SSNEC's 2015-2016 Basic Mathematics Exam Paper. Page 5

$$
\frac{x^{1+1}}{1+1} + \frac{x^{0+1}}{0+1} + C
$$
$$
\frac{x^2}{2} + x + C
$$
The integral is $\boxed{\frac{x^2}{2} + x + C}$.

• D-(1) Calculate the distance between two points. A (4, 4), B (8, 2)

$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$.
Let $(x_1, y_1) = (4, 4)$ and $(x_2, y_2) = (8, 2)$. $d = \sqrt{(8-4)^2 + (2-4)^2}$

$$
d = \sqrt{20}
$$
$$
d = \sqrt{4 \times 5}
$$
$$
d = \boxed{2\sqrt{5}}
$$

• (2) The two lines whose slopes are $m_1$, $m_2$ said to be parallel if: Two lines are parallel if their slopes are equal.

  $$m_1 = \boxed{m_2}$$

• (3) Find the equation of the straight line which is parallel to the line whose gradient is -2 and passes through the original point.

$y - y_1 = m(x - x_1)$. $y - 0 = -2(x - 0)$

$$
y = -2x
$$
The equation of the straight line is $\boxed{y = -2x}$.

Right Column:

• (4) Find the angle $\theta$ between the two straight lines whose gradients are: $m_1 = -\frac{3}{5}$, $m_2 = \frac{1}{4}$

$\tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|$. $\tan \theta = \left| \frac{-\frac{3}{5} - \frac{1}{4}}{1 + (-\frac{3}{5})(\frac{1}{4})} \right|$

$$
\theta = \arctan(1)
$$
$$
\theta = \boxed{45^\circ \text{ or } \frac{\pi}{4} \text{ radians}}
$$

QUESTION THREE:

A- Define the following:

• (1) Statistics: Statistics is the scientific discipline that involves collecting, organizing, analyzing, interpreting, and presenting data. It is used to make inferences and decisions about populations based on sample data.

• (2) Mode: The mode is the value that appears most frequently in a data set. A data set can have one mode (unimodal), multiple modes (multimodal), or no mode if all values appear with the same frequency.