Froggy Jumps
Plane Transformations (uppersixth Science Further maths)Online version
Test your knowledge on transformations in the complex plane!
1
What is a common transformation applied to the complex plane?
2
Which transformation preserves the distance between points in the complex plane?
3
What is the result of a reflection across the real axis in the complex plane?
4
In a dilation transformation, what happens to the distance from the origin?
5
What does a rotation by 90 degrees counterclockwise do to a complex number z?
6
Which transformation can be represented by multiplying a complex number by e^(iθ)?
7
What is the effect of a shear transformation on the complex plane?
8
What type of transformation is a translation in the complex plane?
9
What is the geometric interpretation of multiplying a complex number by a negative?
10
What does the transformation z → az (where a is a complex number) represent?
11
What does the triangle inequality theorem state?
12
Which of the following is a valid triangle according to the triangle inequality?
13
If one side of a triangle is 7 and another is 10, what is the maximum length of the third side?
14
Which inequality represents the triangle inequality for sides a, b, and c?
15
Can a triangle have sides of lengths 2, 2, and 5?
16
What is the minimum length of the third side if two sides are 8 and 6?
17
In a triangle with sides 9, 12, and x, what must x be?
18
Which of these is NOT a consequence of the triangle inequality?
19
If a triangle has sides of lengths 5, 5, and 8, is it valid?
20
What is the relationship between the sides of a triangle?
21
What does arg(z - z1) = θ represent in complex analysis?
22
What does |z - w| represent?
23
In the expression |z - w|, what does '|' denote?
24
What is the least value of |z - w| when arg(z - z1) = θ?
25
If z1 is a fixed point, what does arg(z - z1) = θ imply about z?
26
Which of the following can affect the value of |z - w|?
27
What is the geometric interpretation of arg(z - z1) = θ?
28
If z = re^(iθ), what does r represent?
29
What type of number is z in the context of |z - w|?
30
In the expression |z - w|, which variable is typically fixed?
31
What is direct homothecy?
32
What does the term 'homothetic center' refer to?
33
In indirect homothecy, what happens to the orientation of figures?
34
What is the scale factor in homothecy?
35
Which of the following is NOT a property of homothecy?
36
If a triangle undergoes direct homothecy with a scale factor of 2, what happens to its area?
37
What is the effect of a negative scale factor in indirect homothecy?
38
Which geometric figures can undergo homothecy?
39
What is the relationship between two figures in direct homothecy?
40
In a homothetic transformation, what remains constant?
41
What is the primary focus of the image of a figure in Further Maths?
42
Which mathematical concept is often illustrated by figures?
43
In Further Maths, what does a figure often represent?
44
What type of figures are commonly used in Further Maths?
45
How can figures aid in understanding complex mathematical concepts?
46
What is a common use of figures in Further Maths?
47
Which of the following figures is NOT typically studied in Further Maths?
48
What role do figures play in calculus within Further Maths?
49
Which tool is often used to create figures in Further Maths?
50
What is the significance of the image of a figure in problem-solving?
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