Maths Exam

1. Expand the Brackets

1. Expand the brackets to simplify the following:$$ (-\left(-6g + -4Y\right)) $$
Correct Answer
$$ 6g + 4Y $$
2. Expand the brackets to simplify the following:$$ -4\left(-3c + 3Y\right) $$
Correct Answer
$$ 12c - 12Y $$

2. Expand the Brackets

1. Expand the brackets to simplify the following:$$ {\left(-2P + -6y\right)}^{2} $$
Correct Answer
$$ 4{P}^{2} + 24Py + 36{y}^{2} $$
2. Expand the brackets to simplify the following:$$ {\left(4c + 6Y\right)}^{2} $$
Correct Answer
$$ 16{c}^{2} + 48cY + 36{Y}^{2} $$

3. Collect Like Terms

1. Collect like terms to simplify the following:$$ -3e + 6b + 4Z + -4b $$
Correct Answer
$$ -3e + 2b + 4Z $$
2. Collect like terms to simplify the following:$$ -5R + -5Y + 1l + -6Y $$
Correct Answer
$$ -5R + -11Y + l $$

4. Adding fractions

1. Simplify the following:$$ \frac{4x + -4}{-2x + 2} + \frac{-4x + 4}{-4x + 3} $$
Correct Answer
$$ \frac{-8{x}^{2} + 12x - 4}{8{x}^{2} - 14x + 6} $$
2. Simplify the following:$$ \frac{-3x + 4}{5x + 1} + \frac{5x + -1}{(-x) + -5} $$
Correct Answer
$$ \frac{28{x}^{2} + 11x - 21}{-5{x}^{2} - 26x - 5} $$

5. Evaluate the following equations.

1. Find k to 3 significant figures in the following equation: $$ k = \left(x - 6 - \exp\left(y\right)\right)\sin\left({5}^{z}\right),$$ Given that x = 3.0, y = 3.0, z = -4.0
Correct Answer
-0.0369
2. Find k to 3 significant figures in the following equation: $$ k = \frac{{4}^{\left(3 + x\right)}\cos\left(y\right)}{\sin\left(z\right)},$$ Given that x = 4.0, y = -6.0, z = -4.0
Correct Answer
20800

6. Rearrange the following equation.

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

7. Quadratic Equation

Solve the following equation to get a value for x:$$3{x}^{2} + 4x + -3 = 0$$
Correct Answer
$$\frac{\sqrt{52} - 4}{6}$$ and $$\frac{-4 - \sqrt{52}}{6}$$

8. Expand the Brackets

1. Expand the brackets to simplify the following:$$ 5\left(-3B + -6y\right) $$
Correct Answer
$$ -15B - 30y $$
2. Expand the brackets to simplify the following:$$ 4\left(5e + (-f)\right) $$
Correct Answer
$$ 20e - 4f $$

9. Expand the Brackets

1. Expand the brackets to simplify the following:$$ {\left(3e + -6d\right)}^{2} $$
Correct Answer
$$ 9{e}^{2} - 36ed + 36{d}^{2} $$
2. Expand the brackets to simplify the following:$$ {\left(-6g + 1h\right)}^{2} $$
Correct Answer
$$ 36{g}^{2} - 12gh + {h}^{2} $$

10. Collect Like Terms

1. Collect like terms to simplify the following:$$ -5i + 2j + -3m + 1j $$
Correct Answer
$$ -5i + 3j - 3m $$
2. Collect like terms to simplify the following:$$ -3a + 6j + -6n + 6j $$
Correct Answer
$$ -3a + 12j - 6n $$


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