Accuracy
Right Angled Trig
Non Right Angled Trig
Triangles, Sectors, and Arcs
Surface Area and Volume
100
Round the number 0.045092 to three significant figures.
0.0451
100
In a right-angled triangle, the side opposite a 30° angle is 5 cm. What is the length of the hypotenuse?
10 cm
100
What trigonometric rule should you use to find a missing angle when you are given the lengths of all three sides of a triangle?
Cosine Rule
100
What is the area of a triangle with two sides of 6 cm and 8 cm, and an included angle of 30°?
12 cm2
100
What is the exact volume of a cylinder with a radius of 3 m and a height of 10 m?
90π m³
200
A student estimates the weight of a bag of apples to be 3.5kg. The actual weight is 4.2kg. Calculate the percentage error of the student's estimate.
16.7%
200
A ladder leans against a vertical wall, making a 65° angle with the horizontal ground. If the base of the ladder is 2.5 m from the wall, how long is the ladder?
5.92 m
200
In triangle ABC, side a = 7 cm, side b = 9 cm, and the included angle C = 40°. Find the length of side c.
5.78 cm
200
Find the arc length of a circle sector with a radius of 10 cm and a central angle of 72°.
12.6 cm
200
A sphere has a surface area of 100π cm². What is its radius?
5 cm
300
Ancient Babylonian mathematicians approximated π using the fraction 25/8. Calculate the percentage error of this approximation compared to the exact calculator value of π.
0.528%
300
From the top of a 50 m vertical cliff, the angle of depression to a boat on the water is 22°. How far is the boat from the base of the cliff?
124 m
300
A drone is mapping a triangular nature reserve with boundary checkpoints A, B, and C. The straight distances between checkpoints are AB = 300 m, BC = 450 m, and AC = 600 m. Calculate the size of the interior angle at checkpoint B (∠ABC).
105°
300
A sector of a circle has an area of 50 cm² and a radius of 5 cm. Find the size of the central angle in degrees.
229°
300
A solid cone has a base radius of 6 cm and a slant height of 10 cm. Find its total surface area.
302 cm2 (96π cm²)
400
A rectangular garden is measured as 8 m long and 5 m wide, with both measurements correct to the nearest meter. What is the lower bound of the garden's area?
33.75 m2
400
A rectangle has dimensions 8 cm by 15 cm. Calculate the angle that the diagonal makes with the longest side of the rectangle.
28.1°
400
Two forest fire lookout towers, Tower A and Tower B, are located 8 km apart along a straight road. Both towers spot a plume of smoke from a forest fire at point F. Tower A measures the angle between the road and the fire as 48°. Tower B measures the angle between the road and the fire as 75°. Calculate the distance from Tower A to the fire (AF).
9.21 km
400
A farmer owns a triangular plot of land ABC where AB = 25 m, AC = 35 m, and ∠BAC = 55°. A rotational water sprinkler is installed at corner A with a spray radius of 20 m. The sprinkler rotates through the angle ∠BAC, watering a sector-shaped area within the plot. Calculate the area of the plot that is NOT reached by the sprinkler.
166 m2
400
A solid right pyramid VABCD has a square base ABCD with side length 6 cm. The length of each sloping edge from the top vertex V to a corner of the base is 8 cm. Calculate the total surface area of the pyramid.
125 cm2
500
A solid metal sphere has a radius of 4.5 cm, measured correct to 1 decimal place. Its mass is 3.2 kg, measured correct to 2 significant figures. Given that Density = Mass / Volume and V = (4/3)πr³, calculate the maximum possible density of the sphere in g/cm³.
8.80 g/cm³
500
A right square-based pyramid has a base side length of 10 m and a vertical height of 12 m. Calculate the angle between one of the triangular faces and the square base.
67.4°
500
Ship A is 15 km from Port P on a bearing of 040°. Ship B is 20 km from Port P on a bearing of 160°. Calculate the direct distance between Ship A and Ship B.
30.4 km
500
A circle has a radius of 8 cm. A straight chord connects two points on the circle and has a length of 10 cm. Find the area of the minor sector created by the radii connecting to the ends of this chord.
43.2 cm2
500
A hemisphere and a cone share the exact same base radius r. If the volume of the cone is exactly equal to the volume of the hemisphere, express the height of the cone (h) in terms of r.
h = 2r