Find (i) the amount and (ii) the compound interest of N500,000 for 2 years at 8% per annum

$W = \frac{60}{4} = 15$ weeks.  
The rice would last for $\boxed{\text{15 weeks}}$.

• ii. a family of 6

$W = \frac{60}{6} = 10$ weeks.  
The rice would last for $\boxed{\text{10 weeks}}$.

• iii. a hotel that serves 60 people

The solution is $\boxed{P = 10}$.

Question 3a: Find the sizes of the lettered angles in the following diagram.
The diagram shows a triangle with an altitude drawn from the top vertex to the base.
The square symbol indicates that the line segment is perpendicular to the base, forming a $90^\circ$ angle.
The tick marks on the base indicate that the altitude bisects the base.
When an altitude bisects the base of a triangle, the triangle is an isosceles triangle.
This means the two base angles are equal, and the altitude also bisects the top angle.

Since the triangle is isosceles, the base angles are equal. One base angle is $U$, and the other is $29^\circ$.

Since the triangle is isosceles, the altitude bisects the top angle, so $V = T$.
Consider the right-angled triangle on the right side. The angles are $T$, $90^\circ$, and $29^\circ$.
The sum of angles in a triangle is $180^\circ$.

Since $V = T$, then $V = 61^\circ$.

The placement of $S$ and $74^\circ$ is ambiguous in the diagram. However, if we assume the $74^\circ$ is an angle within the left small triangle, and $S$ is the angle adjacent to the $90^\circ$ angle at the base, this would imply $S=90^\circ$, which is redundant with the square symbol.
Given the common conventions for such diagrams, the $74^\circ$ label is likely intended to be the angle $U$, but this contradicts the isosceles property ($U=29^\circ$).
Assuming the geometric properties (altitude bisects base $\implies$ isosceles triangle) take precedence over potentially misleading numerical labels, we proceed with $U=29^\circ$.
The letter $S$ is placed at the base, to the left of the altitude, adjacent to the $90^\circ$ angle. This is the position of the angle at the foot of the altitude, which is $90^\circ$.
Therefore, $S = 90^\circ$.

The sizes of the lettered angles are:
$U = \boxed{29^\circ}$
$V = \boxed{61^\circ}$
$T = \boxed{61^\circ}$
$S = \boxed{90^\circ}$

Question 3b: Find (i) the amount and (ii) the compound interest of N500,000 for 2 years at 8% per annum.
Given: Principal ($P$) = N500,000, Time ($n$) = 2 years, Rate ($r$) = 8% = 0.08.

The amount is $\boxed{\text{N}583,200}$.

The compound interest is $\boxed{\text{N}83,200}$.

Question 4a: Copy and complete the table below for $y = 3x + 2$.

• For $x = -1$: $3x = 3(-1) = -3$
• For $x = 0$: $3x = 3(0) = 0$
• For $x = 1$: $3x = 3(1) = 3$
• For $x = 2$: $3x = 3(2) = 6$
• For $x = 3$: $3x = 3(3) = 9$

• For $x = -1$: $y = -3 + 2 = -1$
• For $x = 0$: $y = 0 + 2 = 2$
• For $x = 1$: $y = 3 + 2 = 5$
• For $x = 2$: $y = 6 + 2 = 8$
• For $x = 3$: $y = 9 + 2 = 11$

The completed table is: