AFOQT SOLVED QUESTIONS WITH CORRECT ANSWERS
distance formula - pg.54
✔✔midpoint formula - ✔✔pg.54
✔✔zeros/roots of a quadratic are the... - ✔✔x intercepts
✔✔standard form of a quadratic - ✔✔Ax^2 + Bx + C
axis of symmetry: x = -b/2a
vertex: pg. 59
✔✔vertex form of a quadratic - ✔✔y = a(x-h)^2 + k
axis of symmetry: x=h
vertex: (h, k)
✔✔The effect of A (first term) on a parabola - ✔✔if negative: opens downward
if positive: opens upward
if a fraction less than 1: wider
if above 1: narrower
✔✔How to convert standard form to vertex form - ✔✔complete the square
1, move c to the left side of the equation
2. divide the entire equation through by a (to make the coefficient of x^2 be 1).
3. Take half of the coefficient of x, square it, and then add it 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 - ✔✔pg. 61
✔✔if (B^2 - 4AC) is 0, + or - then... - ✔✔0: only 1 real root/ vertex on x axis
+: 2 real roots, 2 x intercepts
-: 2 complex roots, 0 x intercepts
✔✔colinear - ✔✔2 points on the same line
✔✔Line segment - ✔✔line with 2 endpoints and a finite length
,✔✔ray - ✔✔line with one endpoint and extends indefinitely in one direction
✔✔line - ✔✔extends indefinitely in both directions
✔✔complementary angles - ✔✔add up to 90
✔✔supplementary angles - ✔✔add up to 180
✔✔convert radians to degrees - ✔✔1 radian = 57.3 degrees
✔✔circumference/area of a circle - ✔✔C = 2*pi*r
A= pi*r^2
pg.65
✔✔secant - ✔✔line that crosses a circle and touches twice
✔✔chord - ✔✔part of the secant line that lies within the circle
✔✔tangent - ✔✔line that touches a circle or any curve at one point
✔✔arc - ✔✔any portion of a circle between two points. measured in degrees
✔✔minor arc - ✔✔less than 180
✔✔major arc - ✔✔greater than 180
✔✔central angle - ✔✔an angle with its vertex at the center of a circle
✔✔sector - ✔✔part of a circle and its interior that is inside the rays of a central angle
✔✔inscribed angle - ✔✔has a vertex on the circle and is formed by two chords
✔✔circumscribed angle - ✔✔rays tangent to the circle and lies on the outside
✔✔formula for measurement of inscribed angle - ✔✔(1/2) x the central angle with the
same points
✔✔formula for measurement of angles outside of the circle - ✔✔pg. 67
✔✔area of a sector - ✔✔pg. 66
✔✔length of an arc - ✔✔pg. 66
, ✔✔formula for angles inside in the circle - ✔✔pg.67
✔✔formula for angle formed by tangent and secant - ✔✔pg. 68
✔✔area of a triangle - ✔✔(1/2)*b*h
✔✔angle bisector - ✔✔extends from the side opposite an angle to bisect that angle
✔✔altitude (triangles) - ✔✔shortest distance from a vertex to a side
✔✔median (triangles) - ✔✔extends from and angle to bisect the opposite side
✔✔centroid - ✔✔where a triangles three medians meet
✔✔orthocenter - ✔✔formed by the intersection of a triangle's 3 altitudes.
✔✔Third side rule - ✔✔if b and c are two sides of a trianle, the the measure of the third
side a must be between the sum of the other two sides and the difference of the other
two sides: c - b < a < c + b
✔✔Special right triangles - ✔✔45-45-90: x, x, root (2)x
30-60-90: x, root (3)x, 2x
✔✔Parallelogram - ✔✔quadrilateral with two pairs of parallel sides
✔✔formula for the sum of interior angles - ✔✔(n-2) * 180
✔✔apothem - ✔✔shortest distance from the polygons center to one of the sides
✔✔area of a polygon - ✔✔(apothem)(perimeter)/2
pg. 76
✔✔SA/Volume of prism/diagonal - ✔✔pg. 78
✔✔SA/Volume of cube - ✔✔pg.78
✔✔SA/Volume of sphere - ✔✔pg. 78
✔✔SA/Volume of cylinder - ✔✔pg. 78
✔✔Volume of cone - ✔✔pg. 78
distance formula - pg.54
✔✔midpoint formula - ✔✔pg.54
✔✔zeros/roots of a quadratic are the... - ✔✔x intercepts
✔✔standard form of a quadratic - ✔✔Ax^2 + Bx + C
axis of symmetry: x = -b/2a
vertex: pg. 59
✔✔vertex form of a quadratic - ✔✔y = a(x-h)^2 + k
axis of symmetry: x=h
vertex: (h, k)
✔✔The effect of A (first term) on a parabola - ✔✔if negative: opens downward
if positive: opens upward
if a fraction less than 1: wider
if above 1: narrower
✔✔How to convert standard form to vertex form - ✔✔complete the square
1, move c to the left side of the equation
2. divide the entire equation through by a (to make the coefficient of x^2 be 1).
3. Take half of the coefficient of x, square it, and then add it 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 - ✔✔pg. 61
✔✔if (B^2 - 4AC) is 0, + or - then... - ✔✔0: only 1 real root/ vertex on x axis
+: 2 real roots, 2 x intercepts
-: 2 complex roots, 0 x intercepts
✔✔colinear - ✔✔2 points on the same line
✔✔Line segment - ✔✔line with 2 endpoints and a finite length
,✔✔ray - ✔✔line with one endpoint and extends indefinitely in one direction
✔✔line - ✔✔extends indefinitely in both directions
✔✔complementary angles - ✔✔add up to 90
✔✔supplementary angles - ✔✔add up to 180
✔✔convert radians to degrees - ✔✔1 radian = 57.3 degrees
✔✔circumference/area of a circle - ✔✔C = 2*pi*r
A= pi*r^2
pg.65
✔✔secant - ✔✔line that crosses a circle and touches twice
✔✔chord - ✔✔part of the secant line that lies within the circle
✔✔tangent - ✔✔line that touches a circle or any curve at one point
✔✔arc - ✔✔any portion of a circle between two points. measured in degrees
✔✔minor arc - ✔✔less than 180
✔✔major arc - ✔✔greater than 180
✔✔central angle - ✔✔an angle with its vertex at the center of a circle
✔✔sector - ✔✔part of a circle and its interior that is inside the rays of a central angle
✔✔inscribed angle - ✔✔has a vertex on the circle and is formed by two chords
✔✔circumscribed angle - ✔✔rays tangent to the circle and lies on the outside
✔✔formula for measurement of inscribed angle - ✔✔(1/2) x the central angle with the
same points
✔✔formula for measurement of angles outside of the circle - ✔✔pg. 67
✔✔area of a sector - ✔✔pg. 66
✔✔length of an arc - ✔✔pg. 66
, ✔✔formula for angles inside in the circle - ✔✔pg.67
✔✔formula for angle formed by tangent and secant - ✔✔pg. 68
✔✔area of a triangle - ✔✔(1/2)*b*h
✔✔angle bisector - ✔✔extends from the side opposite an angle to bisect that angle
✔✔altitude (triangles) - ✔✔shortest distance from a vertex to a side
✔✔median (triangles) - ✔✔extends from and angle to bisect the opposite side
✔✔centroid - ✔✔where a triangles three medians meet
✔✔orthocenter - ✔✔formed by the intersection of a triangle's 3 altitudes.
✔✔Third side rule - ✔✔if b and c are two sides of a trianle, the the measure of the third
side a must be between the sum of the other two sides and the difference of the other
two sides: c - b < a < c + b
✔✔Special right triangles - ✔✔45-45-90: x, x, root (2)x
30-60-90: x, root (3)x, 2x
✔✔Parallelogram - ✔✔quadrilateral with two pairs of parallel sides
✔✔formula for the sum of interior angles - ✔✔(n-2) * 180
✔✔apothem - ✔✔shortest distance from the polygons center to one of the sides
✔✔area of a polygon - ✔✔(apothem)(perimeter)/2
pg. 76
✔✔SA/Volume of prism/diagonal - ✔✔pg. 78
✔✔SA/Volume of cube - ✔✔pg.78
✔✔SA/Volume of sphere - ✔✔pg. 78
✔✔SA/Volume of cylinder - ✔✔pg. 78
✔✔Volume of cone - ✔✔pg. 78
