Given K = 1, 2, 3, ..., 11. (i) List the prime numbers in K. (ii) Find the probability that a number selected at random from the set K is not a prime number. 1. (b) Factorize completely: (x+y)(2m-n) -

$$
P(\text{not prime}) = \frac{\text{Number of non-prime numbers}}{\text{Total number of numbers}}
$$
$$
P(\text{not prime}) = \frac{6}{11}
$$
The probability is $\boxed{\frac{6}{11}}$.

1. (b)
Factorize completely: $(x+y)(2m-n) - m(x+y)$

The common factor is $(x+y)$.

The completely factorized expression is $\boxed{(x+y)(m-n)}$.

1. (c)
A typist charges GH¢ 68.00 for the first 8 sheets typed, and GH¢ 11.00 for each additional sheet. Calculate the amount earned if the typist typed a total of 35 sheets.

Additional sheets = Total sheets - First 8 sheets
Additional sheets $= 35 - 8 = 27$ sheets.

Cost for additional sheets $= 27 \text{ sheets} \times \text{GH¢ } 11.00/\text{sheet} = \text{GH¢ } 297.00$.

Total amount earned = Cost for first 8 sheets + Cost for additional sheets
Total amount earned $= \text{GH¢ } 68.00 + \text{GH¢ } 297.00 = \text{GH¢ } 365.00$.
The amount earned is $\boxed{\text{GH¢ } 365.00}$.

2. (a)
The image of $P(2, 5)$ when translated by the vector $r = (-3, 8)$.
A translation by vector $(a, b)$ means adding $a$ to the x-coordinate and $b$ to the y-coordinate.
$P'(x', y') = (x+a, y+b)$.

• (i) Find the image of $P(2, 5)$:

  $$P' = (2 + (-3), 5 + 8) = (2 - 3, 5 + 8) = (-1, 13)$$

  The image of $P(2, 5)$ is $\boxed{(-1, 13)}$.

• (ii) Find the image $Q'$ of $Q(-4, -6)$ when translated by $r$:

  $$Q' = (-4 + (-3), -6 + 8) = (-4 - 3, -6 + 8) = (-7, 2)$$

  The image of $Q(-4, -6)$ is $\boxed{(-7, 2)}$.

2. (b)
Joyce and Richard contributed GH¢ 10,000.00 and GH¢ 5,000.00 respectively. Richard is paid one-third of the profit as a manager. The rest of the profit is shared in the ratio of their contributions. Total profit is GH¢ 9,000.00.

Richard's manager's share $= \frac{1}{3} \times \text{GH¢ } 9,000.00 = \text{GH¢ } 3,000.00$.

Remaining profit $= \text{GH¢ } 9,000.00 - \text{GH¢ } 3,000.00 = \text{GH¢ } 6,000.00$.

Joyce's contribution : Richard's contribution $= \text{GH¢ } 10,000.00 : \text{GH¢ } 5,000.00 = 2 : 1$.
Total ratio parts $= 2 + 1 = 3$.

• (i) How much did Joyce receive? Joyce's share from remaining profit $= \frac{2}{3} \times \text{GH¢ } 6,000.00 = \text{GH¢ } 4,000.00$. Joyce received $\boxed{\text{GH¢ } 4,000.00}$.

• (ii) How much did Richard receive in total? Richard's share from remaining profit $= \frac{1}{3} \times \text{GH¢ } 6,000.00 = \text{GH¢ } 2,000.00$. Richard's total receive = Richard's manager's share + Richard's share from remaining profit Richard's total receive $= \text{GH¢ } 3,000.00 + \text{GH¢ } 2,000.00 = \text{GH¢ } 5,000.00$. Richard received in total $\boxed{\text{GH¢ } 5,000.00}$.

3. (a)
Asana's original daily wage was GH¢ 25.00. Her daily wage increased by 10%. She worked for 30 days.

Increase $= 10\% \text{ of GH¢ } 25.00 = 0.10 \times \text{GH¢ } 25.00 = \text{GH¢ } 2.50$.

New daily wage $= \text{GH¢ } 25.00 + \text{GH¢ } 2.50 = \text{GH¢ } 27.50$.

Total paid $= \text{New daily wage} \times \text{Number of days worked}$
Total paid $= \text{GH¢ } 27.50 \times 30 = \text{GH¢ } 825.00$.
She will be paid $\boxed{\text{GH¢ } 825.00}$.

3. (b)
The diagram shows the floor of a room with its dimensions.

Let's determine the missing dimensions first:
The total width is 8 m. The bottom segment is 5 m. So, the top inner horizontal segment is $8 \text{ m} - 5 \text{ m} = 3 \text{ m}$.
The total height on the left is 5 m. The right vertical segment is 3 m. So, the bottom inner vertical segment is $5 \text{ m} - 3 \text{ m} = 2 \text{ m}$.

• (i) Find the perimeter: The perimeter is the sum of all the outer sides. Perimeter $= 8 \text{ m} + 3 \text{ m} + (8-5) \text{ m} + (5-3) \text{ m} + 5 \text{ m} + 5 \text{ m}$ Perimeter $= 8 \text{ m} + 3 \text{ m} + 3 \text{ m} + 2 \text{ m} + 5 \text{ m} + 5 \text{ m}$ Perimeter $= 26 \text{ m}$. The perimeter is $\boxed{26 \text{ m}}$.

• (ii) Find the area: We can divide the L-shaped floor into two rectangles. Method 1: Divide into a top rectangle and a bottom-left rectangle. Rectangle 1 (top): Length $= 8 \text{ m}$, Width $= 3 \text{ m}$. Area$_1 = 8 \text{ m} \times 3 \text{ m} = 24 \text{ m}^2$. Rectangle 2 (bottom-left): Length $= 5 \text{ m}$, Width $= (5-3) \text{ m} = 2 \text{ m}$. Area$_2 = 5 \text{ m} \times 2 \text{ m} = 10 \text{ m}^2$. Total Area $= \text{Area}_1 + \text{Area}_2 = 24 \text{ m}^2 + 10 \text{ m}^2 = 34 \text{ m}^2$.

  Method 2: Divide into a large left rectangle and a small top-right rectangle.
  Rectangle 1 (left): Length $=