Questions: Question 5 a) What is the value of (-7) ×(-2) ×(-2) ? (1 mark) b) Round 45.567 to 2 decimal places. (1 mark) c) 80 students sit a maths test at school. 60% of them get an A or B grade. If 30 received a B grade, how many received an A. (3 marks) d) A Physical Education teacher wants to hire a dance instructor to conduct some classes. The Instructor charges 200 for each class but offers a discount of 5% if three classes are booked at the same time. What is the cost of 3 classes booked at the same time? (2 marks) e) A square has sides 8 cm long. It has the same area as a rectangle where the long side is 4 times the length of the short side. Use algebra to find the dimensions of the rectangle. (5 marks)

Solution Steps

a) To find the value of $(-7) \times (-2) \times (-2)$, multiply the numbers together, keeping in mind the rules for multiplying negative numbers.

b) To round 45.567 to 2 decimal places, use Python's rounding function.

c) To find how many students received an A, first calculate the total number of students who received an A or B grade, then subtract the number of students who received a B grade.

To find the value of $(-7) \times (-2) \times (-2)$: $$(-7) \times (-2) = 14$$ $$14 \times (-2) = -28$$ Thus, the result is $-28$.

To round $45.567$ to 2 decimal places: $$\text{Rounded value} = 45.57$$

First, calculate the total number of students who received an A or B grade: $$\text{Total students} = 80$$ $$\text{Percentage receiving A or B} = 60\% = 0.6$$ $$\text{Students receiving A or B} = 80 \times 0.6 = 48$$ Next, subtract the number of students who received a B grade: $$\text{Students receiving B} = 30$$ $$\text{Students receiving A} = 48 - 30 = 18$$

Final Answer