SAT Algebra Practice: Question Types and 8 Worked Examples
Key Takeaways
- College Board lists 13–15 Algebra questions in the 44-question Digital SAT Math section, roughly a third of your Math score.
- The Algebra domain covers five linear skills: equations in one variable, linear functions, equations in two variables, systems of two linear equations, and linear inequalities.
- Quadratics, exponentials and systems that include a curve belong to Advanced Math, not Algebra, so a weak Algebra result points to straight lines and linear models.
- Two patterns save the most time: the same x coefficient with the same constant means infinitely many solutions, and with a different constant means no solution.
- Most lost marks come from answering the wrong quantity, sign errors, not flipping an inequality sign and rounding the wrong way in a scenario.
Table of Contents
- How many algebra questions are on the Digital SAT?
- What does the SAT Algebra domain cover?
- Which algebra question types does the SAT ask?
- SAT algebra practice: 8 worked examples
- Example 1: Linear equation in one variable
- Example 2: Infinitely many solutions
- Example 3: Linear function in context
- Example 4: Line through two points
- Example 5: System of equations by elimination
- Example 6: A system with no solution
- Example 7: Linear inequality in context
- Example 8: A system of inequalities
- Which SAT algebra mistakes cost the most marks?
- How should you practise SAT algebra?
Algebra is one of the two biggest domains in Digital SAT Math. College Board lists 13–15 Algebra questions in a 44-question Math section, so roughly a third of your Math score rests on linear equations, linear functions, systems and inequalities. Because every question in the domain is linear, it is also one of the most predictable parts of the test to practise.
This guide sets out exactly what College Board puts in the Algebra domain, the question types that come up, the mistakes that cost marks, and eight worked examples with answers. Every example was written by Galvanize for this page, so none of them is a College Board question.
How many algebra questions are on the Digital SAT?
The Math section has 44 questions in two 35-minute modules, 70 minutes in total, according to College Board’s How the SAT Is Structured. Its Math section overview breaks those 44 questions into four domains:
| Math domain | Questions per test | Share of the Math section |
|---|---|---|
| Algebra | 13–15 | About 30–34% |
| Advanced Math | 13–15 | About 30–34% |
| Problem-Solving and Data Analysis | 5–7 | About 11–16% |
| Geometry and Trigonometry | 5–7 | About 11–16% |
Source: College Board, checked 31 October 2026. The percentage column is our own arithmetic on the question counts, not a College Board figure. Questions from all four domains appear in each module, and within a module they run from easiest to hardest, so Algebra questions are spread through the section rather than grouped together.
About 75% of Math questions are four-option multiple choice; the rest are student-produced responses, where you type your own answer. Algebra questions can be either format, so practise getting an exact value, not just recognising the right option.
What does the SAT Algebra domain cover?
College Board’s content domains page says Algebra “measures the ability to analyze, fluently solve, and create linear equations and inequalities, as well as analyze and fluently solve equations and systems of equations using multiple techniques.” It names five skills:
- Linear equations in one variable
- Linear functions
- Linear equations in two variables
- Systems of two linear equations in two variables
- Linear inequalities in one or two variables
Everything in the domain is linear. Quadratics, exponentials, absolute value, polynomials and systems that include a curve belong to Advanced Math on the same page. That boundary matters when you read your practice score report: a weak Algebra bar points to straight lines and linear models, not to quadratics.
Which algebra question types does the SAT ask?
The five skills turn up in a handful of recognisable forms. This grouping is our own, built from the skill list above.
| Skill | What the question looks like | The key move |
|---|---|---|
| Linear equations in one variable | Solve for x; find the value of 3x + 1; decide when an equation has no solution or infinitely many | Expand, collect x terms on one side; compare coefficients and constants |
| Linear functions | A rule such as f(x) = 40 + 12x, a table or a graph; interpret the slope or the starting value | Slope = change in output ÷ change in input, with units |
| Linear equations in two variables | Find the slope or intercept, the equation through two points, or a parallel or perpendicular line | Put the equation in y = mx + b form |
| Systems of two linear equations | Solve for x, y or an expression such as x + y; find a constant that gives no solution or infinitely many | Elimination or substitution; compare slopes for the number of solutions |
| Linear inequalities | “At most” or “at least” scenarios; which point satisfies a pair of inequalities | Solve like an equation, flip the sign when multiplying or dividing by a negative |
Some of these questions are bare equations and some are set in a scenario. College Board says approximately 30% of all Math questions are set in context, across every domain.
SAT algebra practice: 8 worked examples
Try each one before reading the solution. On test day you have about 95 seconds per Math question on average (70 minutes for 44 questions), and most Algebra questions should take less than that.
Example 1: Linear equation in one variable
If 4(x − 3) + 7 = 2x + 9, what is the value of x?
- Expand: 4x − 12 + 7 = 2x + 9, so 4x − 5 = 2x + 9.
- Collect x terms: 2x = 14, so x = 7.
- Check: 4(7 − 3) + 7 = 23 and 2(7) + 9 = 23.
- Answer: x = 7.
The trap: expanding 4(x − 3) as 4x − 3. Multiply every term inside the bracket.
Example 2: Infinitely many solutions
In the equation 3(2x + 5) = 6x + k, k is a constant. For what value of k does the equation have infinitely many solutions?
- Expand the left side: 6x + 15 = 6x + k.
- The x terms already match (6x on both sides). The equation is true for every x only if the constants match too.
- Answer: k = 15.
If k were any other number, the equation would have no solution: 6x + 15 can never equal 6x + 14, for example. Same x coefficient, same constant means infinitely many; same x coefficient, different constant means none.
Example 3: Linear function in context
A water tank holds 1,200 litres. It drains at a constant rate, and after 15 minutes it holds 900 litres. If V(t) is the volume in litres after t minutes, after how many minutes is the tank empty?
- Rate: (1,200 − 900) ÷ 15 = 20 litres per minute, draining.
- Function: V(t) = 1,200 − 20t. The 1,200 is the starting volume; −20 is the change in litres per minute.
- Empty means V(t) = 0: 1,200 − 20t = 0, so t = 60.
- Answer: 60 minutes.
Questions often ask what a number in the function “represents”. Answer with units: “the tank loses 20 litres each minute”, not just “the slope”.
Example 4: Line through two points
A line passes through the points (−2, 5) and (4, −7). What is the y-intercept of the line?
- Slope: (−7 − 5) ÷ (4 − (−2)) = −12 ÷ 6 = −2.
- Use one point: y − 5 = −2(x + 2), so y = −2x + 1.
- Check with the other point: −2(4) + 1 = −7.
- Answer: 1, so the line crosses the y-axis at (0, 1).
The trap: subtracting the coordinates in a different order on top and bottom, which flips the sign of the slope. Keep the same point first in both.
Example 5: System of equations by elimination
3x + 2y = 16 and 5x − 2y = 8. What is the value of x + y?
- The y terms are +2y and −2y, so add the equations: 8x = 24, so x = 3.
- Substitute into the first: 9 + 2y = 16, so y = 3.5.
- Check in the second: 5(3) − 2(3.5) = 15 − 7 = 8.
- Answer: x + y = 6.5.
The trap: stopping at x = 3. The question asks for x + y. On a student-produced response you would enter 6.5 (or 13/2).
Example 6: A system with no solution
In the system 2x − 5y = 7 and ax − 15y = 20, a is a constant. For what value of a does the system have no solution?
- No solution means the lines are parallel: same slope, different intercept.
- The y coefficient goes from −5 to −15, a factor of 3. For the same slope, the x coefficient must also scale by 3: a = 2 × 3 = 6.
- Check the constants: 3 × 7 = 21, not 20, so the lines are different. They never meet.
- Answer: a = 6.
If the second constant had been 21, the two equations would be the same line and the system would have infinitely many solutions.
Example 7: Linear inequality in context
A student has $150 to spend at a fair. Entry costs $18 and each ride costs $4.50. What is the greatest number of rides the student can take?
- “Has $150 to spend” means the total is at most 150: 18 + 4.5r ≤ 150.
- 4.5r ≤ 132, so r ≤ 29.33…
- Rides are whole numbers, and 30 rides would cost 18 + 135 = $153, over the limit.
- Answer: 29 rides (total $148.50).
The trap: rounding 29.33 to the nearest whole number without thinking. With a maximum, round down; with a minimum, round up.
Example 8: A system of inequalities
Which point (x, y) satisfies both y > 2x − 3 and y ≤ −x + 6?
A) (4, 3) B) (1, 2) C) (0, −4) D) (2, 5)
- A) 3 > 2(4) − 3 = 5? No.
- B) 2 > 2(1) − 3 = −1? Yes. 2 ≤ −1 + 6 = 5? Yes.
- C) −4 > 2(0) − 3 = −3? No.
- D) 5 > 2(2) − 3 = 1? Yes. 5 ≤ −2 + 6 = 4? No.
- Answer: B) (1, 2).
Testing the options is often the fastest route here. A point must pass both inequalities; D passes the first and fails the second.
Which SAT algebra mistakes cost the most marks?
- Answering a different quantity. Finding x when the question asks for x + y, 3x + 1 or the value of y (Example 5).
- Sign errors when expanding or subtracting. A minus sign in front of a bracket changes every term inside it.
- Mixing up “no solution” and “infinitely many”. Both need matching x coefficients (or slopes). Matching constants gives infinitely many; different constants give none (Examples 2 and 6).
- Forgetting to flip the inequality sign. Multiplying or dividing both sides by a negative number reverses < and >.
- Interpreting the slope without units. “What does 20 represent?” wants the rate in context: litres per minute, dollars per item.
- Rounding the wrong way in a scenario. “At most” rounds down; “at least” rounds up (Example 7).
How should you practise SAT algebra?
Algebra rewards speed built on accuracy. Aim to solve a standard linear equation or a two-equation system without hesitation, so the time you save goes to the harder questions at the end of each module.
- Work skill by skill first. Take the five College Board skills one at a time until you rarely miss a question in each, then move to mixed sets. Our SAT math practice page is sorted by domain.
- Learn the no-solution and infinitely-many patterns. They turn a long calculation into a 20-second comparison of coefficients.
- Keep an error log. For every miss, write which mistake from the list above caused it and redo the question a week later without the solution.
- See where Algebra fits. Our guide to the four SAT Math domains and the SAT math study guide cover Advanced Math, data analysis and geometry, and the Digital SAT exam overview explains the full test.
- Finish with timed tests. Take a full SAT practice test under real timing and convert your result with the SAT score calculator.
Not sure whether Algebra or another domain is holding your Math score back? Take the free SAT diagnostic test to see your weak areas by domain before you plan your practice. If you are applying to US universities, our admission counselling team can help you set a target SAT score for your college list.
Frequently Asked Questions
How many algebra questions are on the Digital SAT?
College Board lists 13 to 15 Algebra questions in the Math section, which has 44 questions in total across two 35-minute modules. That is roughly 30 to 34% of the Math section.
What topics are in SAT Algebra?
College Board names five skills: linear equations in one variable, linear functions, linear equations in two variables, systems of two linear equations in two variables, and linear inequalities in one or two variables.
Are quadratics part of SAT Algebra?
No. Quadratic, exponential, absolute value, polynomial and other nonlinear equations belong to the Advanced Math domain. The Algebra domain is entirely linear.
What is the difference between Algebra and Advanced Math on the SAT?
Algebra covers linear equations, linear functions, linear systems and linear inequalities. Advanced Math covers nonlinear functions and equations, systems that include a nonlinear equation, and equivalent expressions. Each domain has 13 to 15 questions.
Is SAT Algebra hard?
Most SAT Algebra questions use maths taught in early high school. Questions in each module run from easiest to hardest, so the harder Algebra questions tend to test the same skills in less familiar forms, such as finding a constant that gives a system no solution.
How do I know if a system of equations has no solution?
Write both equations in the same form and compare. If the x and y coefficients are in the same ratio but the constants are not, the lines are parallel and never meet, so there is no solution. If the constants are also in that ratio, the equations describe the same line and there are infinitely many solutions.
Should I use substitution or elimination on SAT systems?
Use elimination when one variable already has matching or opposite coefficients, as adding or subtracting the equations removes it in one step. Use substitution when one equation already gives a variable on its own, such as y = 3x − 2.
Do I have to type my own answer for SAT Algebra questions?
Sometimes. About 75% of SAT Math questions are four-option multiple choice and the rest are student-produced responses, where you enter your own answer. Algebra questions can be either format.
How long should I spend on each SAT Algebra question?
The Math section gives 70 minutes for 44 questions, about 95 seconds per question on average. Many Algebra questions can be done faster, which leaves more time for harder questions later in each module.
When do I flip the inequality sign?
Reverse the sign whenever you multiply or divide both sides of an inequality by a negative number. For example, −2x −3.
Are the examples on this page real SAT questions?
No. All eight examples were written by Galvanize for this page to match the Algebra skills College Board describes. For official questions, use the full-length practice tests in College Board’s Bluebook app.
How should I practise SAT Algebra?
Work the five skills one at a time until you rarely miss a question in each, then move to timed mixed sets. Keep an error log of every miss, note the mistake that caused it, and redo the question a week later without the solution.
