12 exercises · 12 automatically checked · Untimed
12 questions · Shuffled order · Untimed practice
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Two intersecting lines form vertical angles measuring (3x + 7)° and (5x − 19)°. What is x?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 13 Vertical angles are equal, so 3x + 7
Lines and angles / Standard Review: Geometry reference.
A triangle has angles 35° and 68°. What is the third angle, in degrees?
Answer: D / 77 Triangle angles total 180°, so the missing angle is 180 − 35 − 68
Triangles / Standard Review: Geometry reference.
Similar triangles have corresponding sides 6 and 15. The smaller triangle has area 28. What is the area of the larger triangle?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 175 The length factor is 15/6
Similarity and scaling / Standard Review: Example 1.14.
A right triangle has legs 9 and 12. What is its hypotenuse?
Answer: D / 15 Use c2 = 92 + 122 = 225, so the positive length is c
Right triangles / Standard Review: Example 6.03.
In a right triangle, the side opposite an acute angle θ has length 8 and the hypotenuse has length 17. What is sin θ?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 8/17 Sine is opposite divided by hypotenuse. The given side lengths already supply the needed ratio 8/17; the third side need not be found.
Trigonometry / Standard Review: Example 6.12.
An angle measures 150°. What is its measure in radians?
Answer: B / Multiply by π/180: 150π/180
Radians / Standard Review: Example 4.12.
A circle has radius 9. A minor arc subtends a central angle of 80°. Its length is kπ. What is k?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 4 The arc is 80/360
Arcs / Standard Review: Example 6.09.
What is the center of the circle (x + 5)2 + (y − 2)2 = 49?
Answer: B / (−5, 2) Compare with (x − h)2 + (y − k)2
Circle equations / Standard Review: Example 1.15.
What is the distance between (−2, 1) and (4, 9)?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 10 The horizontal and vertical changes are 6 and 8. The distance is = = 10.
Coordinate geometry / Standard Review: Example 6.03.
A trapezoid has parallel bases of lengths 8 and 14 and perpendicular height 5. What is its area?
Answer: C / 55 The average base length is (8 + 14)/2
Area / Standard Review: Example 6.02.
A cone has radius 3 and perpendicular height 8. Its volume is kπ. What is k?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 24 Use V = πr2 h = π(9)(8) = 24π. The question asks for the coefficient 24, not the full volume.
Volume / Standard Review: Example 6.11.
Two similar solids have volumes 64 and 216. A corresponding length in the smaller solid is 10. What is the corresponding length in the larger solid?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 15 The volume factor is 216/64
Solid scaling / Challenge Review: Example 4.11.
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