Free ParaPro Core Plus (Math Version 1) Questions and Answers 2 — Questions and Answers
Question 1: A student is asked to find 15% of 80. Which method is MOST efficient for a student who understands percent basics?
- Dividing 80 by 15
- Finding 10% of 80 (=8), then finding 5% of 80 (=4), and adding them (8+4=12) (Correct answer)
- Multiplying 80 × 15
- Subtracting 15 from 80
Correct answer: Finding 10% of 80 (=8), then finding 5% of 80 (=4), and adding them (8+4=12)
Breaking 15% into 10% + 5% uses easy mental math: 10% of 80 = 8, 5% of 80 = 4, so 15% = 12. This benchmark percent strategy builds number sense.
The benchmark percent strategy decomposes a percent into easy-to-calculate parts. 10% of any number = divide by 10; 5% = half of 10%. So 15% = 10% + 5% = 8 + 4 = 12. This mental math approach is more efficient than formal proportion setup for common percents. Multiplying 80 × 15 gives 1200 (wrong), and dividing or subtracting don't apply the percent correctly.
Question 2: A student solves the equation 2x + 3 = 11 and gets x = 7. Is this correct? What is the proper solution?
- Yes, x = 7 is correct
- No; subtract 3 from both sides to get 2x = 8, then divide by 2 to get x = 4 (Correct answer)
- No; add 3 to both sides to get 2x = 14, then divide by 2 to get x = 7 — actually correct
- No; the equation cannot be solved
Correct answer: No; subtract 3 from both sides to get 2x = 8, then divide by 2 to get x = 4
Subtracting 3 from both sides: 2x = 8; dividing by 2: x = 4. The student's answer of x = 7 is incorrect.
To solve 2x + 3 = 11, apply inverse operations in reverse order: subtract 3 from both sides (2x = 8), then divide both sides by 2 (x = 4). Verification: 2(4) + 3 = 8 + 3 = 11. ✓ The student's answer of x = 7 would give 2(7)+3 = 17 ≠11. The student likely added 3 instead of subtracting.
Question 3: Which of the following represents the correct order of operations for evaluating 3 + 4 × 2²?
- Add first: 7 × 2² = 7 × 4 = 28
- Exponent first: 3 + 4 × 4 = 3 + 16 = 19 (Correct answer)
- Multiply first: 3 + 8² = 3 + 64 = 67
- Left to right: 3+4=7, 7×2=14, 14²=196
Correct answer: Exponent first: 3 + 4 × 4 = 3 + 16 = 19
Order of operations (PEMDAS): exponents first (2²=4), then multiplication (4×4=16), then addition (3+16=19). The answer is 19.
PEMDAS defines the order: 1) Parentheses, 2) Exponents, 3) Multiplication and Division (left to right), 4) Addition and Subtraction (left to right). In 3 + 4 × 2²: first evaluate 2² = 4; then multiply 4 × 4 = 16; then add 3 + 16 = 19. Adding first (7 × 4 = 28) or multiplying before exponents (3 + 8² = 67) violates PEMDAS.
Question 4: A student is graphing the point (3, -2) on a coordinate plane. Where is this point located?
- 3 units left and 2 units up from the origin
- 3 units right and 2 units down from the origin (Correct answer)
- 2 units right and 3 units down from the origin
- 3 units right and 2 units up from the origin
Correct answer: 3 units right and 2 units down from the origin
The ordered pair (x, y) = (3, -2) means 3 units right on the x-axis (positive) and 2 units down on the y-axis (negative).
In the coordinate plane, the ordered pair (x, y) is read: x-coordinate (horizontal movement) first, y-coordinate (vertical) second. Positive x moves right; negative x moves left. Positive y moves up; negative y moves down. (3, -2): move 3 right from origin, then 2 down — landing in Quadrant IV. (3, 2) would be Quadrant I; (-3, 2) would be Quadrant II; (-3, -2) would be Quadrant III.
Question 5: A student needs to compare the fractions 3/4 and 5/7. Which method is MOST reliable?
- Compare the numerators only
- Find a common denominator and compare: 21/28 vs. 20/28, so 3/4 > 5/7 (Correct answer)
- Compare the denominators only
- Guess based on which fraction 'looks bigger'
Correct answer: Find a common denominator and compare: 21/28 vs. 20/28, so 3/4 > 5/7
Converting to a common denominator (28) gives 3/4 = 21/28 and 5/7 = 20/28, revealing that 3/4 > 5/7. This is the most reliable comparison method.
To compare fractions reliably, convert to equivalent fractions with the same denominator. LCM of 4 and 7 is 28. 3/4 = 21/28 and 5/7 = 20/28. Since 21 > 20, then 3/4 > 5/7 (though barely). Comparing only numerators or only denominators fails when fractions have different denominators. Cross-multiplication is an equivalent alternative: 3×7=21, 5×4=20, and since 21>20, 3/4 > 5/7.
Question 6: A student earns $240 for working 15 hours. What is the student's hourly rate?
- $15.00 per hour
- $16.00 per hour (Correct answer)
- $18.00 per hour
- $12.00 per hour
Correct answer: $16.00 per hour
Hourly rate = total earnings ÷ hours worked = $240 ÷ 15 = $16.00 per hour.
Unit rate problems divide a total quantity by the number of units: $240 ÷ 15 hours = $16 per hour. This is a ratio/proportional reasoning problem. Verification: $16 × 15 = $240. ✓ This type of problem appears frequently on the ParaPro math section as an application of division and proportional reasoning in real-world contexts.
Free ParaPro Core Plus (Math Version 1) Questions and Answers 2
A student is asked to find 15% of 80.
Which method is MOST efficient for a student who understands percent basics?