paper 2
Simplify 3(2x - 1) - 2(x + 4).
4x - 11
The determinant of the matrix [[3, 2], [5, 4]] is:
2
If f(x) = 3x - 2, what is f⁻¹(x)?
(x + 2) / 3
If A = [[2, 1], [0, 3]] and B = [[1, 0], [4, -1]], find AB.
[[6, -1], [12, -3]]
A right-angled triangle has legs of length 6 cm and 8 cm. What is the length of its hypotenuse?
10 cm
What is the gradient of the line passing through points (2, 5) and (6, 13)?
2
A regular polygon has an exterior angle of 36°. How many sides does it have?
10
In a right-angled triangle, the opposite side to angle θ is 5 units and the hypotenuse is 13 units. What is the value of sin θ?
5/13
The marks of 7 students are 15, 18, 20, 22, 25, 28, 30. What is the median mark?
22
In a frequency distribution, the score that occurs most frequently is called the:
Mode
A point P(5, -2) is reflected in the x-axis. What are the coordinates of its image P'?
(5, 2)
Calculate the distance between the points P(1, 2) and Q(4, 6).
5 units
An angle subtended by an arc at the center of a circle is 100°. What is the angle subtended by the same arc at any point on the remaining part of the circumference?
50°
A point (3, 4) is mapped to (4, -3). What single transformation occurred?
Rotation 90 degrees clockwise about the origin
A ladder 10 m long leans against a vertical wall. The base of the ladder is 6 m from the wall. What is the angle of elevation of the ladder to the horizontal ground? (Round to nearest degree)
53°
Solve for x: 5x + 7 = 3x - 1.
-4
A shopkeeper buys an item for $150 and sells it for $180. What is the percentage profit?
20%
Factorize completely: 2x² - 8.
2(x - 2)(x + 2)
Find the mean of the numbers: 7, 12, 8, 15, 8.
10
A television set costs $2000 cash. On hire purchase, a deposit of $400 is required, followed by 12 monthly payments of $150. What is the total hire purchase price?
$2200
A household consumes 250 kWh of electricity. The first 100 kWh are charged at $0.50 per kWh, and the remaining at $0.75 per kWh. What is the total electricity bill?
$162.50
A cylinder has a radius of 7 cm and a height of 10 cm. Calculate its volume. (Use π = 22/7)
1540 cm³
Given vectors a = (3, 2) and b = (-1, 4), find a + b.
(2, 6)
Calculate the simple interest on $5000 for 3 years at a rate of 4% per annum.
$600
Find the magnitude of the vector v = (-3, 4).
5
A sector of a circle has a radius of 7 cm and an angle of 90°. What is its area? (Use π = 22/7)
38.5 cm²
Find the equation of the line that passes through the point (0, 5) and has a gradient of -2.
y = -2x + 5
Solve the simultaneous equations: x + y = 7 and x - y = 3.
x = 5, y = 2
Expand and simplify (x + 3)(x - 2).
x² + x - 6
A trapezium has parallel sides of length 8 cm and 12 cm, and a perpendicular height of 5 cm. Calculate its area.
50 cm²
Which integer satisfies the inequality 3x - 2 < 7 and x > 1?
2
The solutions to the equation x² - 5x + 6 = 0 are:
x = 2 or x = 3
Given A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], find A + B.
[[6, 8], [10, 12]]
If 1 US dollar = 2.70 Eastern Caribbean dollars (EC$), how many US dollars can be obtained for EC$ 810?
US$ 300
Make 'r' the subject of the formula A = πr².
r = √(A/π)
For the function f(x) = √(x - 3), what is the domain of x?
x ≥ 3
A rectangle has a length of 10 cm and a width of 4 cm. Calculate its perimeter.
28 cm
The area of a triangle is 48 cm². If its base is 12 cm, what is its perpendicular height?
8 cm
If O is the origin, and P has coordinates (2, -3), what is the position vector OP?
(2, -3)
In triangle ABC, angle A = 45°, angle B = 60°, and side a = 10 cm. What is the length of side b? (sin 45° ≈ 0.707, sin 60° ≈ 0.866)
12.2 cm
Find the Lowest Common Multiple (LCM) of 4 and 6.
12
Calculate the perimeter of a rectangle with length 10 cm and width 5 cm.
30 cm
Which type of chart is best for showing proportions of a whole?
Pie chart
Make 'x' the subject of the formula y = 3x - 2.
x = (y + 2) / 3
If A = [[1, 2], [3, 4]] and B = [[0, 1], [2, 1]], find A + B.
[[1, 3], [5, 5]]
A bag contains 3 red balls and 7 blue balls. What is the probability of picking a red ball?
3/10
Find the magnitude of the vector (3, 4).
5
If vector a = (2, 3) and vector b = (1, -1), find a + b.
(3, 2)
If f(x) = 3x - 1, find f(4).
11
The area of a circle with radius 7 cm is approximately (use π = 22/7):
154 cm²
Find the volume of a cube with side length 5 cm.
125 cm³
A ladder 10m long leans against a wall. If the base of the ladder is 6m from the wall, what is the height the ladder reaches on the wall?
8 m
A triangle has a base of 6 cm and a height of 4 cm. What is its area?
12 cm²
Find the mean of the numbers: 10, 12, 18, 20.
15
A bearing is given as 045°. What is the equivalent compass direction?
North East
A shirt costs $50. If there is a 10% discount, what is the new price?
$45
Two parallel lines are intersected by a transversal. If one interior angle is 70°, what is the measure of the other interior angle on the same side?
110°
Which inequality represents "x is greater than 5"?
x > 5
Find the median of the data set: 1, 5, 2, 7, 3.
3
Calculate 15% of $800.
$120
Express 0.45 as a fraction in its lowest terms.
9/20
If C = [[2, 3], [1, 0]], find 3C.
[[6, 9], [3, 0]]
What is the mode of the data set: 2, 3, 5, 3, 7, 2, 8, 3?
3
Simplify 2³ × 2².
2⁵
A point (2, 3) is reflected in the x-axis. What are its new coordinates?
(2, -3)
Which of the following is a quadratic equation?
x² - 4 = 0
A square has an area of 64 cm². What is the length of one side?
8 cm
Given matrix B = [[1, 0], [0, 1]], what is B + B?
[[2, 0], [0, 2]]
Factorize completely: 2x² - 8.
2(x - 2)(x + 2)
If A = [[2, 1], [3, 4]], what is the determinant of A?
5
Express 0.0000072 in standard form.
7.2 x 10⁻⁶
Calculate the length of the hypotenuse if the two shorter sides of a right-angled triangle are 3 cm and 4 cm.
5 cm
Solve the system: x + y = 7, x - y = 3. Find x.
x = 5
If a fair die is rolled, what is the probability of rolling an even number?
1/2
Simplify 3x - 5y + x + 2y.
4x - 3y
Round 3.14159 to 2 decimal places.
3.14
Share $120 in the ratio 1:2:3. What is the largest share?
$60
Solve for x: 2x + 5 = 11.
x = 3
In a right-angled triangle, the opposite side is 5 cm and the adjacent side is 12 cm. What is tan θ?
5/12
In a right-angled triangle, the opposite side is 8 cm and the hypotenuse is 10 cm. What is the value of sin θ?
0.8
Given that f(x) = 3x^2 - 2x + 1, find the value of f(-1).
6
Given f(x) = x - 2 and g(x) = x^2, find gf(x).
(x - 2)^2
Make 'r' the subject of the formula: A = pi * r^2
r = sqrt(A / pi)
Factorize completely: 2x^2 + x - 6
(2x - 3)(x + 2)
Solve for x: 3x^2 - 12x = 0
x = 0 or x = 4
Solve the equation 2x^2 + 5x - 3 = 0.
x = 1/2 or x = -3
Evaluate: 8^(2/3)
4
Factorize completely: 3x^2y - 6xy^2
3xy(x - 2y)
Solve for x: 4(x - 2) = 2x + 6
x = 7
John is twice as old as Mary. In 5 years, their combined age will be 40. How old is Mary now?
10
Solve for x: (x/3) - 2 = 1
9
Expand and simplify: (x + 3)(2x - 1)
2x^2 + 5x - 3
Make 'x' the subject of the formula: y = (x + 1) / (x - 1)
x = (y + 1) / (y - 1)
Given f(x) = x + 3 and g(x) = 2x, find fg(4).
11
Make 'p' the subject of the formula: A = p(1 + rt)
p = A / (1 + rt)
Solve the equation x^2 - 7x + 10 = 0
x = 2 or x = 5
Simplify: (x^5)^3 / x^2
x^13
Simplify 3(2x - 1) - 2(x + 4)
4x - 11
Simplify: (x^-2)^3
x^-6
Simplify: (10ab^2) / (5a^2b)
2b / a