1.	Expand the Brackets 1. Expand the brackets to simplify the following:$$ 1\left(2i + -3d\right) $$ Correct Answer $$ 2i - 3d $$ 2. Expand the brackets to simplify the following:$$ (-\left(-6a + 1f\right)) $$ Correct Answer $$ 6a - f $$

2.	Expand the Brackets 1. Expand the brackets to simplify the following:$$ {\left(-5c + -3y\right)}^{2} $$ Correct Answer $$ 25{c}^{2} + 30cy + 9{y}^{2} $$ 2. Expand the brackets to simplify the following:$$ {\left(2a + 6d\right)}^{2} $$ Correct Answer $$ 4{a}^{2} + 24ad + 36{d}^{2} $$

3.	Collect Like Terms 1. Collect like terms to simplify the following:$$ 1x + -2d + 6Z + (-d) $$ Correct Answer $$ x + -3d + 6Z $$ 2. Collect like terms to simplify the following:$$ 2a + 1f + 4m + 3f $$ Correct Answer $$ 2a + 4f + 4m $$

4.

Adding fractions 1. Simplify the following:$$ \frac{3x + -4}{3x + 2} + \frac{-3x + 2}{-4x + -4} $$ Correct Answer $$ \frac{-21{x}^{2} + 4x + 20}{-12{x}^{2} - 20x - 8} $$ 2. Simplify the following:$$ \frac{-6x + 2}{-3x + -6} + \frac{(-x) + -4}{-6x + 3} $$ Correct Answer $$ \frac{39{x}^{2} + -12x + 30}{18{x}^{2} + 27x - 18} $$

5.

Evaluate the following equations. 1. Find k to 3 significant figures in the following equation: $$ k = \frac{8 + z - x}{\cos\left(\frac{-3}{y}\right)},$$ Given that x = -4.0, y = -3.0, z = -1.0 Correct Answer 20.4 2. Find h to 3 significant figures in the following equation: $$ h = \left(x + z\right)\left(y - z\right) + \sin\left(x\right)\sin\left(y\right),$$ Given that x = 6.0, y = -5.0, z = 2.0 Correct Answer -56.3

6.

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

7.	Quadratic Equation Solve the following equation to get a value for x:$$-6{x}^{2} + -2x + 5 = 0$$ Correct Answer $$\frac{(-\left(2 + \sqrt{124}\right))}{12}$$ and $$\frac{(-\left(2 - \sqrt{124}\right))}{12}$$

8.	Expand the Brackets 1. Expand the brackets to simplify the following:$$ -3\left(-4a + 5A\right) $$ Correct Answer $$ 12a - 15A $$ 2. Expand the brackets to simplify the following:$$ 4\left(-5P + -6Y\right) $$ Correct Answer $$ -20P - 24Y $$

9.	Expand the Brackets 1. Expand the brackets to simplify the following:$$ {\left(1X + 4A\right)}^{2} $$ Correct Answer $$ {X}^{2} + 8XA + 16{A}^{2} $$ 2. Expand the brackets to simplify the following:$$ {\left(4a + 2Q\right)}^{2} $$ Correct Answer $$ 16{a}^{2} + 16aQ + 4{Q}^{2} $$

10.	Collect Like Terms 1. Collect like terms to simplify the following:$$ -2R + -2f + -3z + 5f $$ Correct Answer $$ -2R + 3f - 3z $$ 2. Collect like terms to simplify the following:$$ -2x + 2j + 1n + -3j $$ Correct Answer $$ -2x + (-j) + n $$