IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Algebra-Changing the subject of the equation
Topic :Algebra- Weightage : 21 %
All Questions for Topic : Fcatorizing Quadratic Expressions,Solving Quadratic Expressions,Changing the subject of the equation
Question (30 marks)
In this question, you will investigate areas of trapeziums.
The parabola $y=x(2-x)$ is shown in the graph below. Different sized isosceles trapeziums are drawn inside the parabola.
Question (a) : 2 marks
Write down the missing values in the table.
▶️Answer/Explanation
Ans:
Question (b) : 2 marks
Describe, in words, two patterns for $L$.
▶️Answer/Explanation
Ans:
Here are two patterns for the longer base $L$ based on the given table:
Arithmetic Sequence: The values of $L$ form an arithmetic sequence where each term is obtained by adding a constant difference to the previous term. In this case, the constant difference is 2. Starting from the initial value of $L = 4$, each subsequent value is obtained by adding 2. So the pattern is that $L$ increases by 2 for each stage, forming an arithmetic sequence.
Even Numbers Pattern: Another pattern we observe is that the values of $L$ are all even numbers. Starting from the initial value of $L = 4$, each subsequent value is obtained by adding 2, which results in even numbers. This pattern of increasing even numbers continues throughout the stages.
To summarize, the two patterns for the longer base $L$ are that it increases by 2 in an arithmetic sequence and that it is directly proportional to the stage number, being twice the value of $n$.