AASA 7th Grade Math 2 — Questions and Answers
Question 1: What is the value of −8 + (−5) − (−3)?
- −10 (Correct answer)
- −16
- −6
- 0
Correct answer: −10
−8 + (−5) = −13. Then −13 − (−3) = −13 + 3 = −10.
Work through each operation step by step. First: −8 + (−5) = −13. Then: −13 − (−3) means −13 + 3 (since subtracting a negative equals adding a positive) = −10. Integer operations with addition and subtraction are core AASA 7th grade math skills aligned to Arizona Academic Standards.
Question 2: A shirt originally costs $40. It is on sale for 25% off. What is the sale price?
- $30 (Correct answer)
- $10
- $35
- $15
Correct answer: $30
25% of $40 = 0.25 × 40 = $10 discount. Sale price = $40 − $10 = $30.
To find a percent discount: multiply the original price by the percent (as a decimal). 25% = 0.25, so discount = 0.25 × $40 = $10. Sale price = $40 − $10 = $30. Alternatively, the sale price is 75% of the original: 0.75 × $40 = $30. Percent problems involving markups, markdowns, tips, and tax are major components of the Arizona AASA 7th grade assessment.
Question 3: Two angles are supplementary. One angle measures 65°. What is the measure of the other angle?
- 115° (Correct answer)
- 25°
- 90°
- 295°
Correct answer: 115°
Supplementary angles sum to 180°. The other angle = 180° − 65° = 115°.
Supplementary angles are two angles whose measures add up to 180°. If one angle is 65°, the supplement is 180° − 65° = 115°. Do not confuse supplementary (sum = 180°) with complementary (sum = 90°). Angle relationships including supplementary, complementary, vertical, and adjacent angles are tested on the AASA 7th grade geometry standards.
Question 4: Solve for x: 3x − 7 = 14
- 7 (Correct answer)
- 3
- 21
- −7
Correct answer: 7
Add 7 to both sides: 3x = 21. Divide by 3: x = 7.
To solve 3x − 7 = 14, use inverse operations to isolate x. Step 1: Add 7 to both sides: 3x − 7 + 7 = 14 + 7, so 3x = 21. Step 2: Divide both sides by 3: x = 21 ÷ 3 = 7. You can verify: 3(7) − 7 = 21 − 7 = 14. Solving two-step equations is a key algebraic skill on the Arizona AASA 7th grade math test.
Question 5: A circle has a diameter of 10 inches. What is its circumference? (Use π ≈ 3.14)
- 31.4 inches (Correct answer)
- 15.7 inches
- 78.5 inches
- 62.8 inches
Correct answer: 31.4 inches
Circumference = π × diameter = 3.14 × 10 = 31.4 inches.
The circumference of a circle can be calculated using C = πd (where d is the diameter) or C = 2πr (where r is the radius). Here, d = 10 inches, so C = 3.14 × 10 = 31.4 inches. Note that 15.7 inches would be the semicircle (half the circumference), and 78.5 square inches would be the area. Circle measurements are part of the AASA 7th grade geometry standards.
Question 6: A bag contains 4 red, 3 blue, and 3 yellow marbles. If one marble is drawn at random, what is the probability of NOT drawing a red marble?
- 3/5 (Correct answer)
- 2/5
- 3/10
- 7/10
Correct answer: 3/5
Total marbles = 10. Non-red marbles = 3 + 3 = 6. Probability = 6/10 = 3/5.
The probability of an event NOT occurring equals 1 minus the probability of it occurring, or you can count favorable outcomes directly. Non-red marbles = 3 blue + 3 yellow = 6. Total marbles = 4 + 3 + 3 = 10. P(not red) = 6/10 = 3/5. Alternatively: P(red) = 4/10 = 2/5, so P(not red) = 1 − 2/5 = 3/5. Compound probability and complementary events are assessed on the AASA 7th grade test.
AASA 7th Grade Math 2
What is the value of −8 + (−5) − (−3)?