A gym charges a $35 sign-up fee plus $22 a month. Kiona has paid $255 in all. For how many months has she paid?Common Core State Standards for Mathematics, HSA-CED.A.1: create equations and inequalities in one variable and use them to solve problems
The perimeter of a rectangle is P = 2l + 2w. Which equation gives the width w?Common Core State Standards for Mathematics, HSA-CED.A.4: rearrange formulas to highlight a quantity of interest
Solve for x: 2(3x + 1) − 4x = 18Common Core State Standards for Mathematics, HSA-REI.B.3: solve linear equations and inequalities in one variable
Solve for x: 3x + 8 = 35Common Core State Standards for Mathematics, HSA-REI.B.3: solve linear equations and inequalities in one variable
Solve for x: 4(x − 3) = 2x + 10Common Core State Standards for Mathematics, HSA-REI.B.3: solve linear equations and inequalities in one variable
Solve for x: 7x − 9 = 3x + 19Common Core State Standards for Mathematics, HSA-REI.B.3: solve linear equations and inequalities in one variable
Solve for x: x/4 + 6 = 9Common Core State Standards for Mathematics, HSA-REI.B.3: solve linear equations and inequalities in one variable
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Linear Equations and Inequalities, continued
Solve px − q = r for x, where p is not 0.Common Core State Standards for Mathematics, HSA-REI.B.3: solve linear equations and inequalities in one variable
Solve the inequality: 3x − 5 > 16Common Core State Standards for Mathematics, HSA-REI.B.3: solve linear equations and inequalities in one variable
Solve the inequality: −2x + 3 ≤ 11Common Core State Standards for Mathematics, HSA-REI.B.3: solve linear equations and inequalities in one variable
Tavita has $60 to spend at a fair. Admission is $12 and each ride costs $4. What is the greatest number of rides he can take?Common Core State Standards for Mathematics, HSA-CED.A.1: create equations and inequalities in one variable and use them to solve problems
What is the slope of the line 6x + 2y = 14?Common Core State Standards for Mathematics, HSA-CED.A.2: create equations in two or more variables to represent relationships between quantities
Which equation is the line through the points (2, 5) and (6, 13)?Common Core State Standards for Mathematics, HSA-CED.A.2: create equations in two or more variables to represent relationships between quantities
Systems of Equations 9
Adult tickets to a play cost $9 and student tickets cost $5. A club sells 70 tickets for $430 in all. How many adult tickets did it sell?Common Core State Standards for Mathematics, HSA-CED.A.3: represent constraints by equations or inequalities, and by systems
How many solutions does the system x + 2y = 6 and 3x + 6y = 18 have?Common Core State Standards for Mathematics, HSA-REI.C.6: solve systems of linear equations exactly and approximately
How many solutions does the system y = 4x − 3 and y = 4x + 6 have?Common Core State Standards for Mathematics, HSA-REI.C.6: solve systems of linear equations exactly and approximately
In the system x + y = 20 and x = 3y, what is the value of x?Common Core State Standards for Mathematics, HSA-REI.C.6: solve systems of linear equations exactly and approximately
Solve the system: 2x + 3y = 19 and 2x − y = 7Common Core State Standards for Mathematics, HSA-REI.C.6: solve systems of linear equations exactly and approximately
Solve the system: 3x + 2y = 16 and 5x − 4y = 12Common Core State Standards for Mathematics, HSA-REI.C.6: solve systems of linear equations exactly and approximately
Solve the system: y = 2x + 1 and y = −x + 10Common Core State Standards for Mathematics, HSA-REI.C.6: solve systems of linear equations exactly and approximately
Two numbers have a sum of 41 and a difference of 13. What is the larger number?Common Core State Standards for Mathematics, HSA-REI.C.6: solve systems of linear equations exactly and approximately
Which point is a solution of both y > x + 1 and y < −x + 9?Common Core State Standards for Mathematics, HSA-REI.D.12: graph the solutions to a linear inequality and to a system of linear inequalities
Functions and Sequences 14
A culture starts with 500 bacteria and doubles every hour, so P(t) = 500 × 2 to the power t. What is P(4)?Common Core State Standards for Mathematics, HSF-LE.A.2: construct linear and exponential functions given a description, a graph or input-output pairs
A function is defined by f(1) = 4 and f(n) = f(n − 1) + 6. What is f(5)?Common Core State Standards for Mathematics, HSF-IF.A.3: sequences are functions, sometimes defined recursively
A geometric sequence begins 3, 6, 12, 24. What is its 8th term?Common Core State Standards for Mathematics, HSF-BF.A.2: write arithmetic and geometric sequences both recursively and with an explicit formula
A phone plan costs C(m) = 0.25m + 40 dollars in a month with m minutes of calls. What does the 40 represent?Common Core State Standards for Mathematics, HSF-LE.B.5: interpret the parameters in a linear or exponential function in terms of a context
A table has x-values 0, 2, 4, 6 and y-values 3, 11, 19, 27. Which function fits every row?Common Core State Standards for Mathematics, HSF-LE.A.2: construct linear and exponential functions given a description, a graph or input-output pairs
An arithmetic sequence begins 7, 12, 17, 22. What is its 20th term?Common Core State Standards for Mathematics, HSF-BF.A.2: write arithmetic and geometric sequences both recursively and with an explicit formula
Each set below pairs an input x with an output y. Which set is a function of x?Common Core State Standards for Mathematics, HSF-IF.A.1: a function assigns to each element of the domain exactly one element of the range
For real numbers, what is the smallest value of x in the domain of f(x) = √(x − 6)?Common Core State Standards for Mathematics, HSF-IF.B.5: relate the domain of a function to its graph and to the relationship it describes
The function h(t) = 50 − 8t gives the liters of water left in a tank after t minutes. What does h(3) = 26 mean?Common Core State Standards for Mathematics, HSF-IF.A.2: use function notation, evaluate functions and interpret statements that use function notation
If f(x) = 4x − 7, what is f(5)?Common Core State Standards for Mathematics, HSF-IF.A.2: use function notation, evaluate functions and interpret statements that use function notation
If g(x) = x² − 3x, what is g(−2)?Common Core State Standards for Mathematics, HSF-IF.A.2: use function notation, evaluate functions and interpret statements that use function notation
What is the average rate of change of f(x) = x² + 3 from x = 2 to x = 5?Common Core State Standards for Mathematics, HSF-IF.B.6: calculate and interpret the average rate of change of a function over a specified interval
Which explicit formula gives the sequence 10, 7, 4, 1, where n = 1 is the first term?Common Core State Standards for Mathematics, HSF-BF.A.2: write arithmetic and geometric sequences both recursively and with an explicit formula
Which situation is modeled by an exponential function and not a linear one?Common Core State Standards for Mathematics, HSF-LE.A.1: distinguish between situations that can be modeled with linear functions and with exponential functions
Exponents and Radicals 12
A car worth $20,000 loses 10% of its value each year, so V = 20,000 × 0.9 to the power t. What is it worth after 2 years?Common Core State Standards for Mathematics, HSF-IF.C.8.b: use the properties of exponents to interpret expressions for exponential functions
One of these sums is an irrational number. Which one?Common Core State Standards for Mathematics, HSN-RN.B.3: the sum of a rational number and an irrational number is irrational
Simplify: (3a²)³Common Core State Standards for Mathematics, HSA-SSE.A.2: use the structure of an expression to identify ways to rewrite it
Simplify: (3x²y)(4x³y⁵)Common Core State Standards for Mathematics, HSA-SSE.A.2: use the structure of an expression to identify ways to rewrite it
Simplify: x⁴ · x⁷Common Core State Standards for Mathematics, HSA-SSE.A.2: use the structure of an expression to identify ways to rewrite it
Simplify: y¹⁰ ÷ y⁴, where y is not 0Common Core State Standards for Mathematics, HSA-SSE.A.2: use the structure of an expression to identify ways to rewrite it
Simplify: √75 + √12Common Core State Standards for Mathematics, HSN-RN.A.2: rewrite expressions involving radicals and rational exponents using the properties of exponents
What is the value of 2⁻⁵?Common Core State Standards for Mathematics, HSN-RN.A.1: the meaning of rational exponents follows from the properties of integer exponents
What is the value of 16 to the power 3/2?Common Core State Standards for Mathematics, HSN-RN.A.2: rewrite expressions involving radicals and rational exponents using the properties of exponents
What is the value of 27 to the power 1/3?Common Core State Standards for Mathematics, HSN-RN.A.1: the meaning of rational exponents follows from the properties of integer exponents
Which expression equals the cube root of x², for x greater than 0?Common Core State Standards for Mathematics, HSN-RN.A.2: rewrite expressions involving radicals and rational exponents using the properties of exponents
Write √72 in simplest radical form.Common Core State Standards for Mathematics, HSN-RN.A.2: rewrite expressions involving radicals and rational exponents using the properties of exponents
Polynomials and Quadratics 15
A ball is thrown up from the ground. Its height in meters after t seconds is h = −5t² + 20t. After how many seconds does it return to the ground?Common Core State Standards for Mathematics, HSA-CED.A.1: create equations and inequalities in one variable and use them to solve problems
Add: (3x² + 5x − 2) + (x² − 7x + 6)Common Core State Standards for Mathematics, HSA-APR.A.1: add, subtract, and multiply polynomials
Expand: (2x − 5)²Common Core State Standards for Mathematics, HSA-APR.A.1: add, subtract, and multiply polynomials
Factor: 2x² + 7x + 3Common Core State Standards for Mathematics, HSA-SSE.B.3.a: factor a quadratic expression to reveal the zeros of the function it defines
Factor: x² + 9x + 20Common Core State Standards for Mathematics, HSA-SSE.B.3.a: factor a quadratic expression to reveal the zeros of the function it defines
Factor: x² − 49Common Core State Standards for Mathematics, HSA-SSE.A.2: use the structure of an expression to identify ways to rewrite it
Multiply: (x + 6)(x − 4)Common Core State Standards for Mathematics, HSA-APR.A.1: add, subtract, and multiply polynomials
Solve: 3x² − 12 = 0Common Core State Standards for Mathematics, HSA-REI.B.4.b: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring
Solve: x² = 169Common Core State Standards for Mathematics, HSA-REI.B.4.b: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring
Solve: x² − 3x − 28 = 0Common Core State Standards for Mathematics, HSA-REI.B.4.b: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring
Subtract: (5x² − x + 4) − (2x² + 3x − 1)Common Core State Standards for Mathematics, HSA-APR.A.1: add, subtract, and multiply polynomials
Use the quadratic formula to solve x² + 4x − 1 = 0.Common Core State Standards for Mathematics, HSA-REI.B.4.b: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring
What are the zeros of f(x) = (x − 4)(x + 9)?Common Core State Standards for Mathematics, HSA-SSE.B.3.a: factor a quadratic expression to reveal the zeros of the function it defines
What is the minimum value of y = x² − 6x + 11?Common Core State Standards for Mathematics, HSA-SSE.B.3.b: complete the square in a quadratic expression to reveal the maximum or minimum value
Which number completes the square in x² + 10x + ___ ?Common Core State Standards for Mathematics, HSA-REI.B.4.a: use the method of completing the square
Statistics 10
A line of fit for the height of a plant is h = 1.8d + 6, where h is centimeters and d is days. What height does it predict on day 15?Common Core State Standards for Mathematics, HSS-ID.B.6.a: use functions fitted to data to solve problems in the context of the data
A line of fit predicts a test score y from hours of study x: y = 2.5x + 40. What does the 2.5 mean?Common Core State Standards for Mathematics, HSS-ID.C.7: interpret the slope and the intercept of a linear model in the context of the data
Five students score 12, 15, 9, 20 and 14 on a quiz. What is the mean score?Common Core State Standards for Mathematics, HSS-ID.A.2: compare center (median, mean) and spread (interquartile range, standard deviation) of data sets
Five workers earn 30, 32, 35, 36 and 37 thousand dollars. A sixth earns 150 thousand. Which measure changes least when the sixth is included?Common Core State Standards for Mathematics, HSS-ID.A.3: interpret differences in shape, center, and spread, accounting for possible effects of outliers
Four scatter plots have the correlation coefficients below. Which plot shows the strongest linear relationship?Common Core State Standards for Mathematics, HSS-ID.C.8: compute and interpret the correlation coefficient of a linear fit
In a set of towns, months with more ice cream sales also have more sunburn cases. Which conclusion do the data support?Common Core State Standards for Mathematics, HSS-ID.C.9: distinguish between correlation and causation
Of 40 ninth graders, 24 play a sport. Of those 24, 15 also play an instrument. What fraction of the students who play a sport also play an instrument?Common Core State Standards for Mathematics, HSS-ID.B.5: summarize categorical data in two-way frequency tables and interpret relative frequencies
Set A is 10, 10, 10, 10 and set B is 4, 8, 12, 16. Both have a mean of 10. Which set has the larger standard deviation?Common Core State Standards for Mathematics, HSS-ID.A.2: compare center (median, mean) and spread (interquartile range, standard deviation) of data sets
What is the interquartile range of 2, 4, 5, 7, 8, 10 and 13?Common Core State Standards for Mathematics, HSS-ID.A.2: compare center (median, mean) and spread (interquartile range, standard deviation) of data sets
What is the median of 3, 18, 7, 12, 9 and 15?Common Core State Standards for Mathematics, HSS-ID.A.2: compare center (median, mean) and spread (interquartile range, standard deviation) of data sets
How this list was compiled: Our own questions. Outline: the Common Core State Standards for Mathematics, high school: Algebra, https://www.thecorestandards.org/Math/Content/HSA/introduction/, with the domain pages Seeing Structure in Expressions (HSA/SSE), Arithmetic with Polynomials (HSA/APR), Creating Equations (HSA/CED), Reasoning with Equations and Inequalities (HSA/REI), Interpreting Functions (HSF/IF), Building Functions (HSF/BF), Linear, Quadratic and Exponential Models (HSF/LE), The Real Number System (HSN/RN) and Interpreting Categorical and Quantitative Data (HSS/ID), and the note on courses and transitions, read 2026-10-10. Each question names the standard it practices and links to that domain page. Every answer is arithmetic or algebra on the numbers the question prints, and each one was worked out again on 2026-10-10. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a state test, a released form, a sample item, a textbook or another practice test.
How it works
Unofficial ninth grade math practice: 73 questions written for this page to the high school algebra, functions and statistics standards of the Common Core. No state's test is copied or followed, so no test length or pass mark is implied.
Read the full guide
What the 73 questions cover
Linear equations and inequalities has 13 questions, systems of equations 9, functions and sequences 14, exponents and radicals 12, polynomials and quadratics 15, and statistics 10.
Ninth grade math is not one course
The standards list high school math by subject, not by grade, and do not set the order of courses. These questions are first-year algebra with the functions and statistics taught beside it. A class that took Algebra I in grade 8, or follows an integrated sequence, will meet some of them in another year.
When you multiply or divide an inequality by a negative number, reverse the sign.
Check a solution in the original equation, not in a later step.
An equation such as x² = 49 has two solutions, 7 and −7.
Questions and answers
Is there a free 9th grade math practice test online?
Yes. All 73 questions run on this page with no sign-up, and a scored quiz draws 25 of them. Your answers stay in this browser.
What math do 9th graders take?
It depends on the school. The Common Core sets high school standards by subject and does not fix the order of courses. It describes a traditional sequence, Algebra I, Geometry and Algebra II, and an integrated one, Mathematics 1, 2 and 3.
Can I print a math practice test for 9th grade?
Yes. The questions print as a paper test, with an answer key if you want one. Choose Save as PDF in the print window to keep the file.