Pre-Algebra Mastery · 100 Essential Questions
Name: _________________________ Date: _____________ Score: ___ / 100
Unit 1 Number Sense & Arithmetic
Q1
What is 3 + 4?
Concept: Basic addition — combining two numbers together.
Q2
What is 12 − 5?
Concept: Subtraction — taking away from a number.
Q3
What is 6 × 7?
Concept: Multiplication — repeated addition. 6 groups of 7.
Q4
What is 48 ÷ 6?
Concept: Division — splitting into equal groups. How many 6s fit in 48?
Q5
What is 2⁵ (2 to the power of 5)?
Concept: Exponents — multiply 2 by itself 5 times: 2×2×2×2×2.
Q6
Round 3.7 to the nearest whole number.
Concept: If the decimal part ≥ 0.5, round up. If < 0.5, round down.
Q7
What is the GCF (Greatest Common Factor) of 12 and 18?
Concept: List factors of each: 12={1,2,3,4,6,12}, 18={1,2,3,6,9,18}. Largest shared factor.
Q8
What is the LCM (Least Common Multiple) of 12 and 18?
Concept: LCM = (12 × 18) ÷ GCF. GCF is 6, so (12 × 18) ÷ 6 = 36.
Q9
In the number 1,234, what digit is in the hundreds place?
Concept: Place values: ones → tens → hundreds → thousands. Count from the right.
Q10
What is |−7| (the absolute value of negative 7)?
Concept: Absolute value = distance from zero on a number line. Always positive.
Unit 2 Fractions
Q11
What is ½ + ⅓?
Concept: Find a common denominator: LCD of 2 and 3 is 6. Then 3/6 + 2/6 = 5/6.
Q12
What is ¾ − ¼?
Concept: Same denominator — just subtract numerators: (3−1)/4 = 2/4 = 1/2.
Q13
What is ⅔ × ¾?
Concept: Multiply straight across: (2×3)/(3×4) = 6/12 = 1/2.
Q14
What is ⅗ ÷ ⅕?
Concept: Dividing fractions — "Keep, Change, Flip": 3/5 × 5/1 = 15/5 = 3.
Q15
Convert the mixed number 1⅔ to an improper fraction.
Concept: (whole × denominator + numerator) / denominator = (1×3+2)/3 = 5/3.
Q16
Simplify 6/8 to its lowest terms.
Concept: GCF of 6 and 8 is 2. Divide both: 6÷2=3, 8÷2=4. Answer: 3/4.
Q17
What is 2¼ + 1½?
Concept: Add whole parts (2+1=3) and fractions (1/4+2/4=3/4). Total: 3¾.
Q18
What is ½ of 20?
Concept: "Of" means multiply: ½ × 20 = 20 ÷ 2 = 10.
Q19
Which fraction is larger: ⅔ or ¾?
Concept: Convert to same denominator (12): 8/12 vs 9/12. So ¾ is larger.
Q20
What is 5/6 − 1/3?
Concept: Convert 1/3 to 2/6. Then 5/6 − 2/6 = 3/6 = 1/2.
Unit 3 Decimals
Q21
What is 0.3 + 0.4?
Concept: Line up decimal points and add: 0.3 + 0.4 = 0.7.
Q22
What is 1.5 − 0.7?
Concept: Line up decimal points, borrow if needed: 15 − 7 = 8, so 0.8.
Q23
What is 0.4 × 0.5?
Concept: Multiply 4×5=20, then count 2 decimal places → 0.20 = 0.2.
Q24
What is 3.6 ÷ 0.9?
Concept: Multiply both by 10: 36 ÷ 9 = 4. (Move the decimal to make divisor whole.)
Q25
Which decimal best represents 2/3?
Concept: Divide 2 ÷ 3 = 0.666… ≈ 0.67 (rounded to hundredths).
Q26
What is 1/8 as a decimal?
Concept: 1 ÷ 8 = 0.125. Or: 1/8 = 125/1000 = 0.125.
Q27
What is 3/4 as a decimal?
Concept: 3 ÷ 4 = 0.75. Memorize: 1/4=0.25, 1/2=0.5, 3/4=0.75.
Q28
What is 1.2 × 3?
Concept: 12 × 3 = 36, then 1 decimal place → 3.6.
Q29
What is 7.5 ÷ 2.5?
Concept: Multiply both by 10: 75 ÷ 25 = 3.
Q30
What is 0.1 + 0.2 + 0.3?
Concept: Add step by step: 0.1+0.2=0.3, then 0.3+0.3=0.6.
Unit 4 Percents
Q31
What is 25% of 80?
Concept: Percent means "per 100." 25% = 0.25. So 0.25 × 80 = 20.
Q32
What is 10% of 150?
Concept: 10% = move decimal one place left. 150 → 15.0 = 15.
Q33
30 is what percent of 50?
Concept: % = (part ÷ whole) × 100 = (30 ÷ 50) × 100 = 0.6 × 100 = 60%.
Q34
What is 20% of 60?
Concept: 20% = 0.20. So 0.20 × 60 = 12.
Q35
A price of $100 increases by 15%. What is the new price?
Concept: New = original + increase = 100 + (15% of 100) = 100 + 15 = $115.
Q36
A $200 jacket is 10% off. What is the sale price?
Concept: Discount = 10% × 200 = $20. Sale price = 200 − 20 = $180.
Q37
A student got 45 out of 60 questions correct. What percent is that?
Concept: (45 ÷ 60) × 100 = 0.75 × 100 = 75%.
Q38
What is 50% of 48?
Concept: 50% = half. Half of 48 = 24.
Q39
A price went from $50 to $80. What is the percent increase?
Concept: % increase = (change ÷ original) × 100 = (30 ÷ 50) × 100 = 60%.
Q40
What is 1% of 300?
Concept: 1% = move decimal two places left: 300 → 3.00 = 3.
Unit 5 Integers
Q41
What is −3 + (−5)?
Concept: Both negative — add their values, keep negative sign: 3+5=8, so −8.
Q42
What is −8 − (−3)?
Concept: Subtracting a negative = adding a positive. −8 − (−3) = −8 + 3 = −5.
Q43
What is −4 × 3?
Concept: Negative × Positive = Negative. 4 × 3 = 12, so answer is −12.
Q44
What is −15 ÷ (−3)?
Concept: Negative ÷ Negative = Positive. 15 ÷ 3 = 5.
Q45
What is (−2)³?
Concept: (−2)³ = (−2)(−2)(−2) = 4 × (−2) = −8. Odd power of negative = negative.
Q46
What is |−9| + |4|?
Concept: |−9| = 9, |4| = 4. Then 9 + 4 = 13.
Q47
What is −6 + 10?
Concept: Different signs — subtract and keep sign of larger: 10−6=4, positive wins → 4.
Q48
What is 3 × (−4) + 5?
Concept: Multiply first: 3×(−4)=−12. Then −12+5=−7.
Q49
What is (−3)²?
Concept: (−3)² = (−3)(−3) = 9. Even power of negative = positive.
Q50
What is −5 + 5?
Concept: Opposites cancel out. Any number + its opposite = 0.
Unit 6 Ratios & Proportions
Q51
Simplify the ratio 6 : 9.
Concept: Divide both by GCF. GCF(6,9) = 3. So 6÷3 : 9÷3 = 2 : 3.
Q52
If 3 pencils cost $1.50, how much do 6 pencils cost?
Concept: Unit price = $1.50 ÷ 3 = $0.50 each. 6 × $0.50 = $3.00.
Q53
Two numbers are in ratio 2 : 5. If their total is 35, what is the smaller number?
Concept: Total parts = 2+5 = 7. Each part = 35÷7 = 5. Smaller = 2×5 = 10.
Q54
Solve the proportion: x/4 = 3/6. What is x?
Concept: Cross multiply: 6x = 12, so x = 2. Or: 3/6 = 1/2, so x = 4 × 1/2 = 2.
Q55
A car travels at 60 mph for 2 hours. How far does it go?
Concept: Distance = Speed × Time = 60 × 2 = 120 miles.
Q56
A map scale is 1 cm : 100 cm. If a road measures 3 cm on the map, how long is it in real life?
Concept: Multiply: 3 × 100 = 300 cm (real length).
Q57
The ratio of boys to girls is 3 : 2. If there are 15 boys, how many girls are there?
Concept: 3 parts = 15, so 1 part = 5. Girls = 2 parts = 2 × 5 = 10.
Q58
Solve: 5/8 = x/40. What is x?
Concept: Cross multiply: 8x = 200, so x = 25. Or: 40 ÷ 8 = 5, then 5 × 5 = 25.
Q59
A car drives 180 miles in 3 hours. What is the unit rate (speed)?
Concept: Unit rate = total ÷ units = 180 ÷ 3 = 60 miles per hour.
Q60
A recipe uses ¼ cup of sugar for 2 servings. How much sugar is needed for 8 servings?
Concept: 8 servings ÷ 2 = 4 times more. So ¼ × 4 = 1 cup.
Unit 7 Algebra Basics
Q61
Solve for x: x + 5 = 12
Concept: Subtract 5 from both sides: x = 12 − 5 = 7.
Q62
Solve for x: 3x = 21
Concept: Divide both sides by 3: x = 21 ÷ 3 = 7.
Q63
Solve for x: 2x + 3 = 11
Concept: Step 1: 2x = 11 − 3 = 8. Step 2: x = 8 ÷ 2 = 4.
Q64
Solve for x: x − 4 = 9
Concept: Add 4 to both sides: x = 9 + 4 = 13.
Q65
Solve for x: 5x − 2 = 18
Concept: Add 2: 5x = 20. Divide by 5: x = 4.
Q66
Evaluate 3x + 2 when x = 4.
Concept: Substitute: 3(4) + 2 = 12 + 2 = 14.
Q67
Simplify: 3x + 5x
Concept: Like terms — same variable, add coefficients: 3 + 5 = 8, so 8x.
Q68
Expand: 2(x + 3). What is the constant term?
Concept: Distributive property: 2×x + 2×3 = 2x + 6. Constant = 6.
Q69
Solve for x: x/3 = 5
Concept: Multiply both sides by 3: x = 5 × 3 = 15.
Q70
Solve for x: 4(x − 1) = 12
Concept: Divide both sides by 4: x−1 = 3. Then x = 3+1 = 4.
Unit 8 Geometry Basics
Q71
What is the perimeter of a rectangle that is 5 units long and 3 units wide?
Concept: Perimeter = 2 × (length + width) = 2 × (5+3) = 2 × 8 = 16.
Q72
What is the area of a rectangle 5 units long and 3 units wide?
Concept: Area = length × width = 5 × 3 = 15 square units.
Q73
What is the area of a triangle with base = 6 and height = 4?
Concept: Area = ½ × base × height = ½ × 6 × 4 = 12.
Q74
What is the circumference of a circle with radius 7? (Use π ≈ 22/7)
Concept: C = 2πr = 2 × (22/7) × 7 = 2 × 22 = 44.
Q75
What is the area of a circle with radius 3? (Use π ≈ 3.14)
Concept: A = πr² = 3.14 × 3² = 3.14 × 9 = 28.26.
Q76
What is the volume of a box that is 3 × 4 × 5 units?
Concept: Volume = length × width × height = 3 × 4 × 5 = 60 cubic units.
Q77
A triangle has angles of 60° and 70°. What is the third angle?
Concept: All angles of a triangle add up to 180°. Third = 180 − 60 − 70 = 50°.
Q78
What is the supplementary angle of 65°?
Concept: Supplementary angles add up to 180°. So: 180 − 65 = 115°.
Q79
What is the complementary angle of 30°?
Concept: Complementary angles add up to 90°. So: 90 − 30 = 60°.
Q80
A right triangle has legs of 3 and 4. What is the length of the hypotenuse?
Concept: Pythagorean theorem: c² = 3² + 4² = 9 + 16 = 25. So c = √25 = 5.
Unit 9 Statistics & Probability
Q81
Find the mean of: 2, 4, 6, 8, 10
Concept: Mean = sum ÷ count = (2+4+6+8+10) ÷ 5 = 30 ÷ 5 = 6.
Q82
Find the median of: 3, 5, 7, 9, 11
Concept: Median = middle value when sorted. List is already sorted: middle is 7.
Q83
Find the mode of: 2, 3, 3, 4, 5
Concept: Mode = most frequent value. 3 appears twice, others once. Mode = 3.
Q84
Find the range of: 5, 8, 12, 3, 9
Concept: Range = max − min = 12 − 3 = 9.
Q85
Find the mean of: 10, 20, 30
Concept: Mean = (10+20+30) ÷ 3 = 60 ÷ 3 = 20.
Q86
Find the median of: 1, 3, 5, 7 (even number of values)
Concept: Even count — median = average of two middle values = (3+5) ÷ 2 = 4.
Q87
A bag has 5 marbles: 1 red, 4 blue. What is the probability of picking the red marble?
Concept: P(event) = favorable outcomes ÷ total outcomes = 1 ÷ 5 = 1/5.
Q88
What is the probability of rolling a 3 on a standard 6-sided die?
Concept: One 3 out of 6 sides → P(3) = 1/6.
Q89
How many possible outcomes are there when flipping 2 coins?
Concept: Each coin has 2 outcomes. Total = 2 × 2 = 4. (HH, HT, TH, TT)
Q90
Which value is the outlier in the data set: 2, 3, 4, 5, 50?
Concept: An outlier is a value far from the rest of the data. 50 is far from 2–5.
Unit 10 Order of Operations & Mixed Review
Q91
What is 2 + 3 × 4? (Apply order of operations)
Concept: PEMDAS — Multiply before Add. 3×4=12, then 2+12=14.
Q92
What is (2 + 3) × 4?
Concept: Parentheses first: 2+3=5. Then 5×4=20.
Q93
What is 3² − 1?
Concept: Exponents first: 3²=9. Then 9−1=8.
Q94
What is 4 + 6 ÷ 2?
Concept: Division before Addition: 6÷2=3, then 4+3=7.
Q95
What is 10 − 2 × 3 + 1?
Concept: Multiply first: 2×3=6. Then left to right: 10−6+1 = 4+1 = 5.
Q96
How many distinct prime factors does 12 have?
Concept: 12 = 2² × 3. The distinct prime factors are 2 and 3 → count = 2.
Q97
Is 17 a prime or composite number?
Concept: A prime number has exactly 2 factors: 1 and itself. 17 has no other divisors.
Q98
How many minutes are in 2.5 hours?
Concept: 1 hour = 60 minutes. 2.5 × 60 = 150 minutes.
Q99
You buy 3 items at $4 each and pay $2 in tax. What is the total cost?
Concept: Cost = 3 × $4 = $12. Total = $12 + $2 tax = $14.
Q100
What is the next number in the pattern: 2, 4, 8, 16, ___?
Concept: Each term doubles: ×2. So 16 × 2 = 32.
Answer Key
1. B — 7
2. C — 7
3. C — 42
4. C — 8
5. C — 32
6. B — 4
7. B — 6
8. C — 36
9. B — 2
10. C — 7
11. C — 5/6
12. B — 1/2
13. B — 1/2
14. B — 3
15. B — 5/3
16. C — 3/4
17. B — 3¾
18. B — 10
19. B — 3/4
20. B — 1/2
21. C — 0.7
22. B — 0.8
23. B — 0.2
24. B — 4
25. C — 0.67
26. B — 0.125
27. C — 0.75
28. B — 3.6
29. B — 3
30. B — 0.6
31. B — 20
32. B — 15
33. C — 60%
34. C — 12
35. B — $115
36. B — $180
37. C — 75%
38. B — 24
39. C — 60%
40. B — 3
41. C — −8
42. B — −5
43. C — −12
44. B — 5
45. D — −8
46. C — 13
47. B — 4
48. B — −7
49. D — 9
50. D — 0
51. B — 2:3
52. C — $3.00
53. B — 10
54. A — 2
55. C — 120
56. C — 300 cm
57. B — 10
58. C — 25
59. B — 60 mph
60. B — 1 cup
61. C — 7
62. C — 7
63. B — 4
64. C — 13
65. A — 4
66. C — 14
67. B — 8x
68. C — 6
69. C — 15
70. C — 4
71. C — 16
72. B — 15
73. B — 12
74. B — 44
75. C — 28.26
76. C — 60
77. A — 50°
78. D — 115°
79. B — 60°
80. C — 5
81. B — 6
82. C — 7
83. B — 3
84. C — 9
85. B — 20
86. B — 4
87. B — 1/5
88. B — 1/6
89. C — 4
90. C — 50
91. B — 14
92. B — 20
93. C — 8
94. B — 7
95. C — 5
96. B — 2
97. A — Prime
98. B — 150
99. C — $14
100. C — 32