ACE-Learning Logo

Math Step-by-step Autograding

Free Worksheets

The general consensus is that Mathematics is difficult and Algebra is challenging. You'll probably feel the same way if you do not have a firm grasp of the basics. A good foundation in Algebra is crucial to your success in Mathematics. Try the following questions to improve your skills.


Install the app to get 1800+ questions. The app checks each of your working step and provides you with instant feedback. With the app, mastering Algebra is a breeze.


Happy learning!


Simplification

Simplification of Linear Expressions

1. 2x-5y+3x
2. 4x+2y-6x+3y
3. -3x-2y--5x+-y
4. 4x+3x-2y
5. 2x-5y+3x
6. 8x+2-3x-5
7. 2x+3y+4+2y-3
8. 3x-4y-1--4x+8y-7
9. 4x+2x-3x+5
10. 7x-3y-2x-6x-5y

Simplification of Linear Expressions with Fractional Coefficients

1. 15x+35x
2. 56x-23x
3. 14x+13y-15x
4. 2x-49y-43x-23y
5. 7x+38-3x8
6. 5x8+3x+14
7. 2x+y3-x2
8. 3x+5y4+2x-y5
9. x-53+x+35+4x-715
10. x+3y3+23x-y2+2y

Addition and Subtraction of Algebraic Fractions

1. 1x+14x
2. 35r+73r
3. 1m-17m
4. 73s-65s
5. 3h8k-52k2
6. 3h8k-52k2
7. 32r+1+42r-3
8. 7y+3-2y
9. 10m+2-9m-2
10. 8y2-4+3y+2

Expansion

Expansion of Linear Expressions

1. 42x-5y
2. -23x-4y
3. 32x-3y+3x
4. 8x-3x+3y
5. 33x+5y+3x-7y
6. 44x-1-35x-6
7. 44x-3y+2+32x+5y-3
8. 26x+5y-3-32x-3y-4
9. 453x+4y+2x-2y
10. -252x-5y-2x-3y

Expansion of Algebraic Expressions

1. 3x4+y
2. -4y2x+3
3. x3x-y
4. -3y2y-3x
5. 2xy+z+3x2y+z
6. 2xy+z+3x2y+z
7. x+2yx+3y
8. 2x+5y3x-y
9. x2+62x+3
10. 22x+13x+2

Expansion using Algebraic Identities

1. x+52
2. 3x+42
3. 3x+42
4. 5-2x2
5. x+2x-2
6. 4x+34x-3
7. x+3y2
8. x-7y2
9. 2x+y2x-y
10. 4x-5y4x+5y

Factorisation

Factorisation by Common Factors

1. 4x+12
2. 6x-9
3. xy-xz
4. xy-xz
5. 5x+5y-5z
6. 20x-18y+14z
7. xy+xw+2xz
8. xx+2+8x+2
9. xx-5-3x-5
10. 8abx-5-12bx-5

Factorisation by Grouping

1. xy+y+x+1
2. ax-2x+a-2
3. xy+3y+2x+6
4. ab-6b-2a+12
5. ax+bx+4a+4b
6. 15pr-10qr-6p+4q
7. pqr+3r+pq+3
8. pqr+3r+pq+3
9. 6xyz+9z+10xy+15
10. 6kmn-8n+21km-28

Factorisation using Algebraic Identities

1. x2+2x+1
2. x2+2x+1
3. x2-9
4. 4x2+12x+9
5. 25x2-20x+4
6. 9x2-16
7. 2x2+12x+18
8. 2x2-20x+50
9. 3x2-48
10. 16-36x2

Factorisation of Quadratic Expressions

1. x2+3x+2
2. x2+4x-12
3. x2-7x+10
4. x2-6x-16
5. 2x2+14x+12
6. 3x2-12x+9
7. 2x2+5x+3
8. 3x2+5x-2
9. 4x2-13x+3
10. 4x2-13x+3

Algebraic Fractions

Addition and Subtraction of Algebraic Fractions

1. 1x+14x
2. 35r+73r
3. 1m-17m
4. 73s-65s
5. 3h8k-52k2
6. 4x+2+3x
7. 32r+1+42r-3
8. 7y+3-2y
9. 10m+2-9m-2
10. 8y2-4+3y+2

Multiplication and Division of Algebraic Fractions

1. x6y×2y5
2. 4p3q×5q22p2
3. 4st33r×5r28st2
4. 2x3y÷x5
5. 3m34n2÷m8n2
6. 5a2b3÷10a33b2
7. x+yx-y×2x-y3x+3y
8. p2q+4q3p-2r×6p-4r3p2+12
9. 6y-4z3y+6z÷4y-2z9y+3z
10. 3k2+knmn-4m2÷2n+6k4m-n

Manipulation of Algebraic Formulae

1. Make x the subject of 2y=3x+5
2. Make m the subject of 4n=9m-3
3. Make a the subject of 2a-13b=5b
4. Make x the subject of 4x-y=x+5
5. Make p the subject of 9p-4d=4p+5
6. Make m the subject of 5m+2n=10m+9
7. Make a the subject of a2b-3d=4x+5
8. Make p the subject of 6p=2q
9. Make m the subject of 7m=3n-4
10. Make x the subject of y=1-4x6+5x

Solving Equations

Solving Linear Equations

1. x+4=7
2. x-2=1
3. 4x=12
4. 2x+3=7
5. 5x+8=3x
6. 4x-5=3x
7. 5x=3x+10
8. 4x+3=2x+9
9. 6x+3=4x-1
10. 7x-2=3x-10

Solving Linear Equations with Brackets

1. 43x+5=7x
2. 22x+3=x+9
3. 34-3x=2x+1
4. 42x-5=5x-6
5. 25-2x=3x-4
6. 46-2x=-3x+4
7. 52x+1=32x+3
8. 33x-5=22x-7
9. 25x-7=-33x+11
10. 33x-5=-42x-9

Solving Linear Equations involving Fractional Coefficients

1. 15x=65
2. 7x5-2x5=8
3. 5x6+4x3=7+x
4. 13x+5=10-16x
5. x+34=6
6. 5x+63-7=0
7. x+75-6=2
8. 42x-115+2=5x
9. 6-x3=x+25
10. 9-x3-x+26=3

Solving Linear Equations involving Algebraic Fractions

1. 6x=3
2. 3x=14
3. 4x+3=-2
4. 2x+4=13
5. xx+5=6
6. xx+1=34
7. 52x=10
8. 13x-2=-8
9. 3x+4=1x+2
10. 4x-2-5x+4=0

Solving Quadratic Equations (by Factorisation)

1. xx+3=0
2. x+1x-4=0
3. x2+3x=0
4. 3x2-6x=0
5. x2-2x-8=0
6. x2+5x+6=0
7. 2x2+5x-12=0
8. x2+10x=-16
9. x-3x-5=3
10. x+2x+4=15

Solving Quadratic Equations (by Completing the Square)

1. x+32=16
2. x-42=4
3. 3x+72=16
4. 2x-72=9
5. x+62-49=0
6. 2x+32-25=0
7. x+42+3=28
8. x2+12x=-20
9. x2+4x-21=0
10. x2+7x+8=2

Solving Quadratic Equations (by General Formula)

1. x2-5x+2=0
2. 3x2-6x+2
3. -2x2-7x+3=0
4. x2-5x=-1
5. 2x2+9x=-3
6. x2+2=5x
7. xx+3-2=0
8. x1-3x+8=0
9. xx+3+2x+5=0
10. xx+3=6x+2

Solving Equations Reducible to Quadratic Equations (by Factorisation)

1. 18x=2x
2. 8x-2=x
3. 43x-5=2x
4. 8x=6-x
5. 12x+7=6-x
6. 8x=3x-2
7. 1x-2=2x-3
8. 194x+3=2x-7
9. 4x+32x=5
10. x-9x-4=x+3

Solving Equations Reducible to Quadratic Equations (by General Formula)

1. 3x=x
2. 5x+2=x
3. 86-5x=-2x
4. 4x-5=x-4
5. 5x=4x-10
6. 2x+4=6-3x
7. x+5x=10
8. xx-1=x-1
9. x+77-x=x
10. x-5x+3=2x+19

Solving Simple Linear Inequalities

1. x+3>7
2. x-5<-6
3. 5x-812
4. 4x+6-10
5. 5x+4<7x
6. 3x+14>10x
7. 6-xx-16
8. 15-xx+7
9. 7x>43x-2
10. 8x+3<37-2x

Solving Linear Inequalities

1. 2x>8
2. 5x<30
3. 4x10
4. 9x6
5. -7x<28
6. -3x>-12
7. -6x-36
8. -5x-40
9. 12x>5
10. 23x<6

Solving Quadratic Inequalities

1. xx+4>0
2. x2x-70
3. x+2x-4>0
4. 3x-4x-5<0
5. x2-6x<0
6. x2-250
7. x2+8>12
8. 16x2+5<21
9. x2+3x-100
10. 3x2+6x-24<0

Solving Equations involving Indices

1. 2x=16
2. 3-x=243
3. 5x=1125
4. 6-x=1216
5. 24x=256
6. 3-4x=81
7. 3-6x=1243
8. 4x=32
9. 25-x=125
10. 25x+3=256

Matrices

Addition and Subtraction of Matrices

1. 61+2-5
2. 7-2--23
3. 47+3-6
4. 50-1-2
5. x2-2x-8=0
6. -97-8-33-10
7. 30-2+-597
8. 04-3-229
9. -4249+-382-2
10. -4-435--661-9

Multiplication of a Matrix by a Real Number

1. 33-6
2. 3-4-2+41
3. 263--75
4. 51-1+9-3
5. 42-5--2-9
6. 34662+-7-10-65
7. 23-93-5-10065
8. 35-73-36-2+2-16-74-30
9. 41-14-12-3-135-302
10. 35-110-47+4-3-4214-5

Multiplication of Matrices

1. 3124
2. -301-25-5
3. -32-15-235-4
4. 2-1-3-35-1
5. -3-25-173-504
6. 1-4-23
7. -243-3-52
8. -134-1-5-243
9. 35341-5-2-405
10. 1-237-4-2-1-14

The Inverse Matrix

1. -4-233
2. 4-6-55
3. 65-3-5
4. -69-55
5. 82-10-5
6. 8-6-105
7. -89-43
8. -8-10-6-9
9. 9-2-32
10. 9-8-64

Using Matrices to Solve Simultaneous Equations

1. 4-23-3xy=-126
2. -4-323xy=191
3. 4-52-5xy=171
4. -6-4-5-5xy=165
5. 82-6-3xy=20-6
6. -8-6-5-5xy=8-5
7. 8946xy=4-4
8. 96-4-4xy=-3-4
9. -98-64xy=612
10. 108-4-2xy=-1812

Calculus

Differentiation (Power Rule)

1. ddx3x2
2. ddx-2x5
3. ddx5x2
4. ddx6x23
5. ddx7x+5
6. ddx2x3+4x-3
7. ddx3x2+1x-4
8. ddx4x2-5x
9. ddxx2+4x2
10. ddx6x3-5x2-82x2

Differentiation (Chain Rule)

1. ddx2x+13
2. ddx15x-6
3. ddx8x-314
4. ddx2x2+34
5. ddx4x2-53
6. ddx5x2+435
7. ddxx2-4x+63
8. ddx5x-x2+3
9. ddx2x4-16
10. ddx12x-374

Differentiation (Product Rule)

1. ddxxx+53
2. ddx2x5x-14
3. ddxx26x+13
4. ddx3x23x2-86
5. ddx2x-14x-55
6. ddxx2+79x2+45
7. ddxx2+2x-4x-13
8. ddxx+35x-44
9. ddxx-4x+7
10. ddxx2+8x2-8

Differentiation (Quotient Rule)

1. ddx4x-3
2. ddx3x2x-1
3. ddxx+34x+1
4. ddxx2+47x+2
5. ddx3xx2+4
6. ddx7x-34x2-11
7. ddxx25-2x2
8. ddxxx2-2
9. ddxxx-4
10. ddx5x-23x-5

Integration involving Functions with Linear Factors

1. x+52dx
2. 6x-12dx
3. 14x-33dx
4. 3x+92dx
5. -22x+33dx
6. 42x+32dx
7. x+3dx
8. 13-x3dx
9. x+25dx
10. 3x-45dx

Not sure if your steps are right or wrong?

Want to Try More Questions?


Get Math Step-by-step Autograding App

Subscription

Not a user yet? Sign up now!
Simply select the subscription period and make payment using Credit Card via PayPal.
After that, your account will be sent to you via email.

Buy now with PayPal