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Grade 10: Math subject test

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Subject practice test

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Subject practice test
1. A fictional geometry rule says: If a quadrilateral is a square, it is a rectangle. Figure 8 is a square. What follows from this rule?
2. Write the converse: If two triangles are congruent, then their corresponding side lengths are equal.
3. Among candidate rectangles with listed side lengths including 8 and 9, which refutes “Every rectangle has four equal side lengths”?
4. Given AB=BC, BC=CD, and AB=11 cm, find CD.
5. Two parallel lines are cut by a transversal. One angle is 47°. Find its corresponding angle.
6. A triangle has interior angles 46° and 66°. Find the third.
7. An isosceles triangle has vertex angle 52°. Find either equal base angle.
8. Two triangle sides have lengths 8 and 9. Which proposed third length makes a nondegenerate triangle?
9. Triangles have matching side lengths 8, 9, 10, and 8, 9, 10. Which criterion establishes congruence?
10. Given triangle ABC congruent to triangle DEF in that order, AB=13, BC=14, AC=15. Find EF.
11. Point P lies on the perpendicular bisector of segment AB. PA=16 cm. Find PB.
12. A construction ray bisects an angle measuring 64°. What is either resulting angle?
13. Two similar triangles have corresponding sides 24 and 48. A second side on the smaller triangle is 32. Find its corresponding larger side.
14. In a right triangle, an acute angle θ has sin θ=1/2 and hypotenuse 16 cm. Find its opposite side.
15. For an acute angle θ in a right triangle, cos θ=4/5 and the hypotenuse is 40 cm. Find the adjacent leg.
16. For an acute angle θ, tan θ=3/4 and its adjacent leg is 32 cm. Find its opposite leg.
17. A parallelogram has one interior angle 58°. Find an adjacent interior angle.
18. A parallelogram diagonal has endpoints (-8,9) and (10,13). At what point do its diagonals meet?
19. A nonvertical line has slope 8/9. Find the slope of a perpendicular line.
20. A triangle has vertices (0,0), (16,0), and (0,9). Find its area.
21. An inscribed angle intercepts an arc of 64°. Find the angle.
22. A triangle includes a radius and the tangent at its endpoint, forming one right angle. Its other known angle is 28°. Find its third angle.
23. A circle has radius 8 cm. Find the exact length of its 90° arc.
24. A circle has radius 16 cm. Find the exact area of its 90° sector.
25. A cylinder has radius 8 cm and height 9 cm. What is its exact volume?
26. A cone has radius 8 cm and perpendicular height 27 cm. Find exact volume.
27. A sphere has radius 24 cm. Find exact volume.
28. A solid has volume 40 cm³. All corresponding lengths are multiplied by 3. Find the similar solid’s volume.
29. A point is uniformly chosen along a segment of length 25. A target subsegment has length 8. What is the chance of landing in the target?
30. A 24-by-16 rectangular region has one 8-by-8 square removed. Find the remaining area.
31. A fictional uniform block has mass 240 grams and volume 24 cm³. Find its density.
32. A rectangular floor is 16 m by 18 m. Identical 2 m by 2 m square mats fit in a grid without gaps. How many fit?

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