CSEC Mathematics Paper 1 January 2019 - Free CXC Past Paper with Answers

$\left(\frac{2}{3}\right)^2$ is equal to

The number 3.14063 written correct to 3 decimal places is

In standard notation, 208.06 is written as

$2.0806 \times 10^1$

$20.806 \times 10^1$

$2.0806 \times 10^2$

$0.20806 \times 10^3$

If $560 is shared in the ratio 2:3:9, the difference between the largest and the smallest shares is

If 60% of a number is 90, what is $\frac{4}{5}$ of the number?

The first three common multiples of 3, 4 and 6 are

If $P = \{2, 3, 5, 7\}$ , $Q=\{2, 3, 6\}$ and $S = \{2, 4, 5\}$ then $P \cap Q \cap S=$

What is $n(Q \cap P)$ ?

Which of the following sets is equivalent to the set {p, q, r, s}?

All students in a class play Scrabble or Checkers or both. If 36% of the students play Scrabble only and 48% of the students play Checkers only, what percentage of students play BOTH games?

Item 11 refers to the following Venn diagram. U Y

In the Venn diagram, X represents the set of factors of 12. Y represents the set of factors of 9. The shaded region represents the set of all factors of

Item 12 refers to the following Venn diagram. UV P

In the Venn diagram, the shaded area represents

A store offers a discount of 15% on the total bill to customers who spend more than $20. If a customer's total bill is $80, how much must she pay?

At a store, sales tax is charged at a rate of 2% on the cost price of an item. The sales tax on a dress which costs $180 is

A plot of land is valued at $18 000. Land tax of $126 is charged annually. At what rate per annum is the land tax charged?

The exchange rate for one United States dollar (US$1.00) is two dollars and seventy cents in Eastern Caribbean currency (EC$2.70). What is the value of US$4.50 in EC currency?

A man's annual salary is $45 000. His tax free allowances total $13 000. He has to pay a tax of 20% on his taxable income.

The tax payable is

A television set costs $350 cash. When bought on hire purchase, a deposit of $35 is required, followed by 12 monthly payments of $30. How much is saved by paying cash?

A man pays 60 cents for every 200 m³ of gas used, plus a fixed charge of $13.75. How much does he pay when he uses 55 000 m³ of gas?

Item 20 refers to the following table which shows the rates charged by an insurance company.

House Insurance 25¢ per $100 Contents Insurance 50¢ per $100

How much will a person pay for insurance, if his house is valued at $50 000, and the contents at $10 000?

The product of (-2a) and (-3a) is

When 6 is added to a number and the sum is divided by 3, the result is 4. This statement written using mathematical symbols is

$\frac{6}{3} + x = 4$

$\frac{6+x}{3} = \frac{4}{3}$

$6 + \frac{x}{3} = 4$

Althea normally saves $x each month; but in June she saved $4 more than twice her usual amount. In June she saved

If $3 + \frac{2}{x} = 1$ , the value of $x$ is

If $x=4$ and $y=2$ , what is the value of $\frac{x^2+3y}{xy}$ ?

The expression $-2(x-4)$ is the same as

If $|A|=0$ , then $A$ is

a non-singular matrix

Item 28 refers to the following matrices, X and Y. $X=\begin{bmatrix} 1 & 3 & -3 \\ 3 & 0 & 5 \end{bmatrix}$ , $Y=\begin{bmatrix} 3 & 0 \\ 2 & 1 \\ 0 & 5 \end{bmatrix}$

What is the order of the matrix product XY?

If the vectors p and q are $\begin{pmatrix} 3 \\ 2 \end{pmatrix}$ and $\begin{pmatrix} -1 \\ 4 \end{pmatrix}$ respectively, then $-p-2q$ is

$\begin{pmatrix} 5 \\ -6 \end{pmatrix}$

$\begin{pmatrix} -2 \\ -6 \end{pmatrix}$

Based on the information above, $\vec{ZR}$ =

$\vec{WX} + \frac{1}{2}\vec{WZ}$

$\vec{WX} - \frac{1}{2}\vec{WZ}$

$\frac{1}{2}\vec{WX} - \vec{WZ}$

$\frac{1}{2}\vec{WX} + \vec{WZ}$

If it took a speedboat 9 hours to travel a distance of 1 080 km, what was its average speed, in kmh⁻¹?

The area of the trapezium is

Item 33 refers to the following circle, with. centre O. B 120° 0 A

If the circumference of the circle is 15 cm, then the length of the minor arc AB, in cm, is

$\frac{360}{120} \times 15$

$\frac{120}{360} \times 15$

$\frac{360}{360-120} \times 15$

$\frac{360-120}{360} \times 15$

The lengths of the sides of a triangle are x, 2x and 2x centimetres. If the perimeter is 20 centimetres, what is the value of x?

A rectangular garden plot, 15 m long and 12 m wide, is used to plant fruits and vegetables. If 80 m² of the plot is used to plant vegetables, what area of the plot is planted with fruits?

The distance around a lake is 8 km. On a map, this distance around the lake is represented by a length of 2 cm. The scale on the map is

Item 37 refers to the following diagram. 3 8 cm

The diagram above, not drawn to scale. shows a cylinder of radius 3 cm and height 8 cm. The volume of the cylinder is

Item 38 refers to the following diagram, not drawn to scale, which shows a cuboid.

The volume of the cuboid is $320 \text{ cm}^3$ and the height is $5 \text{ cm}$ . If the cuboid has a square base, what is the length of one side of the base?

How many students play cricket?

Items 41-42 refer to the following chart which shows the number of books 58 students bought at a sale.

How many students bought exactly 4 books?

The median number of books bought by the students is

Items 43-44 refer to the following diagram, which shows the cumulative frequency polygon of the lengths, in metres, of 20 fish that were caught by two fishermen.

The semi-interquartile range of the lengths of the fish is

A fish is selected at random. What is the probability that it is at LEAST 1.8 m long?

Item 45 refers to the following arrow diagram.

The arrow diagram above describes the relation

x is a multiple of y

Which of the following line graphs represents {x:-2<x≤4}?

-3 -2 -1 0 1 2 3 4 5

Which of the following points lies on the line $y = 2x-3$ ?

If $f(x) = 2x^2-1$ , then $f(-3) =$ .

The maximum point of $y=4x-x^2$ is

The values of $x$ at the points where $y=4x-x^2$ intersects $y=0$ are

Which of the following sets is represented by the function $f: x \to x^2 + 3$ where $x \in \{0, 1, 2, 3\}$ ?

$\{(0, 3), (1, 4), (2, 7), (3, 12)\}$

In the diagram above, if the line $y = x$ is rotated anti-clockwise about O through $90^\circ$ , what is its image?

Items 54-55 refer to the following diagram of a pair of intersecting lines. AC and DE are straight lines intersecting at B. Angle DBA = 58°. D 58 B E C

The measure of angle ABE is