1.	Expand the Brackets 1. Expand the brackets to simplify the following:$$ -5\left((-g) + 2j\right) $$ Correct Answer $$ 5g - 10j $$ 2. Expand the brackets to simplify the following:$$ 3\left(3a + 1b\right) $$ Correct Answer $$ 9a + 3b $$

2.	Expand the Brackets 1. Expand the brackets to simplify the following:$$ {\left(-6g + 5f\right)}^{2} $$ Correct Answer $$ 36{g}^{2} - 60gf + 25{f}^{2} $$ 2. Expand the brackets to simplify the following:$$ {\left((-P) + 6b\right)}^{2} $$ Correct Answer $$ {P}^{2} - 12Pb + 36{b}^{2} $$

3.	Collect Like Terms 1. Collect like terms to simplify the following:$$ -2R + 3h + -2Z + -5h $$ Correct Answer $$ -2R + -2h - 2Z $$ 2. Collect like terms to simplify the following:$$ -5e + -2S + -5k + 1S $$ Correct Answer $$ -5e + (-S) - 5k $$

4.

Adding fractions 1. Simplify the following:$$ \frac{(-x) + 4}{1x + 6} + \frac{2x + -1}{-5x + -6} $$ Correct Answer $$ \frac{7{x}^{2} + -3x - 30}{-5{x}^{2} - 36x - 36} $$ 2. Simplify the following:$$ \frac{-2x + -1}{-5x + -3} + \frac{3x + 1}{-2x + -1} $$ Correct Answer $$ \frac{-11{x}^{2} + -10x - 2}{10{x}^{2} + 11x + 3} $$

5.

Evaluate the following equations. 1. Find B to 3 significant figures in the following equation: $$ B = \frac{-5y + x - z}{\left(y + 4\right)\exp\left(z\right)},$$ Given that x = -4.0, y = -6.0, z = -3.0 Correct Answer -291 2. Find k to 3 significant figures in the following equation: $$ k = \cos\left(x\right) + \ln\left(y\right) - \ln\left(2z\right),$$ Given that x = 1.0, y = 4.0, z = 1.0 Correct Answer 1.23

6.

Rearrange the following equation. 1. Rearrange the following equation to get an expression for m: $$\cos\left(xy + 4z\right) = \frac{-6m}{y} + \ln\left(\sqrt{x}\right),$$ Correct Answer $$m = \frac{\left(\cos\left(xy + 4z\right) - \ln\left(\sqrt{x}\right)\right)y}{-6}$$ 2. Rearrange the following equation to get an expression for m: $$\frac{xz + \frac{-5}{y}}{\sqrt{x - z}} = \left(xm + 3y\right)\left(\exp\left(y\right) - \cos\left(y\right)\right),$$ Correct Answer $$m = \frac{\frac{\frac{xz + \frac{-5}{y}}{\sqrt{x - z}}}{\exp\left(y\right) - \cos\left(y\right)} - 3y}{x}$$

7.	Quadratic Equation Solve the following equation to get a value for x:$$6{x}^{2} + 3x = 6$$ Correct Answer $$\frac{\sqrt{153} - 3}{12}$$ and $$\frac{-3 - \sqrt{153}}{12}$$

8.	Expand the Brackets 1. Expand the brackets to simplify the following:$$ 6\left(4P + 4h\right) $$ Correct Answer $$ 24P + 24h $$ 2. Expand the brackets to simplify the following:$$ -5\left(-6B + 3A\right) $$ Correct Answer $$ 30B - 15A $$

9.	Expand the Brackets 1. Expand the brackets to simplify the following:$$ {\left(-6i + 3j\right)}^{2} $$ Correct Answer $$ 36{i}^{2} - 36ij + 9{j}^{2} $$ 2. Expand the brackets to simplify the following:$$ {\left(4P + 4b\right)}^{2} $$ Correct Answer $$ 16{P}^{2} + 32Pb + 16{b}^{2} $$

10.	Collect Like Terms 1. Collect like terms to simplify the following:$$ (-X) + -2f + -4Z + -2f $$ Correct Answer $$ (-X) + -4f - 4Z $$ 2. Collect like terms to simplify the following:$$ 4e + 5h + -3Z + -6h $$ Correct Answer $$ 4e + (-h) - 3Z $$