DZ01 Mathematics for Elementary Educators III MATH 1330 Version 1
Practice exam for Western Governors University WGU Exams under Western Governors University Exams (College Exams). 5 sample questions.
Sample Questions
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Question 1
Which of the following pairs of angles are supplementary? (Choose all that apply.)
Correct Answer: D
Rationale: Supplementary angles sum to 180 degrees. Steps: 1) Pair A: 45 + 45 = 90, not 180. 2) Pair B: 72 + 100 = 172, not 180. 3) Pair C: 35 + 55 = 90, not 180. 4) Pair D: 60 + 120 = 180, supplementary, correct.
Rationale: Supplementary angles sum to 180 degrees. Steps: 1) Pair A: 45 + 45 = 90, not 180. 2) Pair B: 72 + 100 = 172, not 180. 3) Pair C: 35 + 55 = 90, not 180. 4) Pair D: 60 + 120 = 180, supplementary, correct.
Question 2
Identify which of the following is a property of a right triangle.
Correct Answer: A
Rationale: A right triangle has one 90-degree angle. Steps: 1) Option A: Hypotenuse is opposite the 90-degree angle, correct. 2) Option B: Angles sum to 180 degrees, not 90. 3) Option C: Two sides are legs, one is hypotenuse, not all legs. 4) Option D: Hypotenuse is square root of (leg1 squared + leg2 squared), not leg1 + leg2.
Rationale: A right triangle has one 90-degree angle. Steps: 1) Option A: Hypotenuse is opposite the 90-degree angle, correct. 2) Option B: Angles sum to 180 degrees, not 90. 3) Option C: Two sides are legs, one is hypotenuse, not all legs. 4) Option D: Hypotenuse is square root of (leg1 squared + leg2 squared), not leg1 + leg2.
Question 3
Identify which of the following measurements form a right triangle, given the possible lengths of all three sides
Correct Answer: C
Rationale: Right triangle follows a squared + b squared = c squared, c longest. Steps: 1) Option A: 4 squared + 9 squared = 16 + 81 = 97, not 16 squared = 256. 2) Option B: 12 squared + 14 squared = 144 + 196 = 340, not 26 squared = 676. 3) Option C: 3 squared + 4 squared = 9 + 16 = 25 = 5 squared, correct. 4) Option D: 4 squared + 7 squared = 16 + 49 = 65, not 10 squared = 100.
Rationale: Right triangle follows a squared + b squared = c squared, c longest. Steps: 1) Option A: 4 squared + 9 squared = 16 + 81 = 97, not 16 squared = 256. 2) Option B: 12 squared + 14 squared = 144 + 196 = 340, not 26 squared = 676. 3) Option C: 3 squared + 4 squared = 9 + 16 = 25 = 5 squared, correct. 4) Option D: 4 squared + 7 squared = 16 + 49 = 65, not 10 squared = 100.
Question 4
A circle has a radius of 4.5 cm. What is the area of the circle?
Correct Answer: B
Rationale: Circle area is pi times radius squared, pi = 3.14. Steps: 1) Radius = 4.5 cm, 4.5 squared = 20.25. 2) Area = 3.14 times 20.25 = 63.585 cm squared. 3) Round to 63.59 cm squared, correct. Option A uses radius=3, C is half, D is double.
Rationale: Circle area is pi times radius squared, pi = 3.14. Steps: 1) Radius = 4.5 cm, 4.5 squared = 20.25. 2) Area = 3.14 times 20.25 = 63.585 cm squared. 3) Round to 63.59 cm squared, correct. Option A uses radius=3, C is half, D is double.
Question 5
A circle has an area of 226.865 in squared. Assume pi=3.14. Find the radius of the circle.
Correct Answer: C
Rationale: Area = pi times radius squared, so radius = square root of (area/pi). Steps: 1) Area = 226.865 in squared, pi = 3.14. 2) radius squared = 226.865 / 3.14 = 72.25. 3) radius = square root of 72.25 = 8.5 in, correct. Options A, B, D use wrong units or values.
Rationale: Area = pi times radius squared, so radius = square root of (area/pi). Steps: 1) Area = 226.865 in squared, pi = 3.14. 2) radius squared = 226.865 / 3.14 = 72.25. 3) radius = square root of 72.25 = 8.5 in, correct. Options A, B, D use wrong units or values.