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Precalculus Practice Tests

These Grade 12 Math practice tests cover the algebraic and trigonometric foundations used in advanced mathematics, including functions, polynomial and rational behavior, exponential and logarithmic models, trigonometry, sequences, complex numbers, limits, derivatives, and integrals.

Skills covered

  • Analyzing function domains, ranges, inverses, transformations, compositions, and rates of change
  • Using polynomial factors, rational asymptotes, complex numbers, and binomial coefficients
  • Applying exponential, logarithmic, and trigonometric identities, periods, amplitudes, and conversions
  • Working with arithmetic and geometric sequences, series, and polar complex-number form
  • Evaluating introductory limits, derivatives, integrals, and motion models

How to use these practice tests

Identify the function family or algebraic structure first. Then select the relevant identity, theorem, formula, or graph feature and verify domain restrictions, signs, and units.

For more Grade 12 Math practice, return to the Grade 12 Math category.

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Grade 12 Precalculus Practice Tests

Practice Grade 12 Math questions about functions, polynomial and rational behavior, exponential and logarithmic models, trigonometry, sequences, complex numbers, limits, derivatives, integrals, and advanced algebra.

Choose the best answer. Identify the mathematical structure, apply the appropriate formula or theorem, and check domains, units, signs, and limiting behavior.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is the remainder when p(x)=x3−2x+5p(x)=x^3-2x+5 is divided by x-2?

Please select an answer first.

Correct answer: A

The correct answer is 9.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: By the Remainder Theorem, the remainder is p(2)=8-4+5=9.
  3. Check the result: The correct answer is 9.

By the Remainder Theorem, the remainder is p(2)=8-4+5=9.

2. QuestionMultiple choice

Which is a factorization of x2−9x^2-9?

Please select an answer first.

Correct answer: B

The correct answer is (x−3)(x+3)(x-3)(x+3).

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: This is a difference of squares: x^2-3^2=(x-3)(x+3).
  3. Check the result: The correct answer is (x−3)(x+3)(x-3)(x+3).

This is a difference of squares: x^2-3^2=(x-3)(x+3).

3. QuestionMultiple choice

What is the multiplicity of x=-1 in (x+1)3(x−4)2(x+1)^3(x-4)^2?

Please select an answer first.

Correct answer: C

The correct answer is 3.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: The exponent on the factor x+1 is 3.
  3. Check the result: The correct answer is 3.

The exponent on the factor x+1 is 3.

4. QuestionMultiple choice

What is the end behavior of f(x)=3x5−2x2+1f(x)=3x^5-2x^2+1?

Please select an answer first.

Correct answer: D

The correct answer is Left end down and right end up.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: An odd-degree polynomial with positive leading coefficient falls to the left and rises to the right.
  3. Check the result: The correct answer is Left end down and right end up.

An odd-degree polynomial with positive leading coefficient falls to the left and rises to the right.

5. QuestionMultiple choice

What is the vertical asymptote of f(x)=2x+1x−5f(x)=\frac{2x+1}{x-5}?

Please select an answer first.

Correct answer: A

The correct answer is x=5x=5.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: The denominator is zero at x=5 and no factor cancels.
  3. Check the result: The correct answer is x=5x=5.

The denominator is zero at x=5 and no factor cancels.

6. QuestionMultiple choice

What is the slant asymptote of x2+1x−1\frac{x^2+1}{x-1}?

Please select an answer first.

Correct answer: B

The correct answer is y=x+1y=x+1.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Polynomial division gives x^2+1=(x-1)(x+1)+2, so the quotient is y=x+1.
  3. Check the result: The correct answer is y=x+1y=x+1.

Polynomial division gives x^2+1=(x-1)(x+1)+2, so the quotient is y=x+1.

7. QuestionMultiple choice

Which equation describes a removable discontinuity?

Please select an answer first.

Correct answer: C

The correct answer is A common factor cancels but the original input remains excluded.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: A canceled factor creates a hole because the original rational expression was undefined at that input.
  3. Check the result: The correct answer is A common factor cancels but the original input remains excluded.

A canceled factor creates a hole because the original rational expression was undefined at that input.

8. QuestionMultiple choice

If x+2x+2 is a factor of p(x), what must be true?

Please select an answer first.

Correct answer: D

The correct answer is p(-2)=0.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: The Factor Theorem says x-r is a factor exactly when p(r)=0; here r=-2.
  3. Check the result: The correct answer is p(-2)=0.

The Factor Theorem says x-r is a factor exactly when p(r)=0; here r=-2.

9. QuestionMultiple choice

What is the solution set of x2−5x+6=0x^2-5x+6=0?

Please select an answer first.

Correct answer: A

The correct answer is x=2x=2 or x=3x=3.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Factor x^2-5x+6 as (x-2)(x-3).
  3. Check the result: The correct answer is x=2x=2 or x=3x=3.

Factor x^2-5x+6 as (x-2)(x-3).

10. QuestionMultiple choice

What is the complex conjugate of 4−7i4-7i?

Please select an answer first.

Correct answer: B

The correct answer is 4+7i4+7i.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: The conjugate keeps the real part and changes the sign of the imaginary part.
  3. Check the result: The correct answer is 4+7i4+7i.

The conjugate keeps the real part and changes the sign of the imaginary part.

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