﻿ Maths Exam @Template

### 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 $$6R + -9Q - n$$

 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 = -2.0Correct 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 = 5.0Correct 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 $$6R + -5Q + 6m$$

 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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