In construction, all the lines and arcs that lead to the final results should be left visible, not to be erased. (A) Erased (B) Seen (C) Drawn (D) None of the above

$$14 \div 2 = 7 \text{ remainder } 0$$ $$7 \div 2 = 3 \text{ remainder } 1$$ $$3 \div 2 = 1 \text{ remainder } 1$$ $$1 \div 2 = 0 \text{ remainder } 1$$

The binary representation of 29 is $11101_2$.

• (A) $\boxed{11101}$

30. How many liters of water does a $5\text{m} \times 4\text{m} \times 3\text{m}$ tank hold?

$$\text{Volume} = \text{length} \times \text{width} \times \text{height}$$ $$\text{Volume} = 5 \text{ m} \times 4 \text{ m} \times 3 \text{ m} = 60 \text{ m}^3$$

Recall that $1 \text{ m}^3 = 1000 \text{ liters}$.

$$\text{Volume in liters} = 60 \text{ m}^3 \times 1000 \frac{\text{liters}}{\text{m}^3} = 60000 \text{ liters}$$

• (A) $\boxed{60000 \text{ liters}}$

31. When data is collected without being processed, it is known as:

• (C) Raw Data Raw data refers to information that has been collected but not yet processed, analyzed, or organized.

32. A rectangle has a length of 15 cm and a width of 6 cm. What is its area?

$$\text{Area} = 15 \text{ cm} \times 6 \text{ cm} = 90 \text{ cm}^2$$

• (A) $\boxed{90 \text{ cm}^2}$

33. A rectangular piece of land measure 57m by 42m. What is the perimeter of the land?

$$\text{Perimeter} = 2 \times (57 \text{ m} + 42 \text{ m})$$ $$\text{Perimeter} = 2 \times (99 \text{ m})$$ $$\text{Perimeter} = 198 \text{ m}$$

• (A) $\boxed{198 \text{m}}$

34. Calculate the perimeter of a square with a side length of 9 cm.

$$\text{Perimeter} = 4 \times 9 \text{ cm} = 36 \text{ cm}$$

• (C) $\boxed{36 \text{cm}}$

35. Which is not among the reasons for collecting of data?

• (D) For exercise Data is collected for various purposes like planning, decision-making, and prediction, but not for physical exercise.

36. If the volume of a container is $200 \text{cm}^3$, while its area is $50 \text{cm}^2$, what is height of the container?

$$200 \text{ cm}^3 = 50 \text{ cm}^2 \times \text{Height}$$ $$\text{Height} = \frac{200 \text{ cm}^3}{50 \text{ cm}^2}$$ $$\text{Height} = 4 \text{ cm}$$

• (A) $\boxed{4 \text{cm}}$

37. A triangle whose angles are less than $90^\circ$ is called...

• (D) Acute angle triangle An acute angle triangle is a triangle where all three interior angles are less than $90^\circ$.

38. What instrument is commonly used to construct perpendicular and parallel lines?

• (D) All of the above A ruler (straightedge) and compass are fundamental for classical geometric constructions of perpendicular and parallel lines. A protractor can also be used to draw a $90^\circ$ angle for a perpendicular line.

39. What is the perimeter of a square with side length 6 cm?

$$\text{Perimeter} = 4 \times 6 \text{ cm} = 24 \text{ cm}$$

• (C) $\boxed{24 \text{cm}}$

40. The following are the instrument found in mathematical set except

• (A) Razor blade A standard mathematical set (geometry box) typically includes a set square, protractor, and compass, but not a razor blade.

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SECTION B: ESSAY

1(A) Write 3025 in Roman numerals.

$$3000 = MMM$$ $$20 = XX$$ $$5 = V$$

$$3025 = \boxed{MMMXXV}$$

1(B) What are adjacent angles?
Adjacent angles are two angles that share a common vertex and a common side, but do not overlap.

1(C) What is the value of 8 in the figure 6.0657?
The digit 8 is not present in the figure 6.0657.

2(A) Express 3450cm to metres.

$$3450 \text{ cm} = \frac{3450}{100} \text{ m}$$ $$3450 \text{ cm} = \boxed{34.5 \text{ m}}$$

2(B) If the volume of a cuboid is $150 \text{cm}^3$, calculate the height given that the length is 10cm and the breadth is 5cm.

$$150 \text{ cm}^3 = 50 \text{ cm}^2 \times \text{height}$$ $$\text{height} = \frac{150 \text{ cm}^3}{50 \text{ cm}^2}$$ $$\text{height} = \boxed{3 \text{ cm}}$$

3(A) Construct a parallelogram ABCD with AB = 3cm, BC = 4cm and angle B = 70 degrees.
To construct the parallelogram:

1. Draw a line segment AB of length 3 cm.
2. At point B, use a protractor to draw a ray such that the angle with AB is $70^\circ$.
3. Along this ray, measure and mark point C such that BC is 4 cm.
4. From point A, draw an arc with a radius of 4 cm (equal to BC).
5. From point C, draw an arc with a radius of 3 cm (equal to AB).
6. The intersection of these two arcs is point D.
7. Join AD and CD to complete the parallelogram ABCD.

3(B) Express 504 as a product of its prime factors.

$$504 \div 2 = 252$$ $$252 \div 2 = 126$$ $$126 \div 2 = 63$$

$$63 \div 3 = 21$$ $$21 \div 3 = 7$$

$$504 = 2 \times 2 \times 2 \times 3 \times 3 \times 7 = \boxed{2^3 \times 3^2 \times 7}$$

4(A) Add 15231 and 18162.

$$15231$$ $$+ 18162$$ $$\overline{33393}$$

The sum is $\boxed{33393}$.

4(B) Multiply 23.81 by 8.24.

$$23.81 \times 8.24 = 196.2844$$

The product is $\boxed{196.2844}$.

5(A) If 6 students bought a pen and a book for N50 and N300, respectively, find the total cost of the items.

$$\text{Cost per student} = \text{Cost of pen} + \text{Cost of book}$$ $$\text{Cost per student} = \text{N}50 + \text{N}300 = \text{N}350$$

$$\text{Total cost} = 6 \times \text{Cost per student}$$ $$\text{Total cost} = 6 \times \text{N}350 = \text{N}2100$$

The total cost is $\boxed{\text{N}2100}$.

5(B) Solve, n - 1 = 8.

$$n - 1 = 8$$ $$n - 1 + 1 = 8 + 1$$ $$n = \boxed{9}$$

5(C) Convert 0.075 to fraction in it's lowest form.

Both 75 and 1000 are divisible by 25.

$$\frac{75 \div 25}{1000 \div 25} = \frac{3}{40}$$

The fraction in its lowest form is $\boxed{\frac{3}{40}}$.