Practice IBA Mathematics questions with answers and explanations.
Choose an option to check your answer.
The three interior angles of every Euclidean triangle sum to 180°.
This is a fundamental angle property.
Choose an option to check your answer.
The quadratic factors as (x - 2)(x - 3) = 0.
Therefore, x is 2 or 3.
Choose an option to check your answer.
Triangle angles sum to 180°.
The third angle is 180° - 45° - 65° = 70°.
Choose an option to check your answer.
The discriminant is b² - 4ac.
Here it is 4² - 4(1)(1) = 16 - 4 = 12.
Choose an option to check your answer.
A zero discriminant makes the square-root term in the formula zero.
Both solutions therefore coincide.
Choose an option to check your answer.
Subtract 7 from both sides of the equation.
This gives x = 19 - 7 = 12.
Choose an option to check your answer.
Divide both sides by the coefficient 3.
Thus, x = 27 ÷ 3 = 9.
Choose an option to check your answer.
Subtract 5 to get 2x = 12.
Dividing by 2 gives x = 6.
Choose an option to check your answer.
Move variable terms to one side and constants to the other.
Then 3x = 15, so x = 5.
Choose an option to check your answer.
Multiply both sides by 4.
Thus, x = 7 × 4 = 28.
Choose an option to check your answer.
Adding the equations gives 2x = 14, so x = 7.
Substituting into x + y = 10 gives y = 3.
Choose an option to check your answer.
Substitute x = 2 to obtain 4 + 3y = 13.
Then 3y = 9, so y = 3.
