Practice Symmetry (Meta) in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A property of a mathematical object that remains unchanged under a specified transformation — reflection, rotation, translation, or algebraic substitution.
Looks the same from different perspectives or after certain changes.
Showing a random 20 of 50 problems.
Example 1
easyAcross which axis is the parabola symmetric?
Example 2
hardThe number of symmetries (rotations + reflections) of a regular -gon is _____.
Example 3
easyShow that the equation is symmetric about both coordinate axes and the origin. Verify by substituting and its reflections.
Example 4
easyIs an even or odd function?
Example 5
mediumUse symmetry to find the sum of the roots of without factoring fully.
Example 6
easyHow many degrees of rotational symmetry (smallest positive rotation) does an equilateral triangle have?
Example 7
hardUse a symmetry argument to evaluate .
Example 8
easyIs symmetric about the -axis?
Example 9
mediumUse the symmetry of (odd function) and (even function) to simplify: .
Example 10
mediumIs symmetric about the -axis, -axis, both, or neither?
Example 11
challengeA 3D cube has how many rotational symmetries (including identity)? Reason via faces.
Example 12
mediumHow many rotational symmetries (including the identity) does a regular pentagon have?
Example 13
mediumIf and the expression is symmetric, what is its minimum value over real with the given sum?
Example 14
mediumThe polynomial expression is symmetric in . If , what is its value?
Example 15
challengeSuppose satisfies both (even) and (odd) for all . What must be?
Example 16
easyDetermine whether is odd, even, or neither, by testing the symmetry condition.
Example 17
easyIs even, odd, or neither?
Example 18
hardFind all real solutions of by exploiting its symmetry in .
Example 19
easyIs the expression symmetric in and ?
Example 20
mediumUse symmetry to show the graph of is symmetric about the origin.