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

Here are the solutions to the questions.

1. (a) Copy and complete the table.

| Number | Round to the nearest tenths | Round to the nearest hundredths | Round to the nearest thousandths | | :------------ | :-------------------------- | :------------------------------ | :------------------------------- | | $486.3685$ | $486.4$ | $486.37$ | $486.369$ | | $0.060538$ | $0.1$ | $0.06$ | $0.061$ | | $2.21325535$ | $2.2$ | $2.21$ | $2.213$ |

1. (b) Solve the following:

• a) Between two supplementary angles, one angle is twice the other. Find the size of the larger angle. Step 1: Let the two supplementary angles be $x$ and $y$. Since they are supplementary, their sum is $180^\circ$. $x + y = 180^\circ$ Step 2: One angle is twice the other, so let $y = 2x$. Substitute this into the equation. $x + 2x = 180^\circ$ $3x = 180^\circ$ Step 3: Solve for $x$. $x = \frac{180^\circ}{3} = 60^\circ$ Step 4: Find the other angle, $y$. $y = 2x = 2(60^\circ) = 120^\circ$ The larger angle is $\boxed{*120^\circ*}$

• b) If one part of a complementary angle is $45^\circ$, what is the value of the other side? Step 1: Let the two complementary angles be $A$ and $B$. Since they are complementary, their sum is $90^\circ$. $A + B = 90^\circ$ Step 2: Given one angle is $45^\circ$, substitute $A = 45^\circ$. $45^\circ + B = 90^\circ$ Step 3: Solve for $B$. $B = 90^\circ - 45^\circ = 45^\circ$ The value of the other angle is $\boxed{*45^\circ*}$

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 $\{-1, 0, 1, 2, 3, 4\}$.

| $x$ | $y = 2x^2 - 2$ | | :-- | :------------- | | $-1$ | $2(-1)^2 - 2 = 2(1) - 2 = 0$ | | $0$ | $2(0)^2 - 2 = 2(0) - 2 = -2$ | | $1$ | $2(1)^2 - 2 = 2(1) - 2 = 0$ | | $2$ | $2(2)^2 - 2 = 2(4) - 2 = 6$ | | $3$ | $2(3)^2 - 2 = 2(9) - 2 = 16$ | | $4$ | $2(4)^2 - 2 = 2(16) - 2 = 30$ |

2. (b) Simplify the following algebraic expressions:

• i) $3y + 2x(x+y) - x^2 + y$ Step 1: Distribute $2x$ into the parenthesis. $3y + 2x^2 + 2xy - x^2 + y$ Step 2: Group like terms. $(3y + y) + (2x^2 - x^2) + 2xy$ Step 3: Combine like terms. $\boxed{*4y + x^2 + 2xy*}$

• ii) $2a - 2a(a+2x) + 4$ Step 1: Distribute $-2a$ into the parenthesis. $2a - 2a^2 - 4ax + 4$ Step 2: The terms are already simplified as there are no like terms to combine. $\boxed{*2a - 2a^2 - 4ax + 4*}$

2. (c) The mean (average) of five consecutive natural numbers is 11. Find the first of these numbers. Step 1: Let the first natural number be $n$. The five consecutive natural numbers are $n, n+1, n+2, n+3, n+4$. Step 2: Calculate their sum. $\text{Sum} = n + (n+1) + (n+2) + (n+3) + (n+4) = 5n + 10$ Step 3: The mean is the sum divided by the count (5). Set this equal to 11. $\frac{5n + 10}{5} = 11$ Step 4: Simplify the equation. $n + 2 = 11$ Step 5: Solve for $n$. $n = 11 - 2 = 9$ The first of these numbers is $\boxed{*9*}$

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: $\text{Angle} = \left(\frac{Frequency}{Total Frequency}\right) \times 360^\circ$.

• 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: $\left(\frac{5}{48}\right) \times 360^\circ = 37.5^\circ$

| Phone brand | Tally | Frequency | Angle of sector | | :---------- | :-------------- | :-------- | :-------------- | | Nokia | |||| ||| | 8 | $60^\circ$ | | Samsung | |||| || | 7 | $52.5^\circ$ | | Techno | |||| |||| ||| | 13 | $97.5^\circ$ | | iPhone | |||| |||| |||| | 15 | $112.5^\circ$ | | LG | |||| | 5 | $37.5^\circ$ |

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