IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Function-y=mx+c
Topic :Function- Weightage : 21 %
All Questions for Topic : Mappings,Function notation,Linear functions,y=mx+c,Parallel and Perpendicular lines,System of equations/simultaneous equations,Quadratic functions,Algorithms
Question (33 marks)
The line $\rm{y=2 x+1}$ is shown on the coordinate axes below. Vertical line segments can be added between the line and the $\rm{x}$ axis, one unit apart horizontally. In this question, you will investigate areas of different trapeziums formed.
Question (a) : 2 marks
For stage 3 , show that the area of the trapezium is 6 units squared.
▶️Answer/Explanation
Ans:
To show that the area of the trapezium is 6 square units, we can use the formula for the area of a trapezium:
\[ \text{Area} = \frac{1}{2} (a + b) \times h \]
where \( a \) and \( b \) are the lengths of the parallel sides, and \( h \) is the distance between the parallel sides.
In this case, we are given that the lengths of the parallel sides are $5$ and $7$, and the distance between the parallel sides is $1$.
Substituting the given values into the formula, we have:
\[ \text{Area} = \frac{1}{2} (5 + 7) \times 1 \]
Simplifying the expression:
\[ \text{Area} = \frac{1}{2} \times 12 \times 1 \]
\[ \text{Area} = 6 \]
Therefore, the area of the trapezium is indeed 6 square units.
Question (b) : 1 marks
Write down the missing values in the table up to stage 6 .
▶️Answer/Explanation
Ans:
To fill in the missing values in the table up to stage 6:
To calculate the area of the trapezium at stage 5, we can observe that the area is increasing by 2 units at each stage. Thus, we can add 2 to the previous area (8) to find the area at stage 5, which gives us 10.
Similarly, to calculate the area of the trapezium at stage 6, we can add 2 to the previous area (10) to find the area at stage 6, which gives us 12.
Therefore, the missing values in the table are 10 for stage 5 and 12 for stage 6.