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Math Step-by-step Autograding

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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-8≥12
4. 4x+6≤-10
5. 5x+4<7x
6. 3x+14>10x
7. 6-x≤x-16
8. 15-x≥x+7
9. 7x>43x-2
10. 8x+3<37-2x

Solving Linear Inequalities

1. 2x>8
2. 5x<30
3. 4x≥10
4. 9x≤6
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-7≥0
3. x+2x-4>0
4. 3x-4x-5<0
5. x2-6x<0
6. x2-25≤0
7. x2+8>12
8. 16x2+5<21
9. x2+3x-10≤0
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

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