CSEC Mathematics Paper 2 May/June 1980 - Free CXC Past Paper with Answers

A shopkeeper buys a stove from a manufacturer. The shopkeeper sells the stove for $150.00 at a profit of 20%.

In a survey of 100 students, the numbers of students studying the various sciences (Biology, Chemistry and Physics) were found to be: Physics 27, Physics and Biology 7, Chemistry 30, Chemistry and Physics 10, Biology 43, Biology and Chemistry 8, All three Sciences 3.

An orange is 9 cm in diameter. If $\frac{2}{9}$ of it is juice, how much juice can you get from 7 such oranges? (Vol. of a sphere of radius $r = \frac{4}{3} \pi r^3$. Assume that the orange is a sphere) Two-thirds of the juice is poured into a cylindrical container 14 cm high and diameter 7 cm. How many ice-cubes, each of side 3 cm, can be added from the juice begins to overflow? [Take $\pi$ to be $\frac{22}{7}$]

Find the values of $a$ and $k$ such that $x^2 + x + k$ is equal to $(x + a)^2$ for all values of $x$.

Using a scale of 1 cm to 1 unit on each axis, draw the graph to represent the region described by the four inequalities: $2y \le 9,$ $y + 2x \le 11,$ $2y + x \ge 4,$ and $y > 0,$ by shading the portion included in the region.

Because of swampy ground the path from $A$ to $B$ has to skirt the arc $PQ$ of a circular pond, centre $O$ and radius 14 m. The distances from $A$ and $B$ to the nearest points on the edge of the pond are both 36 m. The angle $\angle AOB = 30^\circ$. Find in metres the total length of the path $APQB$, giving the answer correct to 2 significant figures. [Take $\pi$ to be $\frac{22}{7}$]

Two kinds of food $F_1$ and $F_2$ are to be mixed together so that the vitamin content of the mixture is at least 8 units of Vitamin A, 12 units of Vitamin B and 10 units of Vitamin C. The table below gives the vitamin content for each food, in units per kilogram.

If $x$ kg and $y$ kg are the weights in the mixture of $F_1$ and $F_2$ respectively, write down these conditions as a set of inequalities in and . Find graphically the minimum cost of the mixture if costs $0.60 per kilogram and costs $1.00 per kilogram.

Find the coordinates of the points of intersection of the curve $y = 10 - x - 2x^2$ and the line $y = 7 - 2x$. For what value of $x$ is the expression $10 - x - 2x^2$ a maximum? What is this maximum value?

What is the image of the square $O(0,0)$, $A(0,1)$, $B(1,1)$, $C(1,0)$ under the transformation $T = \begin{pmatrix} 1 & -1 \\ 0 & 1 \end{pmatrix}$? A second transformation $U$ maps $(1,0)$ onto $(4,3)$, $(0,0)$ onto $(0,0)$ and multiplies all lengths by a factor of 5. Write down the matrix of $U$. What is the image of $OABC$ under the composite transformation $UT$, (that is, $T$ followed by $U$).

Given that $\sin \theta = -\frac{1}{2}$, $\cos \theta = -\frac{\sqrt{3}}{2}$, find without use of tables (a) $\tan \theta$ (b) $\tan (\pi + \theta)$. Justify your answers.

$O$ is the centre of a regular hexagon $ABCDEF$ in which $\vec{AB} = \vec{a}$, $\vec{AC} = \vec{b}$.

The table below shows the distribution of marks on a Mathematics test in a certain class of students.

In a car park there are 50 cars. 30 are European models and 20 are Japanese. Furthermore 14 have front wheel drive and 36 do not. Ten of the European cars and 4 of the Japanese have front wheel drive. Two cars are chosen at random. Calculate the probability of each of the following events:

The country of Enon is inhabited by two types of people: liars and truthers. Liars always tell lies and truthers always tell the truth. A visitor to Enon held a conversation with three citizens of Enon: Alan, Beryl and Carole. During the conversation Alan remarked, "Beryl and Carole are liars". Beryl heatedly replied, "I am not a liar", and Carole quietly added, "Beryl is indeed a liar".

If $p$ is logically true, what can you say about the truth or falsity of

Let "$p/q$" mean "$p$ and $q$ are not both true".

Write