Maths Exam

1. Expand the Brackets

1. Expand the brackets to simplify the following:$$ -2\left(-2P + 4j\right) $$
Correct Answer
$$ 4P - 8j $$
2. Expand the brackets to simplify the following:$$ -5\left(1B + 3f\right) $$
Correct Answer
$$ -5B - 15f $$

2. Expand the Brackets

1. Expand the brackets to simplify the following:$$ {\left(3e + 4d\right)}^{2} $$
Correct Answer
$$ 9{e}^{2} + 24ed + 16{d}^{2} $$
2. Expand the brackets to simplify the following:$$ {\left(-3P + 5b\right)}^{2} $$
Correct Answer
$$ 9{P}^{2} - 30Pb + 25{b}^{2} $$

3. Collect Like Terms

1. Collect like terms to simplify the following:$$ -3i + 5d + 1u + -5d $$
Correct Answer
$$ -3i + u $$
2. Collect like terms to simplify the following:$$ -2i + -2j + -3Z + 2j $$
Correct Answer
$$ -2i - 3Z $$

4. Adding fractions

1. Simplify the following:$$ \frac{-4x + 5}{(-x) + -4} + \frac{4x + 5}{-6x + 2} $$
Correct Answer
$$ \frac{20{x}^{2} + -59x - 10}{6{x}^{2} + 22x - 8} $$
2. Simplify the following:$$ \frac{4x + 3}{1x + 4} + \frac{-6x + 6}{5x + -4} $$
Correct Answer
$$ \frac{14{x}^{2} + -19x + 12}{5{x}^{2} + 16x - 16} $$

5. Evaluate the following equations.

1. Find V to 3 significant figures in the following equation: $$ V = \exp\left(\frac{yz}{\cos\left(x\right)}\right),$$ Given that x = 6.0, y = -6.0, z = 3.0
Correct Answer
0.00000000722
2. Find V to 3 significant figures in the following equation: $$ V = \frac{\left(x - 6\right)\left(2 - y\right)}{6z - \cos\left(z\right)},$$ Given that x = 6.0, y = 2.0, z = -4.0
Correct Answer
0.0

6. Rearrange the following equation.

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

7. Quadratic Equation

Solve the following equation to get a value for x:$$-6{x}^{2} + -5x + 3 = 0$$
Correct Answer
$$\frac{(-\left(5 + \sqrt{97}\right))}{12}$$ and $$\frac{(-\left(5 - \sqrt{97}\right))}{12}$$

8. Expand the Brackets

1. Expand the brackets to simplify the following:$$ 5\left(1x + -3f\right) $$
Correct Answer
$$ 5x - 15f $$
2. Expand the brackets to simplify the following:$$ 6\left(3i + 2Y\right) $$
Correct Answer
$$ 18i + 12Y $$

9. Expand the Brackets

1. Expand the brackets to simplify the following:$$ {\left(5x + -2A\right)}^{2} $$
Correct Answer
$$ 25{x}^{2} - 20xA + 4{A}^{2} $$
2. Expand the brackets to simplify the following:$$ {\left(4P + 5A\right)}^{2} $$
Correct Answer
$$ 16{P}^{2} + 40PA + 25{A}^{2} $$

10. Collect Like Terms

1. Collect like terms to simplify the following:$$ -5R + -3j + 1n + 2j $$
Correct Answer
$$ -5R + (-j) + n $$
2. Collect like terms to simplify the following:$$ (-P) + -4Y + 6u + 2Y $$
Correct Answer
$$ (-P) + -2Y + 6u $$


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