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Simplification Expansion Factorisation Algebraic Fractions Solving Equations Matrices Calculus 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 Not sure if your steps are right or wrong? 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