Term Tactics Worksheet
Pre-Algebra Practice Drills
Term Tactics: Practice Problems
Name:
Date:
Period:
A Part 1: Identify the Coefficient
Write the numerical coefficient for each given algebraic term.
1. \( 8x \)
Coefficient:
2. \( 15y^2 \)
Coefficient:
3. \( m \)
Coefficient:
4. \( 24a \)
Coefficient:
5. \( \frac{2}{5}w \)
Coefficient:
6. \( 9c^3 \)
Coefficient:
7. \( 0.7p \)
Coefficient:
8. \( b \)
Coefficient:
9. \( 13k \)
Coefficient:
10. \( 42x^2 \)
Coefficient:
11. \( z \)
Coefficient:
12. \( 1.8t \)
Coefficient:
B Part 2: Expression Component Analysis
List all components for each given expression.
13. Expression: \( 7x + 12 \) Terms: _____
List of Terms
Coefficients
Constant
14. Expression: \( 4a + 9b + 5 \) Terms: _____
List of Terms
Coefficients
Constant
15. Expression: \( 2y^2 + 8y + 11 \) Terms: _____
List of Terms
Coefficients
Constant
16. Expression: \( m + 6n + 19 \) Terms: _____
List of Terms
Coefficients
Constant
17. Expression: \( 5w^2 + 3w + 14 \) Terms: _____
List of Terms
Coefficients
Constant
18. Expression: \( 8p + 3q + 4r + 1 \) Terms: _____
List of Terms
Coefficients
Constant
C Part 3: Specific Coefficient Drills
State the coefficient of the requested variable.
19. In \( 14x + 9 \), coefficient of \( x \):
Answer:
20. In \( y + 25 \), coefficient of \( y \):
Answer:
21. In \( 3a^2 + 8a + 2 \), coeff of \( a^2 \):
Answer:
22. In \( 3a^2 + 8a + 2 \), coeff of \( a \):
Answer:
23. In \( 10m + 4n + 7 \), coeff of \( n \):
Answer:
24. In \( w^3 + 12 \), coefficient of \( w^3 \):
Answer:
Term Tactics Practice • Page 1 of 3 Problems 1–24: Terms & Coefficients
Practice Drills • Part II
Spotting & Combining Like Terms
Name:
D Part 4: Like or Unlike Pairs
Determine whether each pair contains like terms or unlike terms.
25. \( 5x \) and \( 8x \)
Like Unlike
26. \( 4y^2 \) and \( 4y \)
Like Unlike
27. \( 9a \) and \( 9b \)
Like Unlike
28. \( 3m^2 \) and \( 11m^2 \)
Like Unlike
29. \( 12 \) and \( 37 \)
Like Unlike
30. \( 6xy \) and \( 2yx \)
Like Unlike
31. \( 7w^3 \) and \( 7w^2 \)
Like Unlike
32. \( 15c \) and \( c \)
Like Unlike
33. \( 8p \) and \( 8 \)
Like Unlike
34. \( 2a^2b \) and \( 5a^2b \)
Like Unlike
E Part 5: Combining Like Terms
Add the like terms. Write the final simplified term.
\( 6x + 9x \)
= __________
\( 12y + 15y \)
= __________
\( 4m + m \)
= __________
\( 7a^2 + 8a^2 \)
= __________
\( 11w + 23w \)
= __________
\( 18k + 6k \)
= __________
\( 5b + 14b + 3b \)
= __________
\( 8c^2 + c^2 + 12c^2 \)
= __________
\( 20p + 7p + 15p \)
= __________
\( 9x + x + 14x \)
= __________
\( 13y^3 + 2y^3 + 5y^3 \)
= __________
\( 16m + 4m + 9m \)
= __________
Term Tactics Practice • Page 2 of 3 Problems 25–46: Classification & Basic Combining
Practice Drills • Part III
Multi-Term Expressions & Applications
Name:
F Part 6: Multi-Term Combining Drills
Simplify each expression completely by grouping and adding like terms.
\( 5x + 3 + 4x + 9 \)
Work:
= ________________________
\( 8a + 6b + 2a + 7b \)
Work:
= ________________________
\( 12y + 4 + 3y + 15 + 2y \)
Work:
= ________________________
\( 7m^2 + 5m + 3m^2 + 8m + 11 \)
Work:
= ________________________
\( 6p + 9q + 4 + 3p + 2q + 8 \)
Work:
= ________________________
\( 4w^2 + 10w + 12 + 5w^2 + w + 3 \)
Work:
= ________________________
\( 15x + 8y + 2x + 9 + 4y + 1 \)
Work:
= ________________________
\( 3a^2 + 7a + 14 + 8a^2 + 2a + 5 \)
Work:
= ________________________
G Part 7: Algebraic Perimeter Problems
Find the perimeter by writing an expression adding all sides, then simplifying.
55. Triangle Perimeter
Side lengths: \( 2x + 3 \), \( 4x + 1 \), and \( 3x + 5 \).
Add sides & combine:
Perimeter = ____________________
56. Rectangle Perimeter
Length: \( 5y + 4 \) | Width: \( 2y + 1 \).
Add all 4 sides & combine:
Perimeter = ____________________
57. Square Perimeter
Side length: \( 3m + 2 \) (all 4 sides equal).
Add all 4 sides & combine:
Perimeter = ____________________
58. Quadrilateral Perimeter
Sides: \( x + 2 \), \( 3x + 4 \), \( 2x + 1 \), \( 4x + 3 \).
Add all 4 sides & combine:
Perimeter = ____________________
Term Tactics Practice • Page 3 of 3 Problems 47–58: Multi-Term Expressions & Perimeter
Term Tactics Answer Key
Teacher Edition Answer Key • Problems 1–24
Term Tactics: Practice Solutions
PAGE 1 ANSWER KEY
A Part 1: Identify the Coefficient (Solutions)
12 Problems
1. \( 8x \)
Coeff: 8
2. \( 15y^2 \)
Coeff: 15
3. \( m \)
Coeff: 1 (invisible 1)
4. \( 24a \)
Coeff: 24
5. \( \frac{2}{5}w \)
Coeff: 2/5 (or 0.4)
6. \( 9c^3 \)
Coeff: 9
7. \( 0.7p \)
Coeff: 0.7
8. \( b \)
Coeff: 1 (invisible 1)
9. \( 13k \)
Coeff: 13
10. \( 42x^2 \)
Coeff: 42
11. \( z \)
Coeff: 1 (invisible 1)
12. \( 1.8t \)
Coeff: 1.8
B Part 2: Expression Component Analysis (Solutions)
6 Expressions
13. Expression: \( 7x + 12 \) 2 terms
Terms \( 7x, 12 \)
Coeffs 7
Constant 12
14. Expression: \( 4a + 9b + 5 \) 3 terms
Terms \( 4a, 9b, 5 \)
Coeffs 4, 9
Constant 5
15. Expression: \( 2y^2 + 8y + 11 \) 3 terms
Terms \( 2y^2, 8y, 11 \)
Coeffs 2, 8
Constant 11
16. Expression: \( m + 6n + 19 \) 3 terms
Terms \( m, 6n, 19 \)
Coeffs 1, 6
Constant 19
17. Expression: \( 5w^2 + 3w + 14 \) 3 terms
Terms \( 5w^2, 3w, 14 \)
Coeffs 5, 3
Constant 14
18. Expression: \( 8p + 3q + 4r + 1 \) 4 terms
Terms \( 8p, 3q, 4r, 1 \)
Coeffs 8, 3, 4
Constant 1
C Part 3: Specific Coefficient Drills (Solutions)
6 Problems
19. In \( 14x + 9 \), coeff of \( x \):
Answer: 14
20. In \( y + 25 \), coeff of \( y \):
Answer: 1 (\(1y\))
21. In \( 3a^2 + 8a + 2 \), coeff of \( a^2 \):
Answer: 3
22. In \( 3a^2 + 8a + 2 \), coeff of \( a \):
Answer: 8
23. In \( 10m + 4n + 7 \), coeff of \( n \):
Answer: 4
24. In \( w^3 + 12 \), coeff of \( w^3 \):
Answer: 1
Term Tactics Answer Key • Page 1 of 3 Problems 1–24 Solutions
Teacher Edition • Part II Solutions
Spotting & Combining Like Terms
PAGE 2 ANSWER KEY
D Part 4: Like or Unlike Pairs (Solutions)
10 Pairs
25. \( 5x \) and \( 8x \) LIKE
26. \( 4y^2 \) and \( 4y \) UNLIKE (diff exp)
27. \( 9a \) and \( 9b \) UNLIKE (diff var)
28. \( 3m^2 \) and \( 11m^2 \) LIKE
29. \( 12 \) and \( 37 \) LIKE (constants)
30. \( 6xy \) and \( 2yx \) LIKE (\(xy=yx\))
31. \( 7w^3 \) and \( 7w^2 \) UNLIKE (diff exp)
32. \( 15c \) and \( c \) LIKE
33. \( 8p \) and \( 8 \) UNLIKE (var vs const)
34. \( 2a^2b \) and \( 5a^2b \) LIKE
E Part 5: Combining Like Terms (Solutions)
12 Drills
35. \( 6x + 9x \)
= 15x
36. \( 12y + 15y \)
= 27y
37. \( 4m + m \)
= 5m (\(4+1\))
38. \( 7a^2 + 8a^2 \)
= 15a²
39. \( 11w + 23w \)
= 34w
40. \( 18k + 6k \)
= 24k
41. \( 5b + 14b + 3b \)
= 22b
42. \( 8c^2 + c^2 + 12c^2 \)
= 21c²
43. \( 20p + 7p + 15p \)
= 42p
44. \( 9x + x + 14x \)
= 24x
45. \( 13y^3 + 2y^3 + 5y^3 \)
= 20y³
46. \( 16m + 4m + 9m \)
= 29m
Term Tactics Answer Key • Page 2 of 3 Problems 25–46 Solutions
Teacher Edition • Part III Solutions
Multi-Term Expressions & Applications
PAGE 3 ANSWER KEY
F Part 6: Multi-Term Combining Drills (Solutions)
8 Problems
47. \( 5x + 3 + 4x + 9 \)
\( (5x + 4x) + (3 + 9) \)
= 9x + 12
48. \( 8a + 6b + 2a + 7b \)
\( (8a + 2a) + (6b + 7b) \)
= 10a + 13b
49. \( 12y + 4 + 3y + 15 + 2y \)
\( (12y + 3y + 2y) + (4 + 15) \)
= 17y + 19
50. \( 7m^2 + 5m + 3m^2 + 8m + 11 \)
\( (7m^2 + 3m^2) + (5m + 8m) + 11 \)
= 10m² + 13m + 11
51. \( 6p + 9q + 4 + 3p + 2q + 8 \)
\( (6p + 3p) + (9q + 2q) + (4 + 8) \)
= 9p + 11q + 12
52. \( 4w^2 + 10w + 12 + 5w^2 + w + 3 \)
\( (4w^2 + 5w^2) + (10w + w) + (12 + 3) \)
= 9w² + 11w + 15
53. \( 15x + 8y + 2x + 9 + 4y + 1 \)
\( (15x + 2x) + (8y + 4y) + (9 + 1) \)
= 17x + 12y + 10
54. \( 3a^2 + 7a + 14 + 8a^2 + 2a + 5 \)
\( (3a^2 + 8a^2) + (7a + 2a) + (14 + 5) \)
= 11a² + 9a + 19
G Part 7: Algebraic Perimeter Problems (Solutions)
4 Problems
55. Triangle Perimeter
\( P = (2x + 4x + 3x) + (3 + 1 + 5) \)
Perimeter = 9x + 9
56. Rectangle Perimeter
\( P = 2(5y + 4) + 2(2y + 1) = 10y + 8 + 4y + 2 \)
Perimeter = 14y + 10
57. Square Perimeter
\( P = 4(3m + 2) = 3m + 3m + 3m + 3m + 2 + 2 + 2 + 2 \)
Perimeter = 12m + 8
58. Quadrilateral Perimeter
\( P = (x + 3x + 2x + 4x) + (2 + 4 + 1 + 3) \)
Perimeter = 10x + 10
Term Tactics Answer Key • Page 3 of 3 Problems 47–58 Solutions
