• 120 questions

College Algebra Final Exam Practice

Unofficial review questions on the six chapters a one-term college algebra course ends on, each worked out.

Solve |x + 4| < 3.

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Unofficial practice questions, not affiliated with any college or university. Bank checked October 9, 2026.

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All 120 questions

Equations and inequalities 22

  • A rectangle is 3 meters longer than it is wide, and its area is 54 square meters. How wide is it? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Completing the square turns x² + 6x − 2 = 0 into (x + 3)² = k. What is k? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • The product of two consecutive positive even integers is 168. What is the smaller one? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve (x − 1)^(3/2) = 8. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
Show all 120 questions (116 more)

Equations and inequalities, continued

  • Solve 1/x + 1/4 = 1/3. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve 2/(x − 1) = 3/(x + 2). Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve 2x(x − 3) = x − 3. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve 2x² − 7x + 3 = 0. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve x/(x − 3) = 3/(x − 3) + 2. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve x² + 2x + 5 = 0 over the complex numbers. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 4: evaluate all roots of higher degree polynomial and rational functions
  • Solve x² − 2x − 8 < 0. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve x² − 4x − 21 = 0. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve x² − 8x + 13 = 0. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve x² ≥ 25. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve x⁴ − 5x² + 4 = 0. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 4: evaluate all roots of higher degree polynomial and rational functions
  • Solve |2x − 3| = 7. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve |3x − 1| ≥ 5. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve |x + 4| < 3. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve −5 ≤ 3 − 2x < 9. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve √(3x + 4) = x. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve √(x + 5) = 4. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • What is the discriminant of 3x² − 5x + 4 = 0? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations

Functions and their graphs 24

  • A linear function has f(2) = 5 and f(6) = 17. What is f(10)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • A one-to-one function has f(3) = 7 and f(7) = 12. What is f⁻¹(7)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • A piecewise function is f(x) = x + 5 when x < 0 and f(x) = x² when x ≥ 0. What is f(−2) + f(3)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • For f(x) = x² + 3x, simplify the difference quotient (f(x + h) − f(x))/h. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • The graph of y = √x is stretched vertically by a factor of 3 and moved down 2. Which function is the result? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • The graph shows a quadratic function. What is its range? (Picture: A coordinate grid from −5 to 5 with a curve shaped like an upside-down U. It crosses the x-axis at −1 and at 3 and crosses the y-axis at 3.) Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • How is the graph of g(x) = (x − 3)² + 2 moved from the graph of f(x) = x²? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • If f(x) = 2x − 3 and g(x) = x² + 1, what is (f + g)(2)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • If f(x) = 3x + 1 and g(x) = x², what is (f ∘ g)(x)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • If f(x) = x + 2 and g(x) = x − 5, what is (fg)(x)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • If f(x) = x − 4 and g(x) = x², what is (g ∘ f)(2)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • What is the average rate of change of f(x) = x³ − x from x = 1 to x = 3? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • What is the distance between the points (−1, 2) and (5, 10)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • What is the domain of f(x) = 1/(x² − 9)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • What is the domain of f(x) = √(2x − 8)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • What is the inverse of f(x) = (2x + 1)/(x − 3)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • What is the inverse of f(x) = 2x − 6? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • What is the inverse of f(x) = x³ + 4? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • What is the maximum value of f(x) = −x² + 6x + 1? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • What is the range of f(x) = x² + 4? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • What is the vertex of the graph of f(x) = −2x² + 8x − 3? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • Which function is the graph of y = |x| moved left 4 and then reflected in the x-axis? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • Which of these functions is even? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • Which of these functions is odd? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses

Polynomial and rational functions 24

  • A polynomial with real coefficients has the zero 4 − 3i. Which number must also be a zero? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 4: evaluate all roots of higher degree polynomial and rational functions
  • As x grows without bound to the right, what does f(x) = −2x⁴ + 3x³ − 1 approach? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • Between which two integers does f(x) = x³ + x − 3 have a zero? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 4: evaluate all roots of higher degree polynomial and rational functions
  • By the rational zero theorem, which number cannot be a rational zero of f(x) = 2x³ − 5x² + x + 6? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 4: evaluate all roots of higher degree polynomial and rational functions
  • Divide x³ + 2x² − 5x − 6 by x + 1. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 4: evaluate all roots of higher degree polynomial and rational functions
  • The graph of f(x) = (x² − 9)/(x − 3) has a hole. Where is it? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • Multiply (3 + 2i)(1 − 4i). Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 4: evaluate all roots of higher degree polynomial and rational functions
  • Simplify (x² − 4)/(x² + 5x + 6). Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve (x + 3)/(x − 2) ≤ 0. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve (x − 1)(x + 2)(x − 4) > 0. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • What are all the zeros of f(x) = x³ − 3x² + 4x − 12? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 4: evaluate all roots of higher degree polynomial and rational functions
  • What are the zeros of f(x) = x³ − 4x? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 4: evaluate all roots of higher degree polynomial and rational functions
  • What is the degree of f(x) = 4x³ − 7x⁵ + 2x − 9? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • What is the domain of f(x) = (x − 2)/(x² − x − 6)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • What is the greatest number of turning points the graph of a polynomial of degree 5 can have? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • What is the horizontal asymptote of f(x) = (2x + 7)/(x² − 4)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • What is the horizontal asymptote of f(x) = (3x² − 1)/(x² + 5)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • What is the multiplicity of the zero x = 1 of f(x) = (x − 1)²(x + 3)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 4: evaluate all roots of higher degree polynomial and rational functions
  • What is the remainder when x³ − 3x² + 5x − 4 is divided by x − 2? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 4: evaluate all roots of higher degree polynomial and rational functions
  • What is the slant asymptote of f(x) = (x² + 3x + 1)/(x − 1)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • What is the vertical asymptote of f(x) = (x + 1)/(x − 4)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • What is the x-intercept of f(x) = (2x − 6)/(x + 1)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • Which of these is a factor of x³ − 7x + 6? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 4: evaluate all roots of higher degree polynomial and rational functions
  • Which polynomial has leading coefficient 1 and zeros 2 and −5 only? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 4: evaluate all roots of higher degree polynomial and rational functions

Exponential and logarithmic functions 24

  • $2,000 is invested at 5% interest compounded once a year. What is it worth after 2 years? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • A culture starts with 500 bacteria and doubles every 3 hours. How many are there after 12 hours? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • A sample of 80 grams has a half-life of 6 years. How much is left after 18 years? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Evaluate ln(e⁴). Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Evaluate log(1000), the common logarithm. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Evaluate log₂(32). Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Evaluate log₃(1/9). Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Evaluate log₄(32). Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Expand log(x²y). Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve 2 ln(x) = ln(49). Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve 2^(x + 1) = 16. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve 3^x = 81. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve 4^x = 8. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve 5^(2x) = 125. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve e^(2x) = 7 exactly. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve log(x − 1) = 2. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve log₂(x) = 6. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Solve log₃(x) + log₃(x − 2) = 1. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • What is the domain of f(x) = log(x + 6)? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 1: properties of functions, including domain and range, operations, compositions and inverses
  • What is the horizontal asymptote of f(x) = 2^x + 3? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • Where does the graph of f(x) = 3 · 2^x − 1 cross the y-axis? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 3: apply graphing techniques
  • Which function gives the value after t years of $1,000 growing at 4% a year, compounded continuously? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Which statement is 2⁵ = 32 written in logarithmic form? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Write log₂(x) − 3 log₂(y) as a single logarithm. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations

Systems of equations and matrices 16

  • A has rows [1 2] and [3 4]. B has rows [0 1] and [1 0]. What are the rows of the product AB? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • A has rows [1 −2] and [0 5]. B has rows [3 4] and [−1 2]. What are the rows of A + B? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • A is a 2 × 3 matrix and B is a 3 × 4 matrix. What is the size of the product AB? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • A lab mixes a 10% acid solution with a 30% acid solution to make 20 liters of a 25% solution. How many liters of the 30% solution are needed? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • A matrix has rows [1 2 | 5] and [3 −1 | 4]. Which row replaces row 2 after the operation R2 − 3R1? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • For the system 3x + 2y = 8 and x − y = 1, what is the determinant of the coefficient matrix? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • For which value of k does the matrix with rows [k 6] and [2 3] have no inverse? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • How many solutions does the system x − 2y = 4 and −3x + 6y = −12 have? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • Row reduction of a system in x and y ends with the rows [1 0 | 4] and [0 1 | −2]. What is the solution? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • Row reduction of a system in x and y ends with the rows [1 2 | 3] and [0 0 | 5]. How many solutions does the system have? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • Solve the system 2x + y = 7 and x − 3y = −7. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • Solve the system x + y + z = 6, 2x − y + z = 3 and x + 2y − z = 2. Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • What is the determinant of the matrix with rows [3 5] and [2 4]? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • What is the inverse of the matrix with rows [2 1] and [5 3]? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices
  • Where do the graphs of y = x² and y = x + 2 meet? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 2: polynomial, rational, radical, exponential and logarithmic functions and related equations
  • Which augmented matrix, written row by row, represents the system 2x − y = 5 and x + 4y = −3? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, learning outcome 5: recognize, solve and apply systems of linear equations using matrices

Sequences and series 10

  • A sequence starts at 2, and each later term is 3 times the term before it, minus 1. What is the 4th term? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, course description: additional topics such as sequences and series may be included
  • An arithmetic sequence has first term 7 and fifth term 27. What is its common difference? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, course description: additional topics such as sequences and series may be included
  • What is the 7th term of the geometric sequence 5, 10, 20, …? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, course description: additional topics such as sequences and series may be included
  • What is the 20th term of the arithmetic sequence 5, 8, 11, …? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, course description: additional topics such as sequences and series may be included
  • What is the common ratio of the geometric sequence 81, 27, 9, …? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, course description: additional topics such as sequences and series may be included
  • What is the sum of 2k + 1 for k = 1, 2, 3 and 4? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, course description: additional topics such as sequences and series may be included
  • What is the sum of the first 5 terms of the geometric sequence 2, 6, 18, …? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, course description: additional topics such as sequences and series may be included
  • What is the sum of the first 30 terms of the arithmetic sequence 2, 6, 10, …? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, course description: additional topics such as sequences and series may be included
  • What is the sum of the infinite geometric series 12 + 6 + 3 + …? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, course description: additional topics such as sequences and series may be included
  • Which formula gives the nth term of the arithmetic sequence 4, 9, 14, …? Texas Higher Education Coordinating Board, Lower-Division Academic Course Guide Manual, Spring 2021, MATH 1314 College Algebra, course description: additional topics such as sequences and series may be included

How this list was compiled: Our own questions, written to the Texas Higher Education Coordinating Board's published course description and five learning outcomes for MATH 1314 College Algebra, page 163 of the Lower-Division Academic Course Guide Manual, Spring 2021 (https://reportcenter.highered.texas.gov/training-materials/lower-division-academic-course-guide-spring-21/, read 2026-10-09). Each question names the outcome it practices. Every answer is algebra or arithmetic on what the question prints, worked out a second time on 2026-10-09. Licence: Own work. Questions, answer choices, explanations and the graph were written and drawn for this site. Nothing is copied or reworded from a college final, a placement or credit exam, a textbook or another practice test.

How it works

This free college algebra practice test has 120 questions of our own across the chapters a one-term course covers, each with its working. It is unofficial: every college writes its own final exam, and this page copies none.

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Where the chapters come from

This bank follows the Texas Higher Education Coordinating Board's course description of College Algebra (MATH 1314), read October 9, 2026. Sequences and series are topics it says a college may add. So are probability and conics, which are left out here.

Six chapters

Equations and inequalities (22 questions), functions and graphs (24), polynomial and rational functions (24), exponential and logarithmic functions (24), systems and matrices (16), sequences and series (10). The split is ours. Exam mode draws 25 across all six, like a cumulative final.

How the math is written

Integer powers are written x² or x⁻¹; other exponents use a caret, as in 2^x. log alone is base 10, i is the imaginary unit, and a matrix is written row by row.

  • After solving a radical or rational equation, put each answer back into the original; some will not work.
  • A logarithm takes only positive inputs, so reject any solution that makes one zero or negative.

Questions and answers

What is on a college algebra final exam?

Each college writes its own, so your syllabus is the real list. A state course description, such as Texas's for MATH 1314, names functions and their inverses, polynomial, rational, radical, exponential and logarithmic functions, and systems of linear equations solved with matrices.

Are these real college algebra test questions?

No. Each of the 120 college algebra practice questions was written for this page from a public course description. None comes from a college's final, a placement or credit exam, or a textbook, and a score here predicts no grade.

Can I use this as a college algebra quiz on one chapter?

Yes. Each chapter can be answered alone, ten college algebra questions at a time, with the working shown after every answer.

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