Consider the diagrams below: Identify each of them. Find the area of each of the shape.

The area of a circle is given by $A = \pi r^2$. Using $\pi \approx \frac{22}{7}$.
$$
A = \frac{22}{7} \times (3.5 \text{ cm})^2
$$
$$
A = \frac{22}{7} \times (3.5 \times 3.5) \text{ cm}^2
$$
$$
A = \frac{22}{7} \times 12.25 \text{ cm}^2
$$
$$
A = 22 \times 1.75 \text{ cm}^2
$$
$$
A = 38.5 \text{ cm}^2
$$
The area of the circle is $\boxed{38.5 \text{ cm}^2}$.

• For (ii) Rectangle:

The area of a rectangle is given by $A = L \times W$.
$$
A = 8.5 \text{ cm} \times 3.5 \text{ cm}
$$
$$
A = 29.75 \text{ cm}^2
$$
The area of the rectangle is $\boxed{29.75 \text{ cm}^2}$.

2.

a) How many students are in JS3 class?

There are $\boxed{125}$ students in JS3 class.

b) Calculate the mean of the data.

Total students = 125
Number of classes = 7 (A, B, C, D, E, F, G)

The mean of the data is $\boxed{\frac{125}{7} \approx 17.86}$ (rounded to two decimal places).

c) What percentages of the students are in F class?

Students in F class = 15
Total students = 125 (from part a)

$\boxed{12\%}$ of the students are in F class.

3.

a) A book costs N750.00 and a pencil costs N45.00. If Collins wants to buy 6 books and 4 pencils, how much money does he need in total to pay?

Collins needs $\boxed{\text{N}4680.00}$ in total.

b) A man invested N143500.00 at 5% simple interest for 4 years. At the end of the period, how much was his investment altogether?

Principal $P = \text{N}143500.00$
Rate $R = 5\%$
Time $T = 4$ years

His investment altogether was $\boxed{\text{N}172200.00}$.

4.

a) Factorise $x^2 - 4x - 21 = 0$.

The numbers are -7 and 3.

The factorised form is $\boxed{(x - 7)(x + 3) = 0}$, and the solutions are $\boxed{x = 7 \text{ or } x = -3}$.

b) Evaluate $9.95 \times 10^{-4} - 7.3 \times 10^{-5}$ and express your answer on standard form.

Let's convert $7.3 \times 10^{-5}$ to a number with $10^{-4}$.

The result is $\boxed{9.22 \times 10^{-4}}$.