Free Printable Challenging Algebra

1.

Solve the following using order of operations.

$8-6-\frac{28}{7}\left(10-7\right)^2$

2.

Match the following equations with the correct solution.

a)

$3^2-4\left(2-3\right)+1$

1.

$x=14$

b)

$\frac{4+5}{2\left(1-3\right)}\cdot\frac{4}{3}$

2.

$x=-3$

c)

$\left(3-4\right)^2-2\left(\frac{3}{2}\right)$

3.

$x=-2$

d)

$\sqrt[]{14-10}+\frac{2\left(3-1\right)}{2}$

4.

$x=4$

3.

Rewrite the following equation in slope-intercept form (y=mx+b)

$y+2=-3\left(x-1\right)$

4.

What are the solution for x?

$18\le2-8x<26$

a)

$x\ge-2\ or\ x<-3$

b)

$-2\le x<3$

c)

$-2.5\le x<-3.5$

d)

$-3<x\le-2$

5.

Match each of the expressions below with its appropriate factored form.

a)

$6x+15$

1.

$3\left(2x+5\right)$

b)

$9x^2-25$

2.

$\left(3x+5\right)\left(3x-5\right)$

c)

$6x^2+18x$

3.

$6x\left(x+3\right)$

6.

Match each of the expressions below with its appropriate factored form.

a)

$x^2-36$

1.

$\left(x+6\right)\left(x-6\right)$

b)

$x^2-4x-5$

2.

$\left(x-5\right)\left(x+1\right)$

c)

$x^2+6x+9$

3.

$\left(x+3\right)\left(x+3\right)$

7.

Simplify the expression. Your final answer should be reduced.

$\frac{3}{2}-\frac{5}{6}\left(\frac{1}{3}\right)$

8.

Simplify the expression. Your final answer should be reduced.

$-\frac{3}{5}\left(\frac{1}{2}\right)\div\left(-\frac{4}{5}\right)$

9.

Each of the options show an expression that could be simplified using exponent properties. Categorize the expressions that will or will not simplify to x⁶

Categorize the following

$\left(x^2\right)^3$

$\frac{x^{10}}{x^4}$

$\frac{x}{x^{-5}}$

$\left(x^2\right)^4$

$x^2\cdot x^3$

$x^{-6}$

Simplifies to x^6

Does not simplify to x^6

10.

Which of the following is the correct method for rewriting the rational exponent as a radical? Select all that apply.

$4^{\frac{4}{3}}$

a)

$\sqrt[3]{4^4}$

b)

$\left(\sqrt[3]{4}\right)^4$

c)

$\sqrt[4]{4^3}$

d)

$\left(\sqrt[4]{4}\right)^3$

11.

Which of the following shows the correct steps to fully simplify the following radical?

$\sqrt[]{24}$

a)

$\sqrt[]{2}\cdot\sqrt[]{12}=6\sqrt[]{2}$

b)

$\sqrt[]{4}\cdot\sqrt[]{6}=2\sqrt[]{6}$

c)

$\sqrt[]{3}\cdot\sqrt[]{8}=4\sqrt[]{3}$

d)

$\sqrt[]{2}\cdot\sqrt[]{3}\cdot\sqrt[]{4}=4\sqrt[]{6}$

12.

Which of the following are irrational?

a)

$0.333333...$

b)

$0.75$

c)

$\pi$

d)

$\sqrt{2}$

13.

Simplify the following fully:

$\sqrt{52}$

14.

Write the following in standard form:

1,560,000,000,000

15.

Write the following in standard form:

0.000002345

16.

Correct this into standard form

$62\times\ 10^3$

17.

Correct this into standard form

$10.2\times\ 10^{-4}$

18.

Write nth term for the following sequence:

-5, 1, 7, 13, ...

Note: Replace 'n' with 'x' in your answer

19.

What is the next term in the sequence?

4, -6, 9, ...

20.

Make x the subject of the following:

$y=\sqrt{\ x-3}+4$

21.

Make x the subject of the following:

$y=\frac{x+4}{x-3}$

22.

Make x the subject of the following:

$\frac{1}{\sqrt{y+1}}=1+\frac{1}{x}$

Challenging Algebra

Total questions: 22

Worksheet time: 42mins

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