MCA 11th grade math prep

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: c² = a² + b².

Front

Define a quadratic equation.

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the difference between a rational and an irrational number?

Back

A rational number can be expressed as a fraction p/q where p and q are integers and q ≠ 0. An irrational number cannot be expressed as a simple fraction; its decimal representation is non-repeating and non-terminating.

Front

Explain the concept of a function.

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output. It can be represented as f(x).

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

Define the term 'asymptote'.

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

What is the difference between permutations and combinations?

Back

Permutations are arrangements of objects where order matters, while combinations are selections of objects where order does not matter.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

Define the term 'discriminant' in the context of quadratic equations.

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

What is the concept of limits in calculus?

Back

A limit is a value that a function approaches as the input approaches some value. It is fundamental in defining derivatives and integrals.