100+ Free Math 30-1 Practice Questions

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A polynomial function has zeros at x = -2, x = 1, and x = 3, each of multiplicity 1. What is the minimum degree of the polynomial?

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Key Facts: Math 30-1 Exam

Math 30-1 is Alberta's Grade 12 pre-calculus diploma exam: 32 machine-scored (75%) + 3 written-response (25%) questions in 3 hours, worth 30% of the final course mark.

Sample Math 30-1 Practice Questions

Try these sample questions to test your Math 30-1 exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Evaluate log_2(32).

A.4

B.6

C.5

D.16

Explanation: log_2(32) asks for the exponent x such that 2^x = 32. Since 2^5 = 32, the value is 5.

2Express log_b(M) + log_b(N) as a single logarithm.

A.log_b(M + N)

B.log_b(MN)

C.log_b(M/N)

D.log_b(M) · log_b(N)

Explanation: The product law of logarithms states log_b(M) + log_b(N) = log_b(MN). Adding logarithms with the same base corresponds to multiplying their arguments.

3Solve for x: 3^x = 81.

A.3

B.27

C.9

D.4

Explanation: Write 81 as a power of 3: 81 = 3^4. Since the bases are equal, the exponents must be equal, so x = 4.

4Which expression is equivalent to log(x^3)?

A.log(x)/3

B.3 log(x)

C.(log x)^3

D.log(3x)

Explanation: The power law of logarithms states log(x^n) = n·log(x). Therefore log(x^3) = 3 log(x).

5What is the value of log_5(1)?

A.1

B.0

C.5

D.undefined

Explanation: For any positive base b not equal to 1, log_b(1) = 0 because b^0 = 1. Thus log_5(1) = 0.

6Rewrite the logarithmic equation log_4(x) = 3 in exponential form.

A.x = 3^4

B.x = 4/3

C.x = 4^3

D.3 = x^4

Explanation: The definition of a logarithm states log_b(x) = y is equivalent to x = b^y. Here b = 4 and y = 3, so x = 4^3 = 64.

7Solve for x: log_2(x) = 5.

A.10

B.32

C.25

D.7

Explanation: Convert to exponential form: x = 2^5 = 32. Therefore x = 32.

8The expression log_b(M) - log_b(N) is equivalent to which of the following?

A.log_b(M - N)

B.log_b(MN)

C.log_b(M/N)

D.log_b(N/M)

Explanation: The quotient law of logarithms states log_b(M) - log_b(N) = log_b(M/N). Subtraction of logs corresponds to division of the arguments.

9A radioactive substance has a half-life of 8 hours. If the initial mass is 200 g, which equation models the mass M after t hours?

A.M = 200(2)^(t/8)

B.M = 200(1/2)^(8t)

C.M = 200(8)^(t/2)

D.M = 200(1/2)^(t/8)

Explanation: Half-life decay uses M = M_0(1/2)^(t/h), where h is the half-life. With M_0 = 200 and h = 8, the model is M = 200(1/2)^(t/8).

10Solve for x: log(x) + log(x - 3) = 1, where log denotes base 10.

A.x = -2

B.x = 5 or x = -2

C.x = 5

D.x = 10

Explanation: Combine using the product law: log[x(x-3)] = 1, so x(x-3) = 10. This gives x^2 - 3x - 10 = 0, factoring to (x-5)(x+2) = 0. Only x = 5 is valid; x = -2 makes the arguments negative, which is rejected.

About the Math 30-1 Exam

The Mathematics 30-1 Diploma Examination is a Grade 12 provincial standardized exam set by Alberta Education and Childcare for the Math 30-1 pre-calculus course, the stream required for post-secondary programs involving calculus. The digital exam consists of 32 machine-scored questions worth 75% and 3 equally-weighted written-response questions worth 25%, completed in 3 hours with up to 3 additional hours available. The paper format machine-scored component is 24 multiple-choice and 8 numerical-response questions. Content is drawn from Relations and Functions (53-58%), Trigonometry (27-33%), and Permutations, Combinations and Binomial Theorem (14-18%). The diploma result counts for 30% of the final course grade, with the remaining 70% from school-awarded marks. A formula sheet and one approved calculator are permitted.

Questions

100 scored questions

Time Limit

3 hours (extendable to 6 hours)

Passing Score

Diploma exam counts 30% of the final course mark; acceptable standard 50%, standard of excellence 80%

Exam Fee

Free for first-time writers via school; rewriters and non-funded international students pay a rewrite fee through myPass.alberta.ca (Alberta Education and Childcare (Government of Alberta), Provincial Assessment Sector)

Math 30-1 Exam Content Outline

53%-58%

Relations and Functions

Transformations, inverses, polynomial, radical and rational functions, function operations and composition, and exponential and logarithmic functions and equations including the laws of logarithms.

27%-33%

Trigonometry

Angles in standard position, degrees and radians, the unit circle, the six trigonometric ratios, trigonometric equations and identities, and graphing trigonometric functions.

14%-18%

Permutations, Combinations, and Binomial Theorem

Fundamental counting principle, factorial notation, permutations and combinations, and the binomial theorem.

How to Pass the Math 30-1 Exam

What You Need to Know

Passing score: Diploma exam counts 30% of the final course mark; acceptable standard 50%, standard of excellence 80%
Exam length: 100 questions
Time limit: 3 hours (extendable to 6 hours)
Exam fee: Free for first-time writers via school; rewriters and non-funded international students pay a rewrite fee through myPass.alberta.ca

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

Math 30-1 Study Tips from Top Performers

1Master the laws of logarithms and the relationship between exponential and logarithmic forms early, since Relations and Functions is the largest topic at 53-58%.

2Memorize the unit circle exact values and reference-angle rules in both degrees and radians to handle trigonometry quickly.

3Practice numerical-response items separately, recording answers precisely, since these are machine-scored with a limited range of accepted values.

4Distinguish permutations (order matters) from combinations (order does not) using the fundamental counting principle and factorial notation.

5Always check logarithmic and radical solutions for extraneous roots caused by domain restrictions.

6Use the official Alberta formula sheet during practice so you know exactly what is and is not provided.

7Review past released diploma exams and the Assessment Standards and Exemplars document to match the real question style.

Frequently Asked Questions

How is the Math 30-1 diploma exam weighted in my final grade?

The diploma exam counts for 30% of your final course mark, with the other 70% coming from your school-awarded mark. The 30% weighting returned effective September 1, 2023.

What is the format of the Math 30-1 diploma exam?

The digital exam has 32 machine-scored questions (75%) and 3 equally-weighted written-response questions (25%). The paper version's machine-scored component is 24 multiple-choice and 8 numerical-response questions. You get 3 hours with up to 3 additional hours if needed.

What is the difference between Math 30-1 and Math 30-2?

Math 30-1 is the pre-calculus stream required for STEM and university programs that involve calculus, covering relations and functions, trigonometry, and permutations/combinations. Math 30-2 is a different applied stream covering logical reasoning, probability, and relations and functions.

What are the acceptable and excellence standards?

The acceptable standard corresponds to a final course mark of 50% to 79%, while the standard of excellence corresponds to 80% or higher. The exam is designed so acceptable-standard students score at least 50% and excellence-standard students score at least 80%.

Can I use a calculator and formula sheet?

Yes. One approved graphing calculator and a formula sheet are permitted. In the digital format the formula sheet is accessible through the Resources icon, and a paper formula sheet is also allowed.

Is there a fee to write the Math 30-1 diploma exam?

First-time writers are registered free through their school. Rewriters and non-funded international students must register and pay a rewrite fee in advance through myPass.alberta.ca.

100+ Free Math 30-1 Practice Questions

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