| What to create | Quiz |
| Which subject | Mathematics |
| What age group | Year or Grade 9 |
| What topic | Algebra proofs |
| Question types | Open-ended |
| Number of questions | 10 |
| Number of answers | 4 |
| Correct answers | Exactly 1 |
| Show correct answers | |
| Use images (descriptions) | |
| Any other preferences |
Answer each question in the space provided. Show all your work where applicable, and provide detailed explanations to support your answers.
Prove that if ( a = b ), then ( a^2 = b^2 ).
Provide a step-by-step proof for this statement.
Show that the sum of two even integers is always even.
Explain your reasoning with algebraic definitions.
Demonstrate that the product of two odd integers is odd.
Illustrate your proof by defining odd integers first.
Prove that for any integer ( n ), the expression ( n^2 - n ) is even.
Describe your proof and why it holds for all integers.
If two angles are supplementary, prove that the sum of their measures equals ( 180^\circ ).
Support your proof with the definition of supplementary angles.
Show that the difference between any two odd integers is even.
Use algebraic expressions to provide your proof.
Prove that if ( x + 3 = 10 ), then ( x = 7 ).
Detail your proof process step-by-step.
Demonstrate that the square of any integer ( n ) is congruent to ( 0 ) or ( 1 ) modulo ( 4 ).
Provide reasoning and calculations to support your proof.
Explain why the equation ( 4x - 7 = 5x + 1 ) has a unique solution for ( x ).
Offer a proof utilizing properties of equations.
Prove that the distributive property ( a(b + c) = ab + ac ) holds for all real numbers ( a, b, ) and ( c ).
Outline your proof using algebraic manipulation.
Make sure to review each of your proofs for clarity and accuracy. Good luck!