Algebra 1 Semester 1 Final Exam Review: 26 Problems with Answers

An algebra 1 semester 1 final exam review usually covers expressions, solving linear equations and inequalities, functions, slope and linear graphs, systems of equations, and often exponent rules and exponential functions. Below are a topic checklist tied to the Common Core Algebra I course and 26 practice problems with worked answers you can reveal one at a time.

What the first semester of Algebra 1 covers

Most US Algebra 1 courses follow the Common Core State Standards or a state version of them. The Common Core model Algebra I course (Appendix A, Traditional Pathway) has five units:

1. Relationships between quantities and reasoning with equations
2. Linear and exponential relationships
3. Descriptive statistics
4. Expressions and equations (polynomials, factoring, quadratic equations)
5. Quadratic functions and modeling

Appendix A calls these models, not a required order. In many schools the first semester reaches roughly through units 1 and 2, with factoring and quadratics after the break. Compare your own review packet with the checklist below.

Semester 1 topic checklist

Algebra 1 final exam review with answers

Work each problem on paper first, then open the answer.

Expressions

1. Evaluate 3x² − 2x + 5 when x = −2.
   
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   3(−2)² − 2(−2) + 5 = 3(4) + 4 + 5 = 21. Square −2 first; (−2)² is 4, not −4.

2. Simplify 4(2x − 3) − (x − 7).
   
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   8x − 12 − x + 7 = 7x − 5. The minus sign in front of the parentheses changes −7 to +7.

Linear equations and inequalities

3. Solve 5(x − 2) = 3x + 8.
   
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   5x − 10 = 3x + 8, so 2x = 18 and x = 9.

4. Solve x/3 + 2 = (x − 1)/2.
   
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   Multiply every term by 6: 2x + 12 = 3x − 3, so x = 15.

5. Solve P = 2l + 2w for w.
   
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   Subtract 2l: P − 2l = 2w. Divide by 2: w = (P − 2l)/2.

6. Solve −3x + 4 ≤ 19.
   
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   −3x ≤ 15. Dividing by a negative flips the sign: x ≥ −5.

7. Solve −2 < 2x + 4 ≤ 10.
   
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   Subtract 4 from all three parts: −6 < 2x ≤ 6. Divide by 2: −3 < x ≤ 3 (open dot at −3, closed dot at 3).

8. Solve |2x − 3| = 7.
   
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   2x − 3 = 7 or 2x − 3 = −7, so x = 5 or x = −2.

9. A gym charges a $25 sign-up fee plus $15 per month. You can spend at most $160. Write and solve an inequality for the number of months m.
   
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   25 + 15m ≤ 160, so 15m ≤ 135 and m ≤ 9.

Functions

10. Is the relation {(1, 4), (2, 5), (1, 6)} a function?
    
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    No. The input 1 is paired with two outputs, 4 and 6. A function gives each input exactly one output.

11. If f(x) = 2x² − 3x, find f(−3).
    
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    2(9) − 3(−3) = 18 + 9 = 27.

12. State the domain and range of {(−2, 3), (0, 3), (4, −1)}.
    
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    Domain: {−2, 0, 4}. Range: {−1, 3}.

13. Find the average rate of change of f(x) = x² from x = 1 to x = 4.
    
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    (f(4) − f(1)) / (4 − 1) = (16 − 1)/3 = 5.

14. For the sequence 7, 11, 15, … write a formula for the nth term and find the 20th term.
    
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    The common difference is 4, so a_n = 7 + 4(n − 1) = 4n + 3. a₂₀ = 4(20) + 3 = 83.

Linear functions and graphs

15. Find the slope of the line through (−2, 5) and (4, −7).
    
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    m = (−7 − 5)/(4 − (−2)) = −12/6 = −2.

16. Write the equation of the line with slope 2/3 through (3, −1).
    
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    −1 = (2/3)(3) + b gives −1 = 2 + b, so b = −3. y = (2/3)x − 3.

17. For 3x − 4y = 12, find the x-intercept, the y-intercept and the slope.
    
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    Let y = 0: x = 4. Let x = 0: y = −3. Solve for y: y = (3/4)x − 3, so the slope is 3/4.

18. Write the equation of the line parallel to y = −2x + 5 through (1, 4).
    
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    Parallel lines share the slope −2. 4 = −2(1) + b, so b = 6: y = −2x + 6.

19. Write the equation of the line perpendicular to y = 2x − 3 through (4, 1).
    
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    The perpendicular slope is the negative reciprocal, −1/2. 1 = −(1/2)(4) + b, so b = 3: y = −(1/2)x + 3.

Systems of equations

20. Solve by substitution: y = 2x − 1 and 3x + 2y = 12.
    
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    3x + 2(2x − 1) = 12, so 7x − 2 = 12 and x = 2. Then y = 3. (2, 3).

21. Solve by elimination: 2x + 3y = 7 and 4x − 3y = 5.
    
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    Add the equations: 6x = 12, so x = 2. Then 4 + 3y = 7 and y = 1. (2, 1).

22. A school sold 200 tickets. Adult tickets cost $8 and student tickets cost $5. Sales totaled $1,330. How many of each were sold?
    
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    a + s = 200 and 8a + 5s = 1330. Substitute s = 200 − a: 8a + 1000 − 5a = 1330, so 3a = 330. 110 adult and 90 student tickets.

23. How many solutions does the system y = 3x + 2 and 6x − 2y = 8 have?
    
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    The second equation becomes y = 3x − 4. Same slope, different intercepts, so the lines are parallel: no solution.

Exponents and exponential functions

24. Simplify (2x³y)² · 3x⁻²y.
    
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    (2x³y)² = 4x⁶y². Multiply: 12x^{6 + (−2)}y^{2 + 1} = 12x⁴y³.

25. A car worth $18,000 loses 12% of its value each year. What is it worth after 3 years?
    
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    The decay factor is 1 − 0.12 = 0.88. V = 18000(0.88)³ = 18000 × 0.681472 ≈ $12,266.50.

26. Is the table x: 0, 1, 2, 3 and y: 5, 15, 45, 135 linear or exponential? Write its equation.
    
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    Each y is 3 times the one before (a constant ratio, not a constant difference), so it is exponential: y = 5(3)^x.

Common mistakes on the semester final

• Forgetting to flip the inequality sign after multiplying or dividing by a negative number (problem 6).
• Distributing a minus sign to only the first term inside parentheses (problem 2).
• Writing slope as run over rise, or subtracting the points in a different order on top and bottom (problem 15).
• Giving only one answer for an absolute value equation (problem 8).
• Using the percent itself, such as 0.12, as the decay factor instead of 1 − 0.12 (problem 25).
• Stopping after finding x in a system instead of giving an ordered pair.

How to prepare in the last week

1. Day 1: Work all 26 problems and mark each checklist topic solid or shaky.
2. Days 2 to 4: Study one shaky topic per day.
3. Day 5: Take a timed mixed practice test.
4. Day 6: Redo every missed problem, then rest.

Next steps: the free Algebra 1 practice test with answers, the Algebra 1 worksheets with answer keys, and focused lessons on multi-step inequalities, finding slope, domain and range and systems by substitution.

Algebra 1 semester 1 review practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

What is on the Algebra 1 semester 1 final exam?

Most first-semester finals cover expressions, solving linear equations and inequalities, functions and function notation, slope and graphing lines, and systems of equations. Many also include exponent rules and exponential growth. The exact list depends on your teacher's pacing, so compare this checklist with your own review packet or syllabus.

Are quadratics on the semester 1 Algebra 1 final?

Usually not. The Common Core model Algebra I course places factoring, quadratic equations and quadratic functions in its last two units, which usually come in the second semester. Some accelerated or block-schedule courses move faster, so check with your teacher if your class has already started polynomials.

How do I study for my Algebra 1 final in one week?

Start with a full set of mixed review problems to find your weak topics. Spend the next few days on one weak topic per day, then take a timed practice test and redo every missed problem. Short daily sessions are easier to keep up than one long cram session the night before.

Where can I find an Algebra 1 final exam review with answers?

This page has 26 review problems with worked answers you can open one at a time, plus a 10-question quiz. Your teacher's review packet is the best match for your exam, and Effortless Math's free Algebra 1 practice test and worksheets include answer keys for extra practice.

Sources

• Common Core Appendix A: Designing High School Mathematics Courses (Oregon Department of Education) (checked November 2026)
• Common Core: Reasoning with Equations and Inequalities (A-REI) (checked November 2026)
• Common Core: Interpreting Functions (F-IF) (checked November 2026)
• Common Core: Linear, Quadratic and Exponential Models (F-LE) (checked November 2026)