Math Practice Test 3

Correct Answer: 4

Explanation: Use formula: Time = Distance ÷ Rate. Calculate: 240 ÷ 60 = 4 hours. Use calculator: 240 ÷ 60 = 4.

Correct Answer: 2.3

Explanation: Multiply: 5 × 0.45 = 2.25 kg. Round to nearest tenth: 2.25 rounds to 2.3 kg. Use calculator: 5 × 0.45 = 2.25.

Correct Answer: 282.6

Explanation: Calculate step-by-step: Square radius: 3² = 9. Multiply by height: 9 × 10 = 90. Multiply by π: 90 × 3.14 = 282.6 cm³. Use calculator: π × 3² × 10 = 282.6

Correct Answer: 12

Explanation: Use a² + b² = c², where c=13, a=5. Calculate: 5² + b² = 13² → 25 + b² = 169 → b² = 144 → b = √144 = 12 m. This is a 5-12-13 triangle.

Correct Answer: 50

Explanation: Area = (1/2) × base × height. Calculate: 0.5 × 12.5 × 8 = 6.25 × 8 = 50 cm². Remember the 1/2 factor for triangles.

Correct Answer: 11

Explanation: Subtract 3x: 2x – 8 = 14. Add 8: 2x = 22. Divide by 2: x = 11. Check: 5(11)-8=47, 3(11)+14=47 ✓.

Correct Answer: 6x – 2

Explanation: Distribute: 2x + 6 + 4x – 8. Combine like terms: 2x + 4x = 6x. 6 – 8 = -2. Result: 6x – 2.

Correct Answer: 108

Explanation: Calculate 35% of 80: 0.35 × 80 = 28. Add to original: 80 + 28 = 108. Or multiply by 1.35: 80 × 1.35 = 108. Use calculator.

Correct Answer: 160

Explanation: “is” means equals, “of” means multiply. Set up: 32 = 0.20 × n. Solve: n = 32 ÷ 0.20 = 160. Use calculator: 32 ÷ 0.20 = 160.

Correct Answer: 30.4

Explanation: Move decimal in divisor and dividend: 0.6 becomes 6, 18.24 becomes 182.4. Divide: 182.4 ÷ 6 = 30.4. Use calculator: 18.24 ÷ 0.6 = 30.4.

Correct Answer: 16.77

Explanation: Line up the decimals and subtract: 45.67 − 28.90 = 16.77. You can confirm the result with a calculator.

Correct Answer: 1/6

Explanation: Multiply numerators: 7 × 3 = 21. Multiply denominators: 9 × 14 = 126. Result: 21/126. Simplify by dividing by 21: 21÷21=1, 126÷21=6. Final answer: 1/6. Or cancel before multiplying: (7/9)×(3/14) = (1/3)×(1/2) = 1/6.

Correct Answer: 7/24

Explanation: Find common denominator: 24 (8×3). Convert: 5/8 = 15/24, 1/3 = 8/24. Subtract: 15/24 – 8/24 = 7/24. Already in lowest terms.

Correct Answer: 6 1/4

Explanation: Convert to improper fractions: 5/2 + 15/4. Common denominator 4: 10/4 + 15/4 = 25/4. Convert back: 25 ÷ 4 = 6 with remainder 1, so 6 1/4. Or add whole numbers: 2+3=5, add fractions: 1/2+3/4=5/4=1 1/4. Total: 5 + 1 1/4 = 6 1/4.

Correct Answer: 210

Explanation: Divide using long division or calculator: 2,730 ÷ 13 = 210 exactly. Check: 210 × 13 = 2,730. Use calculator’s division function.

Correct Answer: 16,872

Explanation: Break it down: 456 × 30 = 13,680. 456 × 7 = 3,192. Add: 13,680 + 3,192 = 16,872. Use calculator: 456 × 37 = 16,872.

Correct Answer: 3,544

Explanation: To subtract these numbers, you need to borrow because there are zeros in the minuend. Borrow from the thousands place: 6,000 becomes 5,999, and this allows you to subtract each column normally. Subtract 2,456 from 5,999 to get 3,543, then add the extra 1 from the borrowing process, giving a final result of 3,544. You can confirm the answer with a calculator: 6,000 − 2,456 = 3,544.

Correct Answer: 12,356

Explanation: Add the numbers column by column. First, add the ones: 7 + 9 = 16, write 6 and carry 1. Next, add the tens: 6 + 8 + 1 = 15, write 5 and carry 1. Then, add the hundreds: 5 + 7 + 1 = 13, write 3 and carry 1. Finally, add the thousands: 8 + 3 + 1 = 12. The total is 12,356. Use a calculator to verify.

Correct Answer: A) Getting exactly one head and D) Getting the same side on both coins

Explanation: Possible outcomes: HH, HT, TH, TT (4 total). A: Exactly one head = HT or TH = 2 outcomes = 2/4 = 1/2 ✓. B: At least one head = HH, HT, TH = 3/4 ✗. C: Two tails = TT = 1/4 ✗. D: Same side = HH or TT = 2/4 = 1/2 ✓. Select A and D.

Correct Answer: A) The mean is 12 and B) The median is 12

Explanation: Let’s calculate each statistic carefully: Mean (average): Add all numbers: 8 + 10 + 12 + 14 + 16 = 60. Divide by count (5): 60 ÷ 5 = 12. So statement A is correct. Median (middle value): Arrange numbers (already ordered). The middle (3rd) number is 12. So statement B is also correct. Range: Largest – smallest = 16 – 8 = 8. Statement C says 10, which is false. Mode: Number that appears most frequently. All numbers appear once, so there is no mode. Statement D is false. Select A and B.

Correct Answer: A) A square is always a rectangle and C) A rhombus has four equal sides

Explanation: A: Square meets all rectangle requirements (4 right angles, opposite sides equal) ✓. B: Rectangle doesn’t require equal sides to be square ✗. C: Rhombus definition: quadrilateral with 4 equal sides ✓. D: Parallelogram has opposite sides parallel, but angles aren’t necessarily 90° ✗. Select A and C.

Correct Answer: A) -5 + 3 and C) -2 × 3

Explanation: A: -5 + 3 = -2 (negative) ✓. B: 4 – (-2) = 4 + 2 = 6 (positive) ✗. C: -2 × 3 = -6 (negative) ✓. D: -8 ÷ (-2) = 4 (positive) ✗. When signs are different, the result is negative. Select A and C.

Correct Answer: A) 8 and C) 12

Explanation: Factors of 48: numbers that divide 48 exactly. 8 × 6 = 48 ✓. 9 × 5.33… ≠ 48 ✗. 12 × 4 = 48 ✓. 15 × 3.2 ≠ 48 ✗. Select A and C.

Correct Answer: B) $674.10

Explanation: Area: 12 × 15 = 180 sq ft. Carpet cost: 180 × $3.50 = $630. Tax: $630 × 0.07 = $44.10. Total: $630 + $44.10 = $674.10. Use calculator for each step.

Multiple Select Questions (5 questions)

Correct Answer: B) 60 km

Explanation: Set proportion: 2 cm / 15 km = 8 cm / x km. Cross-multiply: 2x = 15 × 8 = 120. Divide: x = 120 ÷ 2 = 60 km. Or: 8 ÷ 2 = 4, then 4 × 15 = 60 km.

Correct Answer: B) 3.45 × 10⁶

Explanation: Move decimal to after first non-zero digit: 3.45. Count moves: 6 places to the left. Large numbers have positive exponents: 10⁶. So 3.45 × 10⁶.

Correct Answer: B) x⁵

Explanation: First apply power of power: (x²)⁴ = x^(2×4) = x⁸. Then divide: x⁸ ÷ x³ = x^(8-3) = x⁵. When dividing same base, subtract exponents.

Correct Answer: B) 10 units

Explanation: Use distance formula: √[(x₂-x₁)² + (y₂-y₁)²]. Calculate: (7-1)² = 6² = 36. (10-2)² = 8² = 64. Sum: 36 + 64 = 100. Square root: √100 = 10 units. This forms a 6-8-10 right triangle.

Correct Answer: A) -3 + 7 – 4 = 0

Explanation: Start at -3. Moving right (positive direction) 7 units: -3 + 7 = 4. Then moving left (negative direction) 4 units: 4 – 4 = 0. The expression is -3 + 7 – 4 = 0.

Correct Answer: C) 55 mph

Explanation: Speed = change in distance ÷ change in time. From any two points: (110-55)÷(2-1) = 55÷1 = 55 mph. The graph shows a constant rate of 55 miles per hour.

Correct Answer: C) Q3

Explanation: Calculate the distance (absolute difference) from $50K for each quarter: Q1: |45,000 – 50,000| = 5,000. Q2: |53,000 – 50,000| = 3,000. Q3: |48,000 – 50,000| = 2,000. Q4: |56,000 – 50,000| = 6,000. Compare distances: 2,000 is the smallest distance. Q3 at $48K is only $2,000 away from $50K, making it the closest. Use your calculator to verify differences: 50000 – 48000 = 2000

Correct Answer: B) 1/2

Explanation: Total marbles = 10 + 6 + 4 = 20. Non-red = 6 blue + 4 green = 10. Probability = 10/20 = 1/2. “NOT red” means everything except red.

Correct Answer: C) 21

Explanation: First order numbers: 15, 18, 20, 22, 25, 30. There are 6 numbers (even), so median is average of middle two: (20 + 22) ÷ 2 = 21. For even count, median = average of (n/2)th and (n/2 + 1)th numbers.

Correct Answer: C) 6

Explanation: Add all numbers: -5 + 8 + 12 + (-3) + 18 = 30. Count: 5 numbers. Divide: 30 ÷ 5 = 6. Use calculator and remember negative signs.

Correct Answer: C) 2,500 meters

Explanation: 1 kilometer = 1,000 meters. Multiply: 2.5 × 1,000 = 2,500 meters. Moving decimal three places to the right.

Correct Answer: B) 50 cm²

Explanation: Area formula: A = (base1 + base2)/2 × height. Calculate: (8 + 12)/2 = 10, then 10 × 5 = 50 cm². The two bases are averaged, then multiplied by height.

Correct Answer: C) 25.12 cm

Explanation: Circumference formula: C = 2πr. Calculate: 2 × 3.14 × 4 = 25.12 cm. Use calculator: 2 × 3.14 × 4 = 25.12.

Correct Answer: C) 115°

Explanation: Alternate interior angles formed by parallel lines and a transversal are always equal in measure. The angles are on opposite sides of the transversal but between the parallel lines.

Correct Answer: A) 2

Explanation: Substitute x = 4: h(4) = -2(4) + 10 = -8 + 10 = 2. Remember to multiply before adding.

Correct Answer: D) Open circle at -2, arrow right

Explanation: For inequalities with > or <, use an open circle (not included). Since x is greater than -2, the arrow points to the right (toward larger numbers). For ≥ or ≤, you would use a closed circle.

Correct Answer: C) 16

Explanation: Subtract 5 from both sides: x/4 = 4. Multiply both sides by 4: x = 16. Check: 16/4 + 5 = 4 + 5 = 9 ✓

Correct Answer: C) 35

Explanation: Follow order of operations (PEMDAS): Square x: 4² = 16. Multiply: 3 × 16 = 48. Multiply: 5 × 4 = 20. Subtract and add: 48 – 20 + 7 = 35. Use calculator carefully, watching the order of operations.

Correct Answer: B) $91.80

Explanation: First discount: $120 × 0.85 = $102.00. Second discount: $102 × 0.90 = $91.80. This is a successive discount, not additive (not 25% off). Always apply each discount to the new price.

Correct Answer: C) 375

Explanation: Multiplying by 100 moves the decimal point two places to the right. 3.75 becomes 375. You can also think: 3.75 × 100 = 3.75 × (10 × 10) = 37.5 × 10 = 375.

Correct Answer: B) 1/2 yard

Explanation: Subtract: 5/6 – 1/3. Convert to common denominator 6: 5/6 – 2/6 = 3/6. Simplify: 3/6 = 1/2. Always find a common denominator before subtracting fractions.

Correct Answer: C) 30

Explanation: Divide: 1,250 ÷ 42 = 29.7619. You can’t have a fraction of a bus, so you must round up to the next whole number to accommodate all students. 29 buses would leave some students behind, so you need 30 buses. Use calculator: 42 × 30 = 1,260, which is enough for 1,250 students.