Part 1: Skills Check

1. Simplify: 3x + 5 − 2x + 7

x + 12

5x + 12

x + 2

6x + 12

2. Simplify: 4(2x − 3) + x

9x − 3

8x − 12

9x − 12

8x − 3

3. Solve: x/5 = −4

−20

−9

1

20

4. Solve: 3x + 8 = 23

x = 5

x = 7

x = 9

x = 15

5. Solve: 4x − 7 = 2x + 9

x = 1

x = 8

x = 11

x = 16

6. Solve: −2x + 5 > 13

x > −4

x < −4

x > 9

x < 9

7. Solve and graph on a number line: −3 ≤ 2x + 1 < 7

8. Use the table to write an equation in slope-intercept form.

x: 0, 1, 2, 3

y: 4, 7, 10, 13

9. A line passes through (0, 3) and (2, 7). Write its equation and identify the slope and y-intercept.

10. A gym charges a $15 sign-up fee plus $8 per month. Write an equation for the total cost C after m months. Find C for 6 months.

11. Solve the system using substitution: y = x + 2 and 2x + y = 11.

12. Solve the system using elimination: 3x + 2y = 16 and 3x − 2y = 8.

Part 2: Algebraic Reasoning and Applications

13. Simplify using exponent rules: x^4 · x^3

14. Simplify using exponent rules: (a^6)/(a^2)

15. Write in scientific notation: 0.00056

16. Add: (3x^2 + 5x − 1) + (2x^2 − x + 6)

17. Multiply: (x + 4)(x − 3)

18. Error analysis: A student simplifies 4(2x − 3) as 8x − 3. Identify the error and give the correct answer.

19. Error analysis: A student solves 5x + 2 = 2x + 17 and gets x = 3. Explain the error and solve correctly.

20. A taxi ride costs $3.50 plus $2.25 per mile. Write a function for the cost C in terms of miles m. How much does a 7-mile ride cost?

21. The temperature was 68°F at noon and decreased 4°F each hour. Write an equation for the temperature T after h hours. What will the temperature be after 5 hours?

22. A rectangle has a length that is 5 feet greater than its width. Its perimeter is 34 feet. Write and solve an equation to find the dimensions.

23. Solve and check: 2(x − 4) + 3 = 17

24. The equation y = −2x + 6 represents a linear relationship. Interpret the slope and y-intercept in a real-world situation where x is time in hours and y is money in dollars.

Answer Key

1. x + 12

2. 9x − 12

3. x = −20

4. x = 5

5. x = 8

6. x < −4

7. −2 ≤ x < 3. Graph: closed circle at −2, open circle at 3, shade between.

8. y = 3x + 4

9. y = 2x + 3; slope = 2; y-intercept = 3.

10. C = 8m + 15; C(6) = $63.

11. (3, 5)

12. (4, 2)

13. x^7

14. a^4

15. 5.6 × 10^−4

16. 5x^2 + 4x + 5

17. x^2 + x − 12

18. The 4 must be distributed to both terms: 8x − 12.

19. After subtracting 2x, the student should have 3x + 2 = 17, so 3x = 15 and x = 5.

20. C = 2.25m + 3.50; C(7) = $19.25.

21. T = 68 − 4h; T(5) = 48°F.

22. Let w be the width. 2w + 2(w + 5) = 34; w = 6 feet and length = 11 feet.

23. x = 11. Check: 2(11 − 4) + 3 = 17.

24. The slope −2 means the amount decreases by $2 per hour. The y-intercept 6 means the starting amount is $6.

Algebra I Semester 1 Review

Algebra I Semester 1 Review

Part 1: Skills Check

Part 2: Algebraic Reasoning and Applications

Answer Key

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