Symmetry
Math ⇒ Geometry
Symmetry starts at 6 and continues till grade 12.
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See sample questions for grade 11
A rectangle (not a square) has how many lines of symmetry?
A regular polygon has 15 lines of symmetry. How many sides does it have?
Describe the symmetry of a circle.
Explain the concept of point symmetry with an example.
Explain why the graph of y = x4 is symmetric about the y-axis.
How many axes of symmetry does a regular hexagon have?
How many lines of symmetry does an isosceles triangle have?
If a figure has rotational symmetry of order 6, what is the smallest angle of rotation that maps the figure onto itself?
If a function f(x) satisfies f(-x) = -f(x), what type of symmetry does its graph have?
If a regular polygon has 12 sides, what is the smallest angle of rotation that maps it onto itself?
State the difference between rotational symmetry and reflectional symmetry.
What is the order of rotational symmetry of a regular decagon?
A regular dodecagon (12-sided polygon) is rotated about its center. What is the smallest positive angle (in degrees) through which it can be rotated so that it maps onto itself and does not coincide with its original position?
A regular polygon has an even number of sides. Prove that it has at least two perpendicular axes of symmetry.
Given the function f(x) = x4 + 2x2 + 1, determine whether its graph is symmetric about the y-axis, the origin, both, or neither.
If a function f(x) is even and g(x) is odd, what is the symmetry of the function h(x) = f(x) + g(x)?
Let S be the set of all 2×2 real matrices A such that A is symmetric (A = AT). Describe the geometric interpretation of the set of all such matrices.
Prove that the graph of the function f(x) = x5 - x3 + x is symmetric with respect to the origin.
