CSEC Mathematics Paper 2 January 2006 - Free CXC Past Paper with Answers

Given that $m = -2$ and $n = 4$, calculate the value of $(2m + n)(2m - n)$.

Solve the simultaneous equations $5x + 6y = 37$ $2x - 3y = 4$.

Factorise completely

$4x^2 - 25$

$6p - 9ps + 4q - 6qs$

$3x^2 + 4x - 4$.

Given the formula $s = \frac{1}{2}(u + v)t$, express $u$ in terms of $v$, $s$, and $t$.

On a certain day, 300 customers visited a bakery that sells bread and cakes. 70 customers bought cakes only 80 customers bought neither bread nor cakes 2x customers bought bread only x customers bought both bread and cakes

U represents the set of customers visiting the bakery on that day, B represents the set of customers who bought bread, and C represents the set of customers who bought cake. Copy and complete the Venn diagram to illustrate the information.

U represents the set of customers visiting the bakery on that day, B represents the set of customers who bought bread, and C represents the set of customers who bought cake. Copy and complete the Venn diagram to illustrate the information.

Write an expression in x to represent the TOTAL number of customers who visited the bakery on that day.

Calculate the number of customers who bought bread ONLY.

The equation of the line $l$ is $y = 4x + 5$.

State the gradient of any line that is parallel to $l$.

Determine the equation of the line parallel to $l$ that passes through the point $(2, -6)$.

An answer sheet is provided for this question.

The diagram above shows the positions of three cities, A, B and C, on the north coast of Africa. The scale of the map is $1 : 20 \ 000 \ 000$.

Use your answer sheet when answering the following questions. Show all lines and angles used in your calculations.

Measure and state, in centimetres, the length of the line segment, BC.

Hence, calculate in kilometres, the actual shortest distance from City B to City C.

Using a protractor, determine the bearing of B from A.

Calculate, using $\pi = 3.14$,

the curved surface area of the cylinder

the surface area of the hemisphere

the TOTAL surface area of the solid paperweight.

Using a ruler, a pencil, and a pair of compasses, construct the parallelogram KLMN, in which $KL = 8$ cm, $KN = 6$ cm, and $\angle LKN = 60^\circ$.

State the coordinates of the points $R'$ and $S'$.

Describe the rotation completely.

On the answer sheet provided, draw and label quadrilateral $P''Q''R''S''$ which is the image of after it has been reflected in the x-axis.

Describe completely, the single transformation that maps quadrilateral $PQRS$ onto $P''Q''R''S''$.

Copy and complete the table of values.

Length of Right Foot      Frequency
(cm)
14 – 16                       4
17 – 19                       —
20 – 22                       8
—                             5
26 – 28                       2

State the lower boundary of the class interval $14 – 16$.

State the width of the class interval $20 – 22$.

A student’s right foot measured 16.8 cm. State the class interval in which this length would lie.

A student was chosen at random from the group, and the length of his right foot was measured. Calculate the probability that the length was GREATER THAN or EQUAL to 20 cm.

State the modal length of a student’s right foot.

Calculate an estimate of the mean length of a student’s right foot using the midpoints of the class intervals in (a) above.

Copy and complete the table of values.

Draw the graph of $h = 20t - 5t^2$ for $0 \le t \le 4$. You may proceed as follows:

Using a scale of 2 cm to represent 0.5 seconds, draw the horizontal $t$-axis for $0 \le t \le 4$.

Using a scale of 1 cm to represent 1 metre, draw the vertical $h$-axis for $0.0 \le h \le 21.0$.

Plot the points from your table of values on the axes drawn.

Join the points with a smooth curve.

Using your graph, calculate estimates of

the GREATEST height above the ground reached by the ball

the number of seconds for which the ball was MORE than 12 metres above the ground

the interval of time during which the ball was moving upwards.

Solve the pair of simultaneous equations $2x + y = 7$ $x^2 - xy = 6$.

Express $4x^2 - 12x - 3$ in the form $a(x+h)^2 + k$, where , and are real numbers.

Using your answer from (b) above, or otherwise, calculate

the minimum value of $4x^2 - 12x - 3$

the value of $x$ for which the minimum occurs

the values of $x$ for which $4x^2 - 12x - 3 = 0$ expressing your answers to 3 significant figures.

A shop stocks $x$ Sonix and $y$ Zent radios. It has shelf space for up to $20$ radios.

Write an inequality to represent this information.

The owner of the shop spends $150$ to purchase each Sonix radio and $300$ for each Zent radio, she has $4,500$ to spend on the purchase of these radios.

Write an inequality to represent this information.

The owner of the shop decides to stock at least $6$ Sonix and at least $6$ Zent radios.

Write TWO inequalities to represent this information.

Write TWO inequalities to represent this information.

Using a scale of $2$ cm to represent $5$ Sonix radios and $2$ cm to represent $5$ Zent radios, draw the horizontal axis for $0 \le x \le 30$ and the vertical axis for .

On these axes, draw the four boundary lines for the four inequalities written in (a) (i), (ii) and (iii) above.

Shade the region on your graph that satisfies ALL four of the inequalities written in (a) (i), (ii) and (iii) above.

State the coordinates of the vertices of the shaded region.

The owner of the shop sells the radios to make a profit of $80 on each Sonix and $100 on each Zent radio.

Express the TOTAL profit in terms of $x$ and $y$.

Calculate the MAXIMUM profit.

Sketch the diagram and label the

equator

Greenwich Meridian

latitude $52^\circ N$

latitude $6^\circ N$.

The Greenwich Meridian passes through London ($52^\circ N, 0^\circ$) and Accra ($6^\circ N, 0^\circ$).

Show on your diagram the position, $L$, of London and $A$, of Accra.

Calculate, to the NEAREST kilometre, the shortest distance between London and Accra along their common circle of longitude. Use $\pi = 3.14$.

Tropical Storm Kyle was reported to be located $5,470$ km due west of Accra.

Show on your diagram a possible point of location of Kyle, $K$.

Calculate the radius of the circle of latitude on which $K$ lies.

Find the inverse of the matrix $M = \begin{pmatrix} 2 & 1 \\ -1 & 3 \end{pmatrix}$.

Calculate the values of $x$ and $y$ for which $M \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 12 \\ 1 \end{pmatrix}$.

Under a transformation $T$, represented by the matrix $\begin{pmatrix} p & q \\ r & s \end{pmatrix}$, the points and are mapped onto and respectively.

Determine the values of $p, q, r$ and $s$.

Calculate the coordinates of the point $C'$ which is the image of $C(-2, 2)$ under $T$.