Prepared for: Math 100 Students | Topics: Algebra Fundamentals through Quadratics
1. What is a variable in algebra?
Answer: A variable is a symbol (usually a letter) that represents an unknown or
changing quantity. Example: x, y, or n.
2. Simplify: 3x + 5x
Answer: 8x (Combine like terms: 3 + 5 = 8)
3. Evaluate 4x − 2 when x = 3.
Answer: 4(3) − 2 = 12 − 2 = 10
4. What is a coefficient?
Answer: A coefficient is the numerical factor multiplied by a variable. In 7x, the
coefficient is 7.
5. Evaluate: 2a + 3b when a = 4, b = 2.
Answer: 2(4) + 3(2) = 8 + 6 = 14
6. Simplify: 9y − 4y + 2y
Answer: 7y
7. What does 'like terms' mean?
Answer: Like terms are terms that have the same variable(s) raised to the same
power. Example: 3x and 5x are like terms.
8. Simplify: 6x + 3 − 2x − 1
Answer: 4x + 2
9. Evaluate: x² + 3x − 4 when x = 2.
Answer: (2)² + 3(2) − 4 = 4 + 6 − 4 = 6
10. What is a constant?
Answer: A constant is a fixed value that does not change. In 3x + 7, the number 7 is a
constant.
, TOPIC 2: Order of Operations
11. State the order of operations (PEMDAS).
Answer: Parentheses, Exponents, Multiplication/Division (left to right),
Addition/Subtraction (left to right).
12. Simplify: 3 + 2 × 4
Answer: 3 + 8 = 11 (Multiply before adding)
13. Simplify: (3 + 2) × 4
Answer: 5 × 4 = 20 (Parentheses first)
14. Simplify: 2³ + 4 × 3 − 6
Answer: 8 + 12 − 6 = 14
15. Simplify: 18 ÷ 3 × 2
Answer: 6 × 2 = 12 (Left to right)
16. Simplify: 5 + 3(4 − 1)²
Answer: 5 + 3(3)² = 5 + 3(9) = 5 + 27 = 32
17. Simplify: 4 × 2 + 6 ÷ 3
Answer: 8 + 2 = 10
18. Simplify: 12 ÷ (2 + 1) × 4
Answer: 12 ÷ 3 × 4 = 4 × 4 = 16
19. Simplify: 7 − 2 + 5 × 3
Answer: 7 − 2 + 15 = 20
20. Simplify: (8 − 3)² ÷ 5
Answer: 25 ÷ 5 = 5
TOPIC 3: Solving One-Step Equations
21. Solve: x + 5 = 12
Answer: x = 7
22. Solve: y − 8 = 3
Answer: y = 11
23. Solve: 3n = 21
Answer: n = 7
24. Solve: x/4 = 6
Answer: x = 24
25. Solve: a + 11 = 20
, Answer: a = 9
26. Solve: 5m = 45
Answer: m = 9
27. Solve: z − 14 = −2
Answer: z = 12
28. Solve: x/3 = −4
Answer: x = −12
29. Solve: 7p = −49
Answer: p = −7
30. Solve: b + (−6) = 10
Answer: b = 16
TOPIC 4: Solving Two-Step Equations
31. Solve: 2x + 3 = 11
Answer: 2x = 8 → x = 4
32. Solve: 3y − 5 = 16
Answer: 3y = 21 → y = 7
33. Solve: 4n + 1 = 25
Answer: 4n = 24 → n = 6
34. Solve: 5m − 2 = 28
Answer: 5m = 30 → m = 6
35. Solve: x/2 + 4 = 9
Answer: x/2 = 5 → x = 10
36. Solve: 6a − 3 = 15
Answer: 6a = 18 → a = 3
37. Solve: 2b + 9 = 1
Answer: 2b = −8 → b = −4
38. Solve: 7p + 2 = 30
Answer: 7p = 28 → p = 4
39. Solve: 3c − 4 = −13
Answer: 3c = −9 → c = −3
40. Solve: n/5 − 3 = 2
Answer: n/5 = 5 → n = 25
1. What is a variable in algebra?
Answer: A variable is a symbol (usually a letter) that represents an unknown or
changing quantity. Example: x, y, or n.
2. Simplify: 3x + 5x
Answer: 8x (Combine like terms: 3 + 5 = 8)
3. Evaluate 4x − 2 when x = 3.
Answer: 4(3) − 2 = 12 − 2 = 10
4. What is a coefficient?
Answer: A coefficient is the numerical factor multiplied by a variable. In 7x, the
coefficient is 7.
5. Evaluate: 2a + 3b when a = 4, b = 2.
Answer: 2(4) + 3(2) = 8 + 6 = 14
6. Simplify: 9y − 4y + 2y
Answer: 7y
7. What does 'like terms' mean?
Answer: Like terms are terms that have the same variable(s) raised to the same
power. Example: 3x and 5x are like terms.
8. Simplify: 6x + 3 − 2x − 1
Answer: 4x + 2
9. Evaluate: x² + 3x − 4 when x = 2.
Answer: (2)² + 3(2) − 4 = 4 + 6 − 4 = 6
10. What is a constant?
Answer: A constant is a fixed value that does not change. In 3x + 7, the number 7 is a
constant.
, TOPIC 2: Order of Operations
11. State the order of operations (PEMDAS).
Answer: Parentheses, Exponents, Multiplication/Division (left to right),
Addition/Subtraction (left to right).
12. Simplify: 3 + 2 × 4
Answer: 3 + 8 = 11 (Multiply before adding)
13. Simplify: (3 + 2) × 4
Answer: 5 × 4 = 20 (Parentheses first)
14. Simplify: 2³ + 4 × 3 − 6
Answer: 8 + 12 − 6 = 14
15. Simplify: 18 ÷ 3 × 2
Answer: 6 × 2 = 12 (Left to right)
16. Simplify: 5 + 3(4 − 1)²
Answer: 5 + 3(3)² = 5 + 3(9) = 5 + 27 = 32
17. Simplify: 4 × 2 + 6 ÷ 3
Answer: 8 + 2 = 10
18. Simplify: 12 ÷ (2 + 1) × 4
Answer: 12 ÷ 3 × 4 = 4 × 4 = 16
19. Simplify: 7 − 2 + 5 × 3
Answer: 7 − 2 + 15 = 20
20. Simplify: (8 − 3)² ÷ 5
Answer: 25 ÷ 5 = 5
TOPIC 3: Solving One-Step Equations
21. Solve: x + 5 = 12
Answer: x = 7
22. Solve: y − 8 = 3
Answer: y = 11
23. Solve: 3n = 21
Answer: n = 7
24. Solve: x/4 = 6
Answer: x = 24
25. Solve: a + 11 = 20
, Answer: a = 9
26. Solve: 5m = 45
Answer: m = 9
27. Solve: z − 14 = −2
Answer: z = 12
28. Solve: x/3 = −4
Answer: x = −12
29. Solve: 7p = −49
Answer: p = −7
30. Solve: b + (−6) = 10
Answer: b = 16
TOPIC 4: Solving Two-Step Equations
31. Solve: 2x + 3 = 11
Answer: 2x = 8 → x = 4
32. Solve: 3y − 5 = 16
Answer: 3y = 21 → y = 7
33. Solve: 4n + 1 = 25
Answer: 4n = 24 → n = 6
34. Solve: 5m − 2 = 28
Answer: 5m = 30 → m = 6
35. Solve: x/2 + 4 = 9
Answer: x/2 = 5 → x = 10
36. Solve: 6a − 3 = 15
Answer: 6a = 18 → a = 3
37. Solve: 2b + 9 = 1
Answer: 2b = −8 → b = −4
38. Solve: 7p + 2 = 30
Answer: 7p = 28 → p = 4
39. Solve: 3c − 4 = −13
Answer: 3c = −9 → c = −3
40. Solve: n/5 − 3 = 2
Answer: n/5 = 5 → n = 25
