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A2 4-6 Cramer's Rule Quiz - Printable Math Worksheets 10th - 12th Grade - Wayground

A2 4-6 Cramer's Rule Quiz

LANCE WESTBROOK

Created by LANCE WESTBROOK

15 questions

10th - 12th Grade

Math

Updated Apr 2026

A2 4-6 Cramer’s Rule Quiz gives Grade 10–12 mathematics students focused practice solving systems of two linear equations with Cramer’s Rule. This 15-question multiple-choice worksheet checks the supporting skills students need: identifying matrix dimensions, recalling the 2×2 determinant formula ad − bc, setting up numerator determinants for x and y, evaluating determinants, and selecting solutions in ordered-pair form. Several items require students to track positive and negative values accurately while interpreting determinant results, including a determinant of zero. Use this quiz to reinforce procedural fluency after instruction or to check whether students can move from determinant setup to a complete solution. The questions progress across computation, matrix interpretation, determinant evaluation, and solving systems, making the worksheet suitable for independent practice, review, or an in-class assessment. It is a free printable worksheet with a complete answer key, designed for high school algebra students practicing Cramer’s Rule.

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A2 4-6 Cramer's Rule Quiz

Total questions: 15

Name
Class
Date
1.

Solve system by using Cramer's Rule. Answers are written in the following form (x,y)
 4x+6y=34x+6y=3  
 8x−3y=18x-3y=1  

a)

 (14,13)\left(\frac{1}{4},\frac{1}{3}\right)  

b)

 (−13,14)\left(-\frac{1}{3},\frac{1}{4}\right)  

c)

 (13,14)\left(\frac{1}{3},\frac{1}{4}\right)  

d)

 (14,−13)\left(\frac{1}{4},-\frac{1}{3}\right)  

2.

Solve system by using Cramer's Rule. Answers are written in the following form (x,y)
 2x+3y=152x+3y=15  
 x−3y=3x-3y=3  

a)

 (1,6)\left(1,6\right)  

b)

 (6,−1)\left(6,-1\right)  

c)

 (6,1)\left(6,1\right)  

d)

 (−1,6)\left(-1,6\right)  

3.
When setting up Cramer's Rule, what is the 2x2 determinant for the numerator for the x in the system?

When setting up Cramer's Rule, what is the 2x2 determinant for the numerator for the x in the system?

 

a)

 ∣−4   −2∣\left|-4\ \ \ -2\right|  
 ∣−5   −4∣ \left|-5\ \ \ -4\right|\   

b)

 ∣−4   −16∣\left|-4\ \ \ -16\right|  
 ∣−5  −26∣\left|-5\ \ -26\right|  

c)

 ∣−16   −2∣\left|-16\ \ \ -2\right|  
 ∣−26    −4∣\left|-26\ \ \ \ -4\right|  

d)

 ∣−4  −4∣\left|-4\ \ -4\right|  
 ∣−2  −5∣\left|-2\ \ -5\right|  

4.
When setting up Cramer's Rule, what is the 2x2 determinant for the numerator for the y in the system?

When setting up Cramer's Rule, what is the 2x2 determinant for the numerator for the y in the system?

 

a)

 ∣−4   −2∣\left|-4\ \ \ -2\right|  
 ∣−5   −4∣ \left|-5\ \ \ -4\right|\   

b)

 ∣−4   −16∣\left|-4\ \ \ -16\right|  
 ∣−5  −26∣\left|-5\ \ -26\right|  

c)

 ∣−16   −2∣\left|-16\ \ \ -2\right|  
 ∣−26    −4∣\left|-26\ \ \ \ -4\right|  

d)

 ∣−4  −4∣\left|-4\ \ -4\right|  
 ∣−2  −5∣\left|-2\ \ -5\right|  

5.
What size is this matrix?

What size is this matrix?

a)

2x2

b)

2x3

c)

3x2

d)

1x6

6.
What is the formula for the determinant of a 2x2 matrix?

What is the formula for the determinant of a 2x2 matrix?

a)

ad-bc

b)

ab-cd

c)

ad+bc

d)

(a+d)(b+c)

7.

Solve system by using Cramer's Rule. Answers are written in the following form (x,y)

−4x+7y=10-4x+7y=10  
x−3y=−10x-3y=-10  

a)

(−8,−10)\left(-8,-10\right)  

b)

(8,6)\left(8,6\right)  

c)

(6,−8)\left(6,-8\right)  

d)

(−10,8)\left(-10,8\right)  

8.
Find the determinant of the above matrix.

Find the determinant of the above matrix.

a)

81

b)

-81

c)

-129

d)

129

9.
Use Cramer's Rule to solve the system. What is the solution?

Use Cramer's Rule to solve the system.  What is the solution?

 

a)


 (1,5)\left(1,5\right) 

b)

No unique solution

c)


 (3, −4)\left(3,\ -4\right)  

d)

 (2,4)\left(2,4\right)  

10.
Evaluate the determinant of the matrix.

Evaluate the determinant of the matrix.

a)

−30-30

b)

−10-10

c)

1010

d)

−55-55

11.
Evaluate the determinant of the matrix.

Evaluate the determinant of the matrix.

a)

−5-5

b)

4545

c)

−10-10

d)

1010

12.
Evaluate the determinant of the matrix.

Evaluate the determinant of the matrix.

a)

00

b)

−10-10

c)

2020

d)

−20-20

13.
Solve the system of equations using Cramer's Rule.

Solve the system of equations using Cramer's Rule.

a)

 (−3,−1)\left(-3,-1\right)  

b)

 (−6,6)\left(-6,6\right)  

c)

 (5,−3)\left(5,-3\right)  

d)

 (2,−6)\left(2,-6\right)  

14.
Solve the system of equations using Cramer's Rule.

Solve the system of equations using Cramer's Rule.

a)


(−2,0)\left(-2,0\right)

b)

(1,4)\left(1,4\right)

c)

(2,6)\left(2,6\right)

d)

(2,−3)\left(2,-3\right)

15.
Solve the system of equations using Cramer's Rule.

Solve the system of equations using Cramer's Rule.

a)


(6,−6)\left(6,-6\right)

b)

(−6,6)\left(-6,6\right)

c)

(−6,2)\left(-6,2\right)

d)

(2,−6)\left(2,-6\right)

WaygroundAnswer Key

A2 4-6 Cramer's Rule Quiz

Total questions: 15

1.
a)

 (14,13)\left(\frac{1}{4},\frac{1}{3}\right)  

2.
c)

 (6,1)\left(6,1\right)  

3.
c)

 ∣−16   −2∣\left|-16\ \ \ -2\right|  
 ∣−26    −4∣\left|-26\ \ \ \ -4\right|  

4.
b)

 ∣−4   −16∣\left|-4\ \ \ -16\right|  
 ∣−5  −26∣\left|-5\ \ -26\right|  

5.
c)

3x2

6.
a)

ad-bc

7.
b)

(8,6)\left(8,6\right)  

8.
c)

-129

9.
d)

 (2,4)\left(2,4\right)  

10.
a)

−30-30

11.
a)

−5-5

12.
a)

00

13.
a)

 (−3,−1)\left(-3,-1\right)  

14.
a)


(−2,0)\left(-2,0\right)

15.
a)


(6,−6)\left(6,-6\right)

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FAQs

What does this Cramer’s Rule worksheet cover?

This 15-question multiple-choice worksheet covers solving 2×2 systems with Cramer’s Rule, including identifying matrix size, using the 2×2 determinant formula ad − bc, setting up the numerator determinants for x and y, evaluating determinants, and reporting solutions as ordered pairs. Students build accuracy by connecting determinant calculations to final system solutions while tracking signs and coordinate order.

How can I use this worksheet to teach Cramer’s Rule?

Introduce the worksheet by modeling the coefficient determinant, then show how replacing the x- or y-coefficient column creates the corresponding numerator determinant. Have students explain why each determinant belongs in the x or y calculation before they complete the solution items, and use the matrix-size and ad − bc questions as a quick check of prerequisite understanding. Review selected multiple-choice distractors to discuss sign errors and reversed ordered pairs.

What mistakes should I watch for when students complete this Cramer’s Rule quiz?

Watch for students using the wrong replaced column when setting up the numerator determinant, reversing ad − bc as they evaluate a 2×2 determinant, or misreading a 3×2 matrix as a 2×3 matrix. In the solution questions, students may also select the correct values in the wrong order or lose a negative sign when converting determinant results into an ordered pair. The item with a zero determinant is useful for checking whether students recognize that determinant evaluation affects whether Cramer’s Rule produces a unique solution.

How do I assign and grade this Cramer’s Rule worksheet?

You can use this Cramer’s Rule worksheet as a printable PDF or assign it as a digital quiz on Wayground. It includes a complete answer key for all 15 multiple-choice questions, and printable student work can be graded by scanning it with the Wayground for Teachers app. The printable format can also support classrooms that are reducing screen time.

How can I differentiate this Cramer’s Rule worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so determinant layouts, matrix dimensions, and ordered-pair answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those options support access to the same Cramer’s Rule practice.

Where can I find more 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 support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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