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UST Middle School Algebra I Challenge

Week 1 — Foundations of Algebra

Focus: Variables, expressions, properties, order of operations

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Weekly Format

Week 1

Part A — 15 Multiple Choice

Part B — 15 Fill in the Blank

Part C — 15 Word / Open-Response Problems

Part D — 5 Challenge Problems

Answer key and step-by-step explanations follow the questions.

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Part A — Multiple Choice

Questions 1–5

1. Evaluate 3x − 4 when x = 3. A) 5 B) 9 C) -3 D) 2

2. Evaluate 3x − 4 when x = 4. A) 8 B) 12 C) 0 D) 5

3. Evaluate 3x − 4 when x = 5. A) 11 B) 15 C) 3 D) 8

4. Evaluate 3x − 4 when x = 6. A) 14 B) 18 C) 6 D) 11

5. Evaluate 3x − 4 when x = 7. A) 17 B) 21 C) 9 D) 14

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Part A — Multiple Choice

Questions 6–10

6. Evaluate 3x − 4 when x = 8. A) 20 B) 24 C) 12 D) 17

7. Evaluate 3x − 4 when x = 9. A) 23 B) 27 C) 15 D) 20

8. Evaluate 3x − 4 when x = 10. A) 26 B) 30 C) 18 D) 23

9. Evaluate 3x − 4 when x = 11. A) 29 B) 33 C) 21 D) 26

10. Evaluate 3x − 4 when x = 12. A) 32 B) 36 C) 24 D) 29

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Part A — Multiple Choice

Questions 11–15

11. Evaluate 3x − 4 when x = 13. A) 35 B) 39 C) 27 D) 32

12. Evaluate 3x − 4 when x = 14. A) 38 B) 42 C) 30 D) 35

13. Evaluate 3x − 4 when x = 15. A) 41 B) 45 C) 33 D) 38

14. Evaluate 3x − 4 when x = 16. A) 44 B) 48 C) 36 D) 41

15. Evaluate 3x − 4 when x = 17. A) 47 B) 51 C) 39 D) 44

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Part B — Fill in the Blank

Questions 16–20

16. Simplify 5x + 3 − 2x + 2: ___.

17. Simplify 5x + 3 − 2x + 3: ___.

18. Simplify 5x + 3 − 2x + 4: ___.

19. Simplify 5x + 3 − 2x + 5: ___.

20. Simplify 5x + 3 − 2x + 6: ___.

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Part B — Fill in the Blank

Questions 21–25

21. Simplify 5x + 3 − 2x + 7: ___.

22. Simplify 5x + 3 − 2x + 8: ___.

23. Simplify 5x + 3 − 2x + 9: ___.

24. Simplify 5x + 3 − 2x + 10: ___.

25. Simplify 5x + 3 − 2x + 11: ___.

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Part B — Fill in the Blank

Questions 26–30

26. Simplify 5x + 3 − 2x + 12: ___.

27. Simplify 5x + 3 − 2x + 13: ___.

28. Simplify 5x + 3 − 2x + 14: ___.

29. Simplify 5x + 3 − 2x + 15: ___.

30. Simplify 5x + 3 − 2x + 16: ___.

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Part C — Word / Open Response

Questions 31–35

31. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 2 GB.

32. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 3 GB.

33. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 4 GB.

34. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 5 GB.

35. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 6 GB.

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Part C — Word / Open Response

Questions 36–40

36. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 7 GB.

37. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 8 GB.

38. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 9 GB.

39. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 10 GB.

40. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 11 GB.

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Part C — Word / Open Response

Questions 41–45

41. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 12 GB.

42. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 13 GB.

43. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 14 GB.

44. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 15 GB.

45. A phone plan costs $25 plus $8 per GB. Write and evaluate an expression for 16 GB.

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Part D — Challenge

Questions 46–50

46. Challenge: Simplify 3(2x−2)−2(x+4).

47. Challenge: Simplify 3(2x−3)−2(x+4).

48. Challenge: Simplify 3(2x−4)−2(x+4).

49. Challenge: Simplify 3(2x−5)−2(x+4).

50. Challenge: Simplify 3(2x−6)−2(x+4).

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Answer Key — Questions 1–5

Answer + How to Solve

1. Answer: A

How to solve: Substitute x=3: 3(3)−4=5.

2. Answer: A

How to solve: Substitute x=4: 3(4)−4=8.

3. Answer: A

How to solve: Substitute x=5: 3(5)−4=11.

4. Answer: A

How to solve: Substitute x=6: 3(6)−4=14.

5. Answer: A

How to solve: Substitute x=7: 3(7)−4=17.

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Answer Key — Questions 6–10

Answer + How to Solve

6. Answer: A

How to solve: Substitute x=8: 3(8)−4=20.

7. Answer: A

How to solve: Substitute x=9: 3(9)−4=23.

8. Answer: A

How to solve: Substitute x=10: 3(10)−4=26.

9. Answer: A

How to solve: Substitute x=11: 3(11)−4=29.

10. Answer: A

How to solve: Substitute x=12: 3(12)−4=32.

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Answer Key — Questions 11–15

Answer + How to Solve

11. Answer: A

How to solve: Substitute x=13: 3(13)−4=35.

12. Answer: A

How to solve: Substitute x=14: 3(14)−4=38.

13. Answer: A

How to solve: Substitute x=15: 3(15)−4=41.

14. Answer: A

How to solve: Substitute x=16: 3(16)−4=44.

15. Answer: A

How to solve: Substitute x=17: 3(17)−4=47.

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Answer Key — Questions 16–20

Answer + How to Solve

16. Answer: 3x + 5