Draw a table for the mapping defined by the rule x → 2x² - 2 on the domain -1, 0, 1, 2, 3, 4.

Since they are supplementary, their sum is $180^\circ$. $x + y = 180^\circ$

Substitute this into the equation. $x + 2x = 180^\circ$ $3x = 180^\circ$

$$
y = 2x = 2(60^\circ) = 120^\circ
$$
The larger angle is $\boxed{\text{}120^\circ\text{}}$

• b) If one part of a complementary angle is $45^\circ$, what is the value of the other side?

Since they are complementary, their sum is $90^\circ$. $A + B = 90^\circ$

$$
B = 90^\circ - 45^\circ = 45^\circ
$$
The value of the other angle is $\boxed{\text{}45^\circ\text{}}$

1. (c) Agogo standing at point P on a school soccer field, moved 20 steps due east to a point Q and then moved 10 steps due south to a point R. Illustrate the movement of Agogo with a diagram.
A diagram illustrating the movement would show:

• A starting point labeled P.
• An arrow pointing right (East) from P, labeled "20 steps", ending at point Q.
• An arrow pointing down (South) from Q, labeled "10 steps", ending at point R.

2. (a) Draw a table for the mapping defined by the rule $x \rightarrow 2x^2 - 2$ on the domain $\{-1, 0, 1, 2, 3, 4\}$.

2. (b) Simplify the following algebraic expressions:

• i) $3y + 2x(x+y) - x^2 + y$

$$
\boxed{\text{}4y + x^2 + 2xy\text{}}
$$

• ii) $2a - 2a(a+2x) + 4$

$$
\boxed{\text{}2a - 2a^2 - 4ax + 4\text{}}
$$

2. (c) The mean (average) of five consecutive natural numbers is 11. Find the first of these numbers.

The five consecutive natural numbers are $n, n+1, n+2, n+3, n+4$.

Set this equal to 11.

The first of these numbers is $\boxed{\text{}9\text{}}$

3. Complete the table.

First, calculate the total frequency:
Total Frequency = $8 + 7 + 13 + 15 + 5 = 48$.

Now, calculate the Angle of Sector for each brand using the formula: $\text{Angle} = \left(\frac{\text{Frequency}}{\text{Total Frequency}}\right) \times 360^\circ$.

• Nokia: $\left(\frac{8}{48}\right) \times 360^\circ = 60^\circ$
• Samsung: $\left(\frac{7}{48}\right) \times 360^\circ = 52.5^\circ$
• Techno: $\left(\frac{13}{48}\right) \times 360^\circ = 97.5^\circ$
• iPhone: $\left(\frac{15}{48}\right) \times 360^\circ = 112.5^\circ$
• LG: $\left(\frac{5}{48}\right) \times 360^\circ = 37.5^\circ$