Congruency & Similarity
Trigonometry
Parabolas
Surface Area
Volume
100
Two triangles have side lengths 3, 4, 5 and 3, 4, 5. Are they congruent? Give the congruency test.
Congruent, SSS
100
In a right triangle, relative to angle θ, identify which sides are the opposite, adjacent and hypotenuse.
AC: Hypotenuse
BC: Opposite
AB: Adjacent
100
For y=2x2 find y when x=3.
18
100
Find the surface area of a cube with side length 4 cm.
96 cm²
100
Find the volume of a rectangular prism measuring 8 × 5 × 3 cm.
120 cm³
200
Triangle A has sides 6, 8, 10. Triangle B has sides 9, 12, 15. Are they congruent, similar, or neither?
Similar
200
A right triangle has opposite side 6 cm and hypotenuse 10 cm. Find θ to the nearest degree.
37°
200
The point (4,32) lies on y=ax2 . Find a.
a=2
200
A rectangular prism measures 8 × 5 × 3 cm. Find its total surface area.
158 cm²
200
A triangular prism has a triangular cross-section with base 6 cm, height 4 cm, and prism length 10 cm. Find its volume.
120 cm³
300
Two similar triangles have corresponding sides 6 cm and 9 cm. A second side on the smaller triangle is 10 cm. Find the corresponding side on the larger triangle.
15 cm
300
From a point 20 m from the base of a building, the angle of elevation to the top is 38°. Find the building's height to the nearest metre.
≈ 16 m
300
A parabola has equation y=ax2 and passes through (−3,−18). Find its equation and state its concavity.
y=−2x2, downward
300
A closed cylinder has radius 4 cm and height 10 cm. Find its total surface area in terms of π.
112π cm2
300
A cylinder has radius 4 cm and height 12 cm. Find its volume in terms of π.
192π cm3
400
A person 1.8 m tall casts a 1.2 m shadow. At the same time, a tree casts an 8 m shadow. Find the height of the tree. Explain why similarity can be used.
12 m
400
From the top of a 30 m cliff, the angle of depression to a boat is 24°. How far is the boat horizontally from the base of the cliff? (Round your answer to 1 dp)
≈ 67.4 m
400
A parabola y=ax2 passes through (6,-27). Find aa, then determine the value of y when x=−10.
a=−3/4, y=−75
400
An open-top rectangular box measures 12 × 8 × 5 cm. Find its surface area if the height is 5 cm.
280 cm²
400
A composite solid consists of a rectangular prism 10 × 6 × 4 cm with another rectangular prism 4 × 3 × 5 cm sitting on top. Find the total volume.
300 cm³
500
△ABC has sides 6, 12, 10. △DEF has sides 9, 18, 15. The area of △ABC is 24 cm². Find the area of △DEF.
54 cm²
500
From point A, the angle of elevation to the top of a tower is 30°. You walk 20 m directly toward the tower to point B, where the angle is 50°. Find the height of the tower to the nearest metre.
≈ 34.8 m
500
A parabola y=ax2 passes through point (p,12). When the x-coordinate is doubled to 2p, what is the new y-coordinate? No calculator.
48
500
A cube has total surface area 294 cm². Find its volume.
343 cm³
500
A cylinder and a rectangular prism have the same volume. The cylinder has radius 5 cm and height 8 cm. The prism has base dimensions 10 cm × 4 cm. Find the height of the prism in terms of π.
5π cm