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PreCal 9.1/9.3 Quiz Review - Printable Math Worksheets 12th Grade - Wayground

PreCal 9.1/9.3 Quiz Review

Khaliah Jones

Created by Khaliah Jones

20 questions

12th Grade

Math

Updated Jun 2026

PreCal 9.1/9.3 Quiz Review is a Grade 12 mathematics worksheet for reviewing fundamental counting and probability skills. Its 20 mixed-format questions ask students to calculate arrangements, identify when to use permutations, combinations, or factorials, apply the Multiplication Principle of Counting, and interpret equivalent factorial and combination expressions. Students also solve counting problems involving roles, committees, teams, cards, surveys, and number formation. The review extends these skills to probability situations, including two-dice outcomes and probabilities based on color proportions. Fill-in-the-blank, matching, multiple-select, dropdown, drag-and-drop, and multiple-choice items require students to select methods, organize reasoning, identify equivalent expressions, and enter numerical answers accurately. Designed for Grade 12 precalculus instruction, this free printable worksheet includes a complete answer key and can support review, independent practice, or preparation for an assessment.

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PreCal 9.1/9.3 Quiz Review

Total questions: 20

Name
Class
Date
1.

What is the total number of different 13-letter arrangements that can be formed using the letters in the word ENLIGHTENMENT?

*make sure to type your commas!!

(a)  

2.

Decide whether you'd solve using a Permutation, Combination, or simply need a single factorial, then match the cards accordingly.

Permutation

A lock has a code of 3 numbers between 1 and 15. How many codes can be created if no numbers repeat

Combination

The principal would like to assemble a committee of 8 students from the 12-member student council.

Factorial

Ribbons are being awarded for 1st through 5th place to the top 5 dogs in a dog show.

3.

There are 9 different actors auditioning for the roles of Larry, Curly and Moe. How many ways could the roles be cast?

*Check ALL that apply!

a)

9P3_9P_3  

b)

9C3_9C_3  

c)

504

d)

84

4.

₇P₃ is equivalent to ​ (a)   /​ (b)   ​

Choose from the below words
7!
4!
3!
11!
5.

Check all options equivalent to ₈C₆

a)

8!2!\frac{8!}{2!}  

b)

8!6!2!\frac{8!}{6!2!}  

c)

8x72x1\frac{8x7}{2x1}  

d)

4!4!  

e)

2828  

6.

Excluding Q, X, and Z, how many 3-letter crossword puzzle entries can be formed that contain no repeated letters?

Drag your answers into the blanks to explain how this problem can be solved using the Multiplication Principle of Counting

​ ​ (a)   x​ (b)   x​ ​ (c)  

Choose from the below words
23
22
21
26
25
3
2
1
24
7.

Match the following questions with their solutions

15!15!  

How many ways can 15 people be lined up for a photograph?

₁5P3₁₅P₃  

The Math club (15 members) is electing a President, VP & Treasurer. How many ways can this be done?

₁5C3₁₅C₃  

The Ice Cream Parlor has 15 different flavors. How many triple-flavored sundaes can be made?

8.

A baseball team has 15 players, but there are only 9 positions. How many different choices are there for how to put 9 players on the field?

*Remember to type your commas!

(a)  

9.

From a standard deck of cards, how many ways can you pick a heart, a Jack, and then a spade? Provided you put the cards back into the deck.



(a)  

10.

How many odd 2-digit positive integers greater than 30 are there?

a)

5

b)

35

c)

40

d)

30

11.

You are taking a survey on your experience at Express Oil. For the first four questions you can answer "Agree" or "Disagree," for the last two you can answer "Extremely Satisfied," "Satisfied," or Unsatisfied."

How many total outcomes are there for this survey?

a)

24⋅322^4\cdot3^2  

b)

42⋅234^2\cdot2^3  

c)

₄C2⋅2C3₄C₂\cdot₂C₃  

d)

₄P2⋅2P3₄P₂\cdot₂P₃  

12.

How would you solve the following problem:

A committee must be formed with 4 teachers and 5 students. If there are 10 teachers and 8 students to choose from, how many different ways could the committee be made?

Solution:

There are ​ ​ (a)   teachers, and ​ ​ (b)   students. We'd ​ (c)   these ​ (d)   to find the final answer.

Choose from the below words
₁₀C₄
₈C₅
multiply
combinations
add
​₈C₄
₁₀P₄
₅P₄
₁₀C₈
permutations
13.
A white and red die have been rolled. What's the probability that the sum is less than 8?

A white and red die have been rolled.

What's the probability that the sum is less than 8?

a)

712\frac{7}{12}  

b)

2135\frac{21}{35}  

c)

512\frac{5}{12}  

d)

12\frac{1}{2}  

14.
A white and red die have been rolled. What's the probability that the sum is NOT prime?

A white and red die have been rolled.

What's the probability that the sum is NOT prime?

a)

712\frac{7}{12}  

b)

2135\frac{21}{35}  

c)

512\frac{5}{12}  

d)

12\frac{1}{2}  

15.
The given table lists the color proportions for a brand's new winter vests as they're displayed on the racks in their store.…

The given table lists the color proportions for a brand's new winter vests as they're displayed on the racks in their store. If a vest is chosen at random from the rack, what is the probability that the vest is brown or green?



(a)  

16.
The given table lists the color proportions for a brand's new winter vests as they're displayed on the racks in their store.…

The given table lists the color proportions for a brand's new winter vests as they're displayed on the racks in their store. If vests are chosen at random from two different racks, what is the probability that the vests are tan or yellow?

a)

1

b)

0.25

c)

0.12

d)

0.0036

17.
The given table lists the color proportions for a brand's new winter vests as they're displayed on the racks in their store.…

The given table lists the color proportions for a brand's new winter vests as they're displayed on the racks in their store. If a vest is chosen at random from the rack, what is the probability that the vest is neither red nor green?



(a)  

18.
The given table lists the color proportions for a brand's new winter vests as they're displayed on the racks in their store.…

The given table lists the color proportions for a brand's new winter vests as they're displayed on the racks in their store.

Is this a VALID probability function?

​ (a)   ​ , because the proportions ​ (b)   to ​ (c)   ​

Choose from the below words
Yes
sum
1
1.1
No
multiply
19.

Lin and Kam are friends that work together on a team of 12 total people. Their manager is going to randomly select 2 people from the team of 12 to attend a conference.

What is the probability that Lin and Kam are the 2 people chosen?

a)

1₁2C2\frac{1}{₁₂C₂}  

b)

1₁2P2\frac{1}{₁₂P₂}  

c)

₁0C2₁2C2\frac{₁₀C₂}{₁₂C₂}  

d)

₂C1₁2C2\frac{₂C₁}{₁₂C₂}  

20.

Michael is taking a quiz in his music history class. The teacher writes the names of 6 songs on the board, and then plays 4 songs out of the 6, one after the other in a random sequence. Michael then needs to identify each of the songs in the sequence they were played.

Suppose that Michael hasn't studied and is randomly guessing the songs.

What is the probability that Michael correctly identifies all 4 songs in the correct order?

a)

115\frac{1}{15}  

b)

124\frac{1}{24}  

c)

130\frac{1}{30}  

d)

1360\frac{1}{360}  

WaygroundAnswer Key

PreCal 9.1/9.3 Quiz Review

Total questions: 20

1.
86,486,400
2.

Permutation

 - 

A lock has a code of 3 numbers between 1 and 15. How many codes can be created if no numbers repeat

, 

Combination

 - 

The principal would like to assemble a committee of 8 students from the 12-member student council.

, 

Factorial

 - 

Ribbons are being awarded for 1st through 5th place to the top 5 dogs in a dog show.

3.
a)

9P3_9P_3  

, c)

504

4.
7!, 4!
5.
b)

8!6!2!\frac{8!}{6!2!}  

, c)

8x72x1\frac{8x7}{2x1}  

, e)

2828  

6.
23, 22, 21
7.

15!15!  

 - 

How many ways can 15 people be lined up for a photograph?

, 

₁5P3₁₅P₃  

 - 

The Math club (15 members) is electing a President, VP & Treasurer. How many ways can this be done?

, 

₁5C3₁₅C₃  

 - 

The Ice Cream Parlor has 15 different flavors. How many triple-flavored sundaes can be made?

8.
5,005
9.
676, 13x4x13, 13 x 4 x 13
10.
b)

35

11.
a)

24⋅322^4\cdot3^2  

12.
₁₀C₄, ₈C₅, multiply, combinations
13.
a)

712\frac{7}{12}  

14.
a)

712\frac{7}{12}  

15.
0.3
16.
c)

0.12

17.
0.7
18.
Yes, sum, 1
19.
a)

1₁2C2\frac{1}{₁₂C₂}  

20.
d)

1360\frac{1}{360}  

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FAQs

What does the PreCal 9.1/9.3 Quiz Review worksheet cover?

This Grade 12 review covers permutations, combinations, factorials, the Multiplication Principle of Counting, and introductory probability. Across 20 fill-in-the-blank, matching, multiple-select, dropdown, drag-and-drop, and multiple-choice items, students classify counting situations, calculate arrangements and selections, recognize equivalent expressions, and solve dice and proportion-based probability problems.

How can I use this worksheet to teach permutations, combinations, and probability?

Introduce the review by having students sort its counting situations according to whether order matters, whether items are selected, or whether a factorial is sufficient. Then use the matching and dropdown items to discuss method selection before students complete the numerical problems involving roles, committees, cards, and surveys. Finish with the dice and color-proportion probability questions so students apply counting outcomes to probability.

What mistakes should I watch for when students complete this counting and probability review?

Watch for students using combinations when assigning distinct roles, or permutations when forming groups where order does not matter. Students may also misread equivalent notation such as nP r and nC r, skip a factor in a Multiplication Principle drag-and-drop item, or fail to account for replacement in the card-selection problem. In the probability items, check that students count the requested outcomes, such as sums below a value or sums that are not prime, rather than the complementary set.

How do I assign and grade the PreCal 9.1/9.3 Quiz Review?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for checking the fill-in-the-blank, matching, selection, and calculation items. Printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format also gives schools an option for reducing screen time during review.

How can I differentiate this worksheet for students who need a more accessible format?

Because this review combines numerical entry with matching, selection, dropdown, and drag-and-drop items, you can adjust font spacing and font size to make the prompts and answer choices easier to track. Wayground’s Advanced Settings also provide a dyslexia-friendly font and translation options for the worksheet text, including its counting and probability questions.

Where can I find more free worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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