in (d) (i) above.

The Universal set, $U$, is given as $U = \{1, 2, 3, \dots, 13, 14, 15\}$. The sets $A$ and $B$ are subsets of $U$ such that $A = \{\text{Factors of } 12\}$ $B = \{\text{Multiples of } 3\}$. (i) List the members of the set $A$. (ii) List the members of the set $B$. (iii) Represent the sets, $A$, $B$ and $U$, on a Venn diagram. (iv) List the members of $(A \cup B)'$.

(i) Draw a line segment, $PQ$, 7 cm long. (ii) Using only a ruler, a pencil and a pair of compasses, construct a line segment, $LM$, the perpendicular bisector of $PQ$, such that $LM$ cuts $PQ$ at $$, and cm. (iii) Form parallelogram by joining the points $ P, L, Q $ and . (iv) Measure and state the size of the angle . (v) What type of parallelogram is ? Give a reason for your answer.

Triangle $DEF$, shown below, undergoes a rotation such that its image is triangle $D'E'F'$.

(i) Describe COMPLETELY this rotation by stating a) the coordinates of the centre b) the direction of turn c) the size of the angle turned. (ii) Triangle $DEF$ is mapped onto triangle $ABC$ under a translation, $T = \begin{pmatrix} -6 \\ -3 \end{pmatrix}$. State the coordinates of $ A, B $ and , the images of $ D, E $ and , under .

The figure below, not drawn to scale, represents the journey of an aircraft flying from $Y$ to $X$ and then from $X$ to $Z$.

The bearing of $X$ from $Y$ is . The bearing of from is . is due east of . (i) Copy and complete the diagram, showing CLEARLY the bearings and . (ii) Determine the size of the angle . (iii) Calculate, to the NEAREST whole number, the distance given that km.

The triangular prism, shown in the diagram below, not drawn to scale, is 18 cm long. Triangle $GHI$ has a height of 3 cm, $HI = 8$ cm and $GH = GI$.

Calculate (i) the area of triangle $GHI$ (ii) the volume of the triangular prism (iii) the length of $GI$ (iv) the TOTAL surface area of the prism.

The triangular prism is melted down and made into a cube. Calculate the length of an edge of the cube.

Calculate (i) the TOTAL number of seedlings in the sample (ii) an estimate of the mean height of the seedlings in the sample.

Using a scale of 2 cm to represent a height of 5 cm on the $x$-axis, and 2 cm to represent 5 seedlings on the $y$-axis, draw on graph paper the frequency polygon to represent the data given in the table.

Calculate the probability that a seedling, selected at random, measures at most 12 cm in height.

On the answer sheet provided, draw the next TWO shapes to continue the sequence.

For EACH shape drawn, in Part (a), complete the table by stating (i) the area of the shape (ii) the perimeter of the shape.

A shape in the sequence has an area of 12 square units. What is the perimeter of this shape?

A shape in the sequence has a perimeter of 40 units. What is the area of this shape?

On the answer sheet provided, draw TWO shapes EACH made up of 4 unit squares so that one has a perimeter of 8 units and the other has a perimeter of 16 units.

Given that $m * l = m^2 - lm$, (i) evaluate $5 * 3$ (ii) solve for $g$ given that $g * 4 = -3$.

An athlete runs on a track so that his distance, $d$ metres, from the starting point after $t$ seconds is as shown in the table below.

(i) a) Using a horizontal scale of 1 cm to represent 1 second and a vertical scale of 1 cm to represent 10 metres, construct a distance-time graph to show the motion of the athlete. b) Draw a smooth curve through all the plotted points. (ii) Use your graph to estimate a) the distance travelled by the athlete after 3 seconds b) the average speed of the athlete during the interval seconds to seconds c) the speed of the athlete 6 seconds after leaving the starting point.

Solve for $p$ and $r$ given $3p + 2r = 7$ $p^2 - 2r = 11$.

Two functions, $g$ and $h$, are defined as $g: x \to \frac{2x + 3}{x - 4}$ and

Calculate, giving reasons for your answer, the size of (i) angle $MCD$ (ii) angle $CMD$.

Explain why the quadrilateral $OCMD$ is cyclic.

Given that the radius of the circle shown in the diagram above is 6.5 cm, calculate (i) the area of triangle $OCD$ (ii) the area of the shaded segment of the circle. [Use $\pi = 3.14$]

Draw a diagram to represent the information, CLEARLY showing (i) the line segment which represents 10 metres. (ii) the angles whose measures are $14^\circ$, $21^\circ$ and $112^\circ$ (iii) TWO right angles.

Calculate, to the NEAREST metre, the distance (i) $QK$ (ii) $SK$ (iii) $QS$.

A vertical pole 4 m high is placed at $Q$. An instrument placed on the top of this pole measures the angle of elevation of the top of the tower. Calculate the size of this angle of elevation.

Copy the diagram on graph paper and draw and label the vectors $\vec{OW}$ and $\vec{OE}$ such that and .

Write down in terms of $p$ and $q$, the vectors $\vec{PQ}$ and $$. Hence, state the relationship between and .

The point $D$ is such that $\vec{OD} = \vec{QE}$. (i) Write down, in terms of and , the vector . (ii) Hence, state the coordinates of .

Calculate the magnitude of the vector $\vec{OW}$.

Using a scale of 1 cm to represent 1 unit on BOTH the x and y-axes, draw on graph paper the triangle $PQR$ and $P'Q'R'$ such that $P(-3, -2)$, $Q(-2, -2)$, $R(-2, -4)$ and $P'(6, 4)$, $Q'(4, 4)$ and $R'(4, 8)$.

Describe FULLY the transformation, $G$, which maps triangle $PQR$ onto triangle $P'Q'R'$.

The transformation, $M$, is a reflection in the line $y = -x$. On the same diagram, draw and label the triangle $P''Q''R''$, the image of triangle under the transformation .

Write down the $2 \times 2$ matrix for (i) transformation $G$ (ii) transformation $M$ (iii) transformation $G$ followed by $M$.