Challenging Grade 7 Mathematics Quiz

To find the sum of 15.75, 12.5, and 18.25, we can add them step by step. First, adding 15.75 and 12.5 gives 28.25. Next, adding 28.25 to 18.25 results in 46.5. This methodical addition confirms that the total of these three numbers is indeed 46.5.

To solve the equation 46.5 - 28.5, you subtract 28.5 from 46.5. Performing the calculation: 46.5 - 28.5 equals 18. This result indicates the difference between these two numbers, confirming that the value of 18 is the accurate answer.

To calculate 43 x 180, you can break it down into simpler components. First, multiply 43 by 100 to get 4300, then multiply 43 by 80 to get 3440. Adding these two results together (4300 + 3440) gives you 7740. This method utilizes the distributive property of multiplication, making it easier to handle larger numbers by breaking them into manageable parts.

To find the area of a rectangle, you multiply its length by its width. In this case, the length is 7 meters and the width is 12 meters. Calculating the area involves the formula: Area = Length × Width. Therefore, Area = 7m × 12m = 84 m². This calculation confirms that the area of the rectangle is 84 square meters.

To find the number of girls in the school, first calculate the number of boys. If 40% of 500 learners are boys, that equates to 200 boys (0.40 x 500 = 200). To find the number of girls, subtract the number of boys from the total number of learners: 500 - 200 = 300. Thus, there are 300 girls in the school.

To convert hectometers (hm) to meters (m), you multiply the number of hectometers by 100, since 1 hectometer equals 100 meters. Therefore, for 72.8 hm, the calculation is 72.8 × 100 = 7280 m. This conversion demonstrates the relationship between the two units, allowing for accurate measurement in different contexts.

To find the total area of a swimming pool floor that consists of a rectangular section and a semicircular section, you first calculate the area of the rectangle using the formula length × width. Then, for the semicircle, use the formula (π × radius²) / 2. By adding both areas together, you arrive at the total area. The given answer of 103.25 m² suggests that the dimensions used in the calculations yield this specific total, indicating the rectangle and semicircle dimensions were chosen to fit this area precisely.

To find the perimeter of a rectangle, you use the formula: Perimeter = 2 × (length + width). In this case, the length is 8.5 meters and the width is 6 meters. Adding these together gives 14.5 meters. Multiplying by 2 results in a perimeter of 29 meters. Therefore, the perimeter of the rectangular room is 29 meters.

To determine the number of tiles needed, first convert the area from square meters to square centimeters: 51 m² = 5,100,000 cm². Each tile covers 50 cm x 50 cm, which equals 2,500 cm². Dividing the total area by the area of one tile gives 5,100,000 cm² ÷ 2,500 cm² = 2,040 tiles. Since tiles cannot be purchased in fractions, round up to the nearest whole number, resulting in 204 tiles needed to ensure complete coverage of the area.

To find the area of a triangle, use the formula: Area = (base × height) / 2. In this case, the base is 12 cm and the height is 8 cm. Substituting these values into the formula gives: Area = (12 cm × 8 cm) / 2 = 96 cm² / 2 = 48 cm². Thus, the area of the triangle is 48 cm².

To find the volume of a swimming pool, you multiply its length, width, and depth. In this case, the pool measures 20 meters in length, 10 meters in width, and 2 meters in depth. The calculation is as follows: 20m x 10m x 2m = 400m³. Thus, the total volume of the swimming pool is 400 cubic meters.

To find the number of liters in 400 m³, we use the conversion factor that 1 m³ equals 1000 liters. By multiplying the volume in cubic meters (400 m³) by the conversion factor (1000 liters/m³), we calculate: 400 m³ × 1000 liters/m³ = 400,000 liters. Thus, there are 400,000 liters in 400 m³.

When an angle of 75° is constructed, it means that the measure of the angle is precisely 75 degrees from the reference line. This is a direct representation of the angle itself, indicating that it is neither acute nor obtuse but specifically defined as 75°. Therefore, the angle formed is exactly 75°, matching the construction.