Algebra 1 Final Exam Study Guide: 9 Topics, Step by Step
- qian58
- May 25
- 6 min read
Updated: May 28
Use our guide to get instant feedback on every step so you see your mistakes and fix them before the exam.
You're probably doing algebra the hard way
You solve a problem, check the answer key, and realize you got it wrong. But you don't know why, and you wasted 10 mins without learning anything.
This page is different. As you solve, our AI tells you if each line is correct or not. So you catch mistakes while you're practicing, not after.
Watch: type a step and moment.of.math checks it instantly. Green means you're on track. Red means something is off.
Algebra 1 can be a really tough subject. It's a whole new way of thinking about math, and it can be tough to know where to start. If you have a Common Core cirriculum, we have made a guide with practical strategies organized around 9 topics that may show up on your exam. Work through each section, try the practice problems, and head into test day with real confidence.
The Topics You Need to Know
What sets this guide apart: you don't just review, you actually try each problem right here on the page, get instant feedback on your work, and see exactly where you need to improve. That's how you build real understanding.
Scroll down for practice problems and links for deeper help on each topic.
Linear Equations & Inequalities
Check the example if you need a refresher. If you want to work through the problem yourself, right-click and delete each line of math below the blue "Given" box. To learn more or get more practice, click the link below the box.
Problem: Solve for x: 3x + 5 = 20
Goal: Get numbers on one side and x on another.
+5 is on x's side — subtract it from both sides.
3 is still on x's side — divide both sides by 3.
x is alone. All done!
Note that inequalities work exactly the same. The only thing that you have to remember is that if you multiply or divide by a negative number, flip the inequality.
If you found this scratchpad helpful, get our Chrome extension to use it with almost any algebra problem!
Systems of Equations & Inequalities
Check the example if you need a refresher. If you want to work through the problem yourself, right-click and delete each line of math below the blue "Given" box. To learn more or get more practice, click the link below the box.
Problem: Problem: Solve the system of equations:
y = 2x
x + y = 12
Y is already isolated in equation (1), so we know y = 2x. Anywhere we see y in equation (2), we can replace it with 2x — now equation (2) only has x in it, which we can solve.
Now that we know x = 4, we can substitute it back into either equation. We now have only one unknown left (y), so we can isolate it and solve.
If you found this scratchpad helpful, get our Chrome extension to use it with almost any algebra problem!
Functions
Check the example if you need a refresher. If you want to work through the problem yourself, right-click and delete each line of math below the blue "Given" box. To learn more or get more practice, click the link below the box.
Problem: Marcus is saving money. He starts with $40 and saves $15 every week. The total amount he has saved after x weeks is modeled by y = 40 + 15x.
(a) How much money did Marcus start with? (b) How much does he save each week? (c) How much will he have after 6 weeks?
This box is interactive. You can delete lines and try them yourself.
It also checks your work in real time. See what happens if you change some of the math lines.
If you found this scratchpad helpful, get our Chrome extension to use it with almost any algebra problem!
Quadratics
Check the example if you need a refresher. If you want to work through the problem yourself, right-click and delete each line of math below the blue "Given" box. To learn more or get more practice, click the link below the box.
Problem: Solve by factoring: x² − 5x + 6 = 0
This box is interactive. You can delete lines and try them yourself.
It also checks your work in real time. See what happens if you change some of the math lines.
If you found this scratchpad helpful, get our Chrome extension to use it with almost any algebra problem!
Exponents & Exponential Functions
Check the example if you need a refresher. If you want to work through the problem yourself, right-click and delete each line of math below the blue "Given" box. To learn more or get more practice, click the link below the box.
Problem: A population of bacteria doubles every hour starting from 500. Which equation gives the population y after x hours?
(1) y = 500 + 2x (2) y = 500 × 2^x (3) y = 2 × 500^x
This box is interactive. You can delete lines and try them yourself.
It also checks your work in real time. See what happens if you change some of the math lines.
If you found this scratchpad helpful, get our Chrome extension to use it with almost any algebra problem!
Statistics
Check the example if you need a refresher. If you want to work through the problem yourself, right-click and delete each line of math below the blue "Given" box. To learn more or get more practice, click the link below the box.
Problem: In a class of 30 students, 18 prefer math and 12 prefer English. Of the students who prefer math, 10 are in 9th grade and 8 are in 10th grade.
What percentage of the students who prefer math are in 10th grade?
This box is interactive. You can delete lines and try them yourself.
It also checks your work in real time. See what happens if you change some of the math lines.
If you found this scratchpad helpful, get our Chrome extension to use it with almost any algebra problem!
Linear Functions and Slope.
Check the example if you need a refresher. If you want to work through the problem yourself, right-click and delete each line of math below the blue "Given" box. To learn more or get more practice, click the link below the box.
Problem: A car rental company charges a flat fee of $25 plus $0.40 per mile. Write a function for the total cost C after m miles. What is the slope and what does it mean in context?
Things to remember:
The y-intercept (25) is the flat fee — what you pay before driving a single mile.
The slope (0.40) is the rate of change — cost increases by $0.40 per additional mile.
If you found this scratchpad helpful, get our Chrome extension to use it with almost any algebra problem!
Word Problems
Check the example if you need a refresher. If you want to work through the problem yourself, right-click and delete each line of math below the blue "Given" box. To learn more or get more practice, click the link below the box.
Problem: Two friends are saving money. Alex has $120 and saves $15 per week. Jordan has $60 and saves $25 per week. After how many weeks will they have the same amount?
Steps:
Write an expression for each: Alex = 120 + 15w; Jordan = 60 + 25w.
Set them equal
Solve
If you found this scratchpad helpful, get our Chrome extension to use it with almost any algebra problem!
Polynomials and Factoring
Check the example if you need a refresher. If you want to work through the problem yourself, right-click and delete each line of math below the blue "Given" box. To learn more or get more practice, click the link below the box.
Problem: (x + 3)(x − 5)
Goal: use the FOIL (first, outer, inner, last)
First = x^2
Outer = -5x
Inner = 3x
Last = -15
Combine these to get x^2-2x-15
If you found this scratchpad helpful, get our Chrome extension to use it with almost any algebra problem!
Catch your algebra mistakes before they cost you
The scratchpad in this guide runs on moment.of.math — a free Chrome extension that checks your algebra line by line, on any problem. It can generate new variations problems, so you can get as much practice as you need. On many homework sites, it automatically detects the math on the page, so you don't have to copy anything over. Try it on tonight's homework.
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