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Maths Exam

1. Expand the Brackets

1. Expand the brackets to simplify the following:$$ -4\left(5i + 1y\right) $$
Correct Answer
$$ -20i - 4y $$
2. Expand the brackets to simplify the following:$$ -5\left(-2X + -3b\right) $$
Correct Answer
$$ 10X + 15b $$

2. Expand the Brackets

1. Expand the brackets to simplify the following:$$ {\left(1X + -6f\right)}^{2} $$
Correct Answer
$$ {X}^{2} - 12Xf + 36{f}^{2} $$
2. Expand the brackets to simplify the following:$$ {\left(-5c + (-j)\right)}^{2} $$
Correct Answer
$$ 25{c}^{2} + 10cj + {j}^{2} $$

3. Collect Like Terms

1. Collect like terms to simplify the following:$$ -2P + -4y + 2v + 4y $$
Correct Answer
$$ -2P + 2v $$
2. Collect like terms to simplify the following:$$ 6R + -6Q + (-n) + -3Q $$
Correct Answer
$$ 6R + -9Q - n $$

4. Adding fractions

1. Simplify the following:$$ \frac{2x + -1}{(-x) + 6} + \frac{4x + -2}{-4x + -3} $$
Correct Answer
$$ \frac{-12{x}^{2} + 24x - 9}{4{x}^{2} - 21x - 18} $$
2. Simplify the following:$$ \frac{(-x) + 4}{5x + 1} + \frac{3x + 4}{-5x + -2} $$
Correct Answer
$$ \frac{20{x}^{2} + 5x - 4}{-25{x}^{2} - 15x - 2} $$

5. Evaluate the following equations.

1. Find V to 3 significant figures in the following equation: $$ V = \frac{yz\cos\left(\frac{z}{x}\right)}{\sin\left(z\right)},$$ Given that x = 2.0, y = -2.0, z = -2.0
Correct Answer
-2.38
2. Find B to 3 significant figures in the following equation: $$ B = \frac{2xy + x - 2\cos\left({6}^{z}\right)}{2},$$ Given that x = -2.0, y = -1.0, z = 5.0
Correct Answer
1.85

6. Rearrange the following equation.

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

7. Expand the Brackets

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

8. Expand the Brackets

1. Expand the brackets to simplify the following:$$ {\left(4c + -3Y\right)}^{2} $$
Correct Answer
$$ 16{c}^{2} - 24cY + 9{Y}^{2} $$
2. Expand the brackets to simplify the following:$$ {\left(6e + 6A\right)}^{2} $$
Correct Answer
$$ 36{e}^{2} + 72eA + 36{A}^{2} $$

9. Collect Like Terms

1. Collect like terms to simplify the following:$$ -5e + -3f + 1k + 1f $$
Correct Answer
$$ -5e + -2f + k $$
2. Collect like terms to simplify the following:$$ 6R + (-Q) + 6m + -4Q $$
Correct Answer
$$ 6R + -5Q + 6m $$

10. Adding fractions

1. Simplify the following:$$ \frac{-6x + -5}{3x + 4} + \frac{3x + -6}{-4x + -1} $$
Correct Answer
$$ \frac{33{x}^{2} + 20x - 19}{-12{x}^{2} - 19x - 4} $$
2. Simplify the following:$$ \frac{-2x + -6}{6x + 3} + \frac{-5x + 3}{5x + 1} $$
Correct Answer
$$ \frac{-40{x}^{2} + -29x + 3}{30{x}^{2} + 21x + 3} $$


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