IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Geometry–Enlargement by a rational factor
Topic :Geometry- Weightage : 21 %
All Questions for Topic : Volume and capacity (additional shapes),Enlargement around a given point,Enlargement by a rational factor,Gradients of perpendicular lines,Identical representation of transformations
Question
In this task you will investigate the area and perimeter of squares.
In the two squares below the vertex of the smaller square is the midpoint of the side of the larger square. The side length of the smaller square is 3 units.
Question (a)
Show that the side length of the larger square is $3 \sqrt{2}$ units.
▶️Answer/Explanation
Ans:
$\begin{aligned} & a^2+a^2=3^2 \\ & a^2=\frac{9}{2} \\ &\text{side length = 2a} \Rightarrow2 \times \frac{3}{\sqrt{2}}\end{aligned}$
Question (b)
Write down the missing values in the table up to row 6 .
▶️Answer/Explanation
Ans:
The pattern in the given table seems to involve doubling the area of the square at each stage. Let’s continue filling in the missing values:
The missing values have been filled in by doubling the area from the previous stage.
Question (c)
Describe in words two patterns in the table for area of square (A).
▶️Answer/Explanation
Ans:
There are two distinct patterns in the table for the area of the square (\(A\)):
1. Exponential Growth: The area of the square doubles with each successive stage. This exponential growth is evident in the fact that the area \(A\) is being multiplied by a factor of 2 for each increase in the stage number \(n\).
2. Multiplying by 9: The initial area of the square (\(A = 9\)) is being multiplied by 9 at each stage. This multiplication by 9 results in the new area for the next stage.
These patterns highlight the exponential nature of the growth and the repeated multiplication by 9, leading to the sequence of areas in the table.