AFOQT Math Knowledge TEST QUESTIONS WITH
100% CORRECT SOLUTIONS
Convert standard form to vertex form (quadratic equation) - ✔✔Complete the square
1. Move c to the left side of equation
2. Divide entire equation by a
3. Take half of the coefficient of x, square that number, and then add the result to both
sides of the equation
4. Convert the right side of the equation to a perfect binomial squared, (x+m)^2
5. Isolate y to put the equation in proper vertex form
Quadratic formula - ✔✔x = -b ± √(b² - 4ac)/2a
In standard form, ax^2 + bx + c, where a, b, and c (Just the numbers) can be plugged into
the quadratic formula to find the x-intercepts, roots, zeros, or solutions.
a formula used to solve all quadratic equations
Discriminant - ✔✔b²-4ac
a function of the coefficients of a polynomial equation whose value gives information
about the roots of the polynomial.
If B^2-4ac=0 - ✔✔1 real root; vertex on the x-axis
If B^2-4ac is positive - ✔✔2 real roots; two x-intercepts
If B^2-4ac is negative - ✔✔0 real roots, 2 complex roots; no x-intercepts
, Pi - ✔✔The ratio of a circle's circumference to its diameter (3.14)
Circumference of a circle - ✔✔2πr
Area of a circle - ✔✔A=πr²
Diameter of a circle - ✔✔2r
A line that passes through the center of the circle, connecting any two points
Secant line - ✔✔A line that cuts across a circle and touches it twice
Chord - ✔✔The part of a secant line that lies within a circle
Tangent - ✔✔A line that touches a circle or any curve at one point is tangent to the
circle or curve. Always exterior to the circle
Arc - ✔✔Any portion of a circle between two points on the circle. Measure in degrees
Length of the arc - ✔✔Linear measurement
Minor arc - ✔✔the small arc between the two points (less than 180 degrees)
Major arc - ✔✔An arc of a circle whose measure is greater than 180 degrees.
100% CORRECT SOLUTIONS
Convert standard form to vertex form (quadratic equation) - ✔✔Complete the square
1. Move c to the left side of equation
2. Divide entire equation by a
3. Take half of the coefficient of x, square that number, and then add the result to both
sides of the equation
4. Convert the right side of the equation to a perfect binomial squared, (x+m)^2
5. Isolate y to put the equation in proper vertex form
Quadratic formula - ✔✔x = -b ± √(b² - 4ac)/2a
In standard form, ax^2 + bx + c, where a, b, and c (Just the numbers) can be plugged into
the quadratic formula to find the x-intercepts, roots, zeros, or solutions.
a formula used to solve all quadratic equations
Discriminant - ✔✔b²-4ac
a function of the coefficients of a polynomial equation whose value gives information
about the roots of the polynomial.
If B^2-4ac=0 - ✔✔1 real root; vertex on the x-axis
If B^2-4ac is positive - ✔✔2 real roots; two x-intercepts
If B^2-4ac is negative - ✔✔0 real roots, 2 complex roots; no x-intercepts
, Pi - ✔✔The ratio of a circle's circumference to its diameter (3.14)
Circumference of a circle - ✔✔2πr
Area of a circle - ✔✔A=πr²
Diameter of a circle - ✔✔2r
A line that passes through the center of the circle, connecting any two points
Secant line - ✔✔A line that cuts across a circle and touches it twice
Chord - ✔✔The part of a secant line that lies within a circle
Tangent - ✔✔A line that touches a circle or any curve at one point is tangent to the
circle or curve. Always exterior to the circle
Arc - ✔✔Any portion of a circle between two points on the circle. Measure in degrees
Length of the arc - ✔✔Linear measurement
Minor arc - ✔✔the small arc between the two points (less than 180 degrees)
Major arc - ✔✔An arc of a circle whose measure is greater than 180 degrees.
