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Change of subject of formula - Printable Mathematics Worksheets year 8 - Wayground

Change of subject of formula

16 questions

8th - 10th Grade

Mathematics

This Grade 8–10 mathematics worksheet gives students focused practice changing the subject of a formula through 16 multiple-choice questions. Students rearrange equations to isolate variables such as x, y, a, b, and r, including linear formulas, equations with constants, a circle-area formula, and formulas requiring a square root. Several questions also ask students to evaluate a rearranged formula using given values. The worksheet helps learners apply inverse operations, manage brackets and fractions, and recognize equivalent algebraic forms. It is suitable for guided practice, independent classwork, homework, or a quick check of algebraic manipulation skills. This free printable worksheet includes a complete answer key, making it useful for Grade 8 to Grade 10 mathematics instruction and review.

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Worksheets

Change of subject of formula

Total questions: 16

Name
Class
Date
1.

A=5ab [b]

a)

b=A/5a

b)

b=5Aab

c)

b=5Ab

d)

b=5a/A

2.
Make x the subject of y = mx + 1
a)
x = (y - 1)/m
b)
x = y - 1/m
c)
x = y/m - 1
d)
x = my - 1
3.

Which of the following has "a" as the subject of the formula?

a)
b)
c)
d)
4.
Solve for y:
3x + y = 12
a)
y = -3x +12
b)
x = y + 4
c)
x = y + 12
d)
y = 3x -12
5.
If m = 3, c = 5 and y = 11, calculate x:
y = mx + c
a)
x = 2
b)
x = 38
c)
x = 8.67
d)
x = -2.67
6.
Make x the subject:
N = (180 + x)/2
a)
x = 2N -180
b)
x = N - 180
c)
x = N/2 -180
d)
x = N -180/2
7.
Make r the subject:
A = πr2
a)
r = √(A/π)
b)
r = √Aπ
c)
r = Aπ2
d)
r = (Aπ)2
9.
Make a the subject of
a + b = c + d
a)
a = c + d - b
b)
a = b + c + d
c)
a = b + c - d
d)
a = c - b - d
9.
Make a the subject of
a + b = c + d
a)
a = c + d - b
b)
a = b + c + d
c)
a = b + c - d
d)
a = c - b - d
10.
a)
b)
c)
d)
11.

If 2x - 3y = 6z, then y =

a)
b)
c)
d)
12.

If x = 9 (y + z), then y =

a)
b)
c)
d)
13.
a)
b)
c)
d)
14.
a)
b)
c)
d)
15.
a)
b)
c)
d)
16.

 dx+e=fdx+e=f 
 Which expression represents the value of x in the equation:

a)

 x=f+edx=\frac{f+e}{d} 

b)

 x=f−edx=\frac{f-e}{d} 

c)

 x=de−fx=\frac{d}{e-f}  

d)

 x=de+fx=\frac{d}{e+f}  

Answer Key

Change of subject of formula

Total questions: 16

1.
a)

b=A/5a

2.
a) x = (y - 1)/m
3.
c)
4.
a) y = -3x +12
5.
a) x = 2
6.
a) x = 2N -180
7.
a) r = √(A/π)
9.
a) a = c + d - b
9.
a) a = c + d - b
10.
d)
11.
b)
12.
c)
13.
b)
14.
a)
15.
a)
16.
b)

 x=f−edx=\frac{f-e}{d} 

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FAQs

What does this worksheet cover?

This worksheet covers changing the subject of a formula using 16 multiple-choice questions. Students isolate different variables in linear equations and formulas, simplify expressions such as y = mx + c, rearrange a circle-area formula to find r, and substitute values after making x the subject.

How can I use this worksheet to teach changing the subject of a formula?

Model one item by identifying the target variable and applying inverse operations one step at a time, then use a similar question for guided practice. For example, compare the rearrangement of y = mx + 1 with N = (180 + x)/2 to discuss why subtraction and multiplication must be applied in the correct order. Students can then complete the multiple-choice items and explain why the other options do not isolate the requested variable.

What mistakes should I watch for when students complete this worksheet?

Watch for students subtracting or dividing the wrong term, losing brackets in expressions such as (y - 1)/m, or failing to divide every term by the coefficient. In the circle-area item, students may choose A/π instead of taking the square root to find r. When substituting values into y = mx + c, check that students rearrange for x before calculating and preserve the signs.

How do I assign and grade this worksheet?

This changing-the-subject worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key for all 16 multiple-choice questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app. The PDF option can also support schools that are reducing screen time.

How can I differentiate this formula-rearrangement worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the algebraic expressions, fractions, and answer choices are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language while students practise isolating variables in the multiple-choice equations.

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 help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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