ACE-Learning | Math Step-by-step Autograding

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 1000+ 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 Expansion Factorisation Solving Linear Equations Solving Quadratic Equations Solving Inequalities

Simplification

Simplification of Linear Expressions

1.	$2 x - 5 y + 3 x$
2.	$4 x + 2 y - 6 x + 3 y$
3.	$- 3 x - 2 y - (- 5 x) + (- y)$
4.	$4 x + (3 x - 2 y)$
5.	$2 x - 5 y + 3 x$
6.	$(8 x + 2) - (3 x - 5)$
7.	$(2 x + 3 y + 4) + (2 y - 3)$
8.	$(3 x - 4 y - 1) - (- 4 x + 8 y - 7)$
9.	$4 x + [2 x - (3 x + 5)]$
10.	$7 x - 3 y - [2 x - (6 x - 5 y)]$

Simplification of Linear Expressions with Fractional Coefficients

1.	$\frac{1}{5} x + \frac{3}{5} x$
2.	$\frac{5}{6} x - \frac{2}{3} x$
3.	$\frac{1}{4} x + \frac{1}{3} y - \frac{1}{5} x$
4.	$2 x - \frac{4}{9} y - \frac{4}{3} x - \frac{2}{3} y$
5.	$\frac{7 x + 3}{8} - \frac{3 x}{8}$
6.	$\frac{5 x}{8} + \frac{3 x + 1}{4}$
7.	$\frac{2 x + y}{3} - \frac{x}{2}$
8.	$\frac{3 x + 5 y}{4} + \frac{2 x - y}{5}$
9.	$\frac{x - 5}{3} + \frac{x + 3}{5} + \frac{4 x - 7}{15}$
10.	$\frac{x + 3 y}{3} + \frac{2 (3 x - y)}{2} + 2 y$

Addition and Subtraction of Algebraic Fractions

1.	$\frac{1}{x} + \frac{1}{4 x}$
2.	$\frac{3}{5 r} + \frac{7}{3 r}$
3.	$\frac{1}{m} - \frac{1}{7 m}$
4.	$\frac{7}{3 s} - \frac{6}{5 s}$
5.	$\frac{3 h}{8 k} - \frac{5}{2 k^{2}}$
6.	$\frac{3 h}{8 k} - \frac{5}{2 k^{2}}$
7.	$\frac{3}{2 r + 1} + \frac{4}{2 r - 3}$
8.	$\frac{7}{y + 3} - \frac{2}{y}$
9.	$\frac{10}{m + 2} - \frac{9}{m - 2}$
10.	$\frac{8}{y^{2} - 4} + \frac{3}{y + 2}$

Expansion

Expansion of Linear Expressions

1.	$4 (2 x - 5 y)$
2.	$- 2 (3 x - 4 y)$
3.	$3 (2 x - 3 y) + 3 x$
4.	$8 x - 3 (x + 3 y)$
5.	$3 (3 x + 5 y) + 3 x - 7 y$
6.	$4 (4 x - 1) - 3 (5 x - 6)$
7.	$4 (4 x - 3 y + 2) + 3 (2 x + 5 y - 3)$
8.	$2 (6 x + 5 y - 3) - 3 (2 x - 3 y - 4)$
9.	$4 [5 (3 x + 4 y) + 2 (x - 2 y)]$
10.	$- 2 [5 (2 x - 5 y) - 2 (x - 3 y)]$

Expansion of Algebraic Expressions

1.	$3 x (4 + y)$
2.	$- 4 y (2 x + 3)$
3.	$x (3 x - y)$
4.	$- 3 y (2 y - 3 x)$
5.	$2 x (y + z) + 3 x (2 y + z)$
6.	$2 x (y + z) + 3 x (2 y + z)$
7.	$(x + 2 y) (x + 3 y)$
8.	$(2 x + 5 y) (3 x - y)$
9.	$(x^{2} + 6) (2 x + 3)$
10.	$2 (2 x + 1) (3 x + 2)$

Expansion using Algebraic Identities

1.	${(x + 5)}^{2}$
2.	${(3 x + 4)}^{2}$
3.	${(3 x + 4)}^{2}$
4.	${(5 - 2 x)}^{2}$
5.	$(x + 2) (x - 2)$
6.	$(4 x + 3) (4 x - 3)$
7.	${(x + 3 y)}^{2}$
8.	${(x - 7 y)}^{2}$
9.	$(2 x + y) (2 x - y)$
10.	$(4 x - 5 y) (4 x + 5 y)$

Factorisation

Factorisation by Common Factors

1.	$4 x + 12$
2.	$6 x - 9$
3.	$x y - x z$
4.	$x y - x z$
5.	$5 x + 5 y - 5 z$
6.	$20 x - 18 y + 14 z$
7.	$x y + x w + 2 x z$
8.	$x (x + 2) + 8 (x + 2)$
9.	$x (x - 5) - 3 (x - 5)$
10.	$8 a b (x - 5) - 12 b (x - 5)$

Factorisation by Grouping

1.	$x y + y + x + 1$
2.	$a x - 2 x + a - 2$
3.	$x y + 3 y + 2 x + 6$
4.	$a b - 6 b - 2 a + 12$
5.	$a x + b x + 4 a + 4 b$
6.	$15 p r - 10 q r - 6 p + 4 q$
7.	$p q r + 3 r + p q + 3$
8.	$p q r + 3 r + p q + 3$
9.	$6 x y z + 9 z + 10 x y + 15$
10.	$6 k m n - 8 n + 21 k m - 28$

Factorisation using Algebraic Identities

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

Factorisation of Quadratic Expressions

1.	$x^{2} + 3 x + 2$
2.	$x^{2} + 4 x - 12$
3.	$x^{2} - 7 x + 10$
4.	$x^{2} - 6 x - 16$
5.	$2 x^{2} + 14 x + 12$
6.	$3 x^{2} - 12 x + 9$
7.	$2 x^{2} + 5 x + 3$
8.	$3 x^{2} + 5 x - 2$
9.	$4 x^{2} - 13 x + 3$
10.	$4 x^{2} - 13 x + 3$

Solving Linear Equations

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

Solving Linear Equations with Brackets

1.	$4 (3 x + 5) = 7 x$
2.	$2 (2 x + 3) = x + 9$
3.	$3 (4 - 3 x) = 2 x + 1$
4.	$4 (2 x - 5) = 5 x - 6$
5.	$2 (5 - 2 x) = 3 x - 4$
6.	$4 (6 - 2 x) = - 3 x + 4$
7.	$5 (2 x + 1) = 3 (2 x + 3)$
8.	$3 (3 x - 5) = 2 (2 x - 7)$
9.	$2 (5 x - 7) = - 3 (3 x + 11)$
10.	$3 (3 x - 5) = - 4 (2 x - 9)$

Solving Linear Equations involving Fractional Coefficients

1.	$\frac{1}{5} x = \frac{6}{5}$
2.	$\frac{7 x}{5} - \frac{2 x}{5} = 8$
3.	$\frac{5 x}{6} + \frac{4 x}{3} = 7 + x$
4.	$\frac{1}{3} x + 5 = 10 - \frac{1}{6} x$
5.	$\frac{x + 3}{4} = 6$
6.	$\frac{5 x + 6}{3} - 7 = 0$
7.	$\frac{x + 7}{5} - 6 = 2$
8.	$\frac{4 (2 x - 11)}{5} + 2 = 5 x$
9.	$\frac{6 - x}{3} = \frac{x + 2}{5}$
10.	$\frac{9 - x}{3} - \frac{x + 2}{6} = 3$

Solving Linear Equations involving Algebraic Fractions

1.	$\frac{6}{x} = 3$
2.	$\frac{3}{x} = \frac{1}{4}$
3.	$\frac{4}{x + 3} = - 2$
4.	$\frac{2}{x + 4} = \frac{1}{3}$
5.	$\frac{x}{x + 5} = 6$
6.	$\frac{x}{x + 1} = \frac{3}{4}$
7.	$\frac{5}{2 x} = 10$
8.	$\frac{1}{3 x - 2} = - 8$
9.	$\frac{3}{x + 4} = \frac{1}{x + 2}$
10.	$\frac{4}{x - 2} - \frac{5}{x + 4} = 0$

Solving Quadratic Equations

Solving Quadratic Equations (by Factorisation)

1.	$x (x + 3) = 0$
2.	$(x + 1) (x - 4) = 0$
3.	$x^{2} + 3 x = 0$
4.	$3 x^{2} - 6 x = 0$
5.	$x^{2} - 2 x - 8 = 0$
6.	$x^{2} + 5 x + 6 = 0$
7.	$2 x^{2} + 5 x - 12 = 0$
8.	$x^{2} + 10 x = - 16$
9.	$(x - 3) (x - 5) = 3$
10.	$(x + 2) (x + 4) = 15$

Solving Quadratic Equations (by Completing the Square)

1.	${(x + 3)}^{2} = 16$
2.	${(x - 4)}^{2} = 4$
3.	${(3 x + 7)}^{2} = 16$
4.	${(2 x - 7)}^{2} = 9$
5.	${(x + 6)}^{2} - 49 = 0$
6.	${(2 x + 3)}^{2} - 25 = 0$
7.	${(x + 4)}^{2} + 3 = 28$
8.	$x^{2} + 12 x = - 20$
9.	$x^{2} + 4 x - 21 = 0$
10.	$x^{2} + 7 x + 8 = 2$

Solving Inequalities

Solving Simple Linear Inequalities

1.	$x + 3 > 7$
2.	$x - 5 < - 6$
3.	$5 x - 8 \geq 12$
4.	$4 x + 6 \leq - 10$
5.	$5 x + 4 < 7 x$
6.	$3 x + 14 > 10 x$
7.	$6 - x \leq x - 16$
8.	$15 - x \geq x + 7$
9.	$7 x > 4 (3 x - 2)$
10.	$8 x + 3 < 3 (7 - 2 x)$

Solving Linear Inequalities

1.	$2 x > 8$
2.	$5 x < 30$
3.	$4 x \geq 10$
4.	$9 x \leq 6$
5.	$- 7 x < 28$
6.	$- 3 x > - 12$
7.	$- 6 x \geq - 36$
8.	$- 5 x \leq - 40$
9.	$\frac{1}{2} x > 5$
10.	$\frac{2}{3} x < 6$

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.