NCSSM PLACEMENT TEST WITH COMPLETE
SOLUTIONS 100% 2024 latest update
Tangent
intersects a circle in only 1 place.
Secant
intersects a circle in 2 places.
Intersection of a tangent and a radius
form right angles when they intersect.
Equation of a circle
x minus h squared plus y minus k squared equals radius squared.
Circumference of a circle
2 times pi times radius or pi times diameter.
Area of a circle
pi times radius squared.
Central angle
is equal to its intercepted arc.
Inscribed angle
is equal to ½ its intercepted arc.
Angle formed by 2 chords intersecting in a circle
is equal to the sum of the arcs divided by 2.
Angle formed by 2 secants
is equal to the major arc minus the minor arc divided by 2.
Angle formed by a secant and a tangent
is equal to the major arc minus the minor arc divided by 2.
Angle formed by two tangents
is equal to the major arc minus the minor arc divided by 2.
Lengths of 2 intersecting chords
part of the first chord times the other part of the first chord equals a part of the second chord times
the other part of the second chord.
Lengths of an intersecting diameter and chord that meet at right angles (perpendicular)
,if a diameter meets a chord at a right angle (perpendicular), the diameter divides the chord into 2
equal parts.
Lengths of 2 intersecting secants
the whole length of the first secant times the outside length of the first secant equals the whole
length of the second secant times the outside length of the second secant.
Lengths of an instersecting secant and tangent
the whole length of the first secant times the outside length of the first secant equals the length of
the tangent squared.
Lengths of intersecting tangents
Tangents to a circle sharing a common vertex are equal.
Angles
acute angles are less than 90 degrees. Right angles are 90 degrees. obtuse angles are between 90 and
180 degrees. Straight angles are 180 degrees and reflex angles are greater than 180 degrees.
Adjacent angles
share a common vertex, a common side, but not common interior points.
Complementary angles
2 angles when added together that equal 90 degrees.
They do not have to be adjacent angles.
Supplementary angles
2 angles when added together that equal 180 degrees.They do not have to be adjacent angles.
Vertical angles
vertical angles are congruent.
Alternate interior angles
alternate interior angles are congruent.
Corresponding angles
corresponding angles are congruent.
Sum of the angles in a triangle
the 3 angles of a triangle add up to 180 degrees.
Triangles classified by sides
scalene triangles have no equal sides.
isosceles triangles have at least 2 equal sides.
equilateral triangles have 3 equal sides.
,Triangles classified by angles
acute triangles have 3 acute angles.
right triangles have a 90 degree and 2 acute angles.
obtuse triangles have an obtuse and 2 acute angles.
Exterior angle of a triangle
the exterior angle of a triangle equals the sum of the 2 opposite interior angles.
Isosceles triangles
sides opposite congruent angles are congruent.
angles opposite congruent sides are congruent.
Triangle inequality theorem
the sum of 2 sides of a triangle must be greater than the 3rd side.
Mid segment of a triangle
a mid segment connects the midpoint of 2 sides of a triangle and is equal to ½ the side not containing
the 2 midpoints.
Median
bisects the opposite side into 2 congruent line segments.
they meet in a triangle at a point called the centroid.
median segments are in a ratio of 2 to 1.
Angle bisector
bisects an angle into 2 congruent angles.
they meet in a triangle at a point called the incenter.
Altitude
makes a right angle with the opposite side.
they meet in a triangle at a point called the orthocenter.
Perpendicular bisector
bisects and makes a right angle with a side of a triangle.They meet in a triangle at a point called the
circumcenter.
Similar triangles
angles in similar (∼) triangles are congruent.
sides are in proportion.
angles are in a proportion of one to one. (1:1)
Proving triangles similar
need only 2 angles to be congruent to probe 2 triangles similar.
Proving triangles congruent
, can not be angle angle side (A.S.S.) or side side angle(S.S.A.).
C.P.C.T.C.
corresponding parts of congruent triangles are congruent.
Pythagorean theorem
a squared plus b squared equals c squared.
the hypotenuse is always c.
Proving right triangles congruent
hypotenuse leg.
Right triangle ratios
Slope
from left to right. up the hill is positive slope. down the hill is negative slope. a horizontal line has 0
slope and a verical line as an undefined slope.
Point slope form of a line
y minus y one equals slope (m) times x minus x one.
Slope intercept form of a line
y equals slope (m) times x plus the y intercept (b)
Slope formula
y two minus y one divided by x two minus x one.
rise over run.
Distance formula
the square root of x two minus x one squared plus y two minus y one squared.
Midpoint formula
x one plus x two divided by two is the x coordinate.
y one plus y two divided by two is the y coordinate.
Find the endpoint of a line given the midpoint and the other endpoint
the integers added to the coordinates of C to get the coordinates of M are added to the coordinates
of M to get the coordinates of D.
Finding the slope and y intercept of a line
y must be positive and isolated on one side of the equation.
Slopes of parallel lines
have the same slope and a different y intercept.
SOLUTIONS 100% 2024 latest update
Tangent
intersects a circle in only 1 place.
Secant
intersects a circle in 2 places.
Intersection of a tangent and a radius
form right angles when they intersect.
Equation of a circle
x minus h squared plus y minus k squared equals radius squared.
Circumference of a circle
2 times pi times radius or pi times diameter.
Area of a circle
pi times radius squared.
Central angle
is equal to its intercepted arc.
Inscribed angle
is equal to ½ its intercepted arc.
Angle formed by 2 chords intersecting in a circle
is equal to the sum of the arcs divided by 2.
Angle formed by 2 secants
is equal to the major arc minus the minor arc divided by 2.
Angle formed by a secant and a tangent
is equal to the major arc minus the minor arc divided by 2.
Angle formed by two tangents
is equal to the major arc minus the minor arc divided by 2.
Lengths of 2 intersecting chords
part of the first chord times the other part of the first chord equals a part of the second chord times
the other part of the second chord.
Lengths of an intersecting diameter and chord that meet at right angles (perpendicular)
,if a diameter meets a chord at a right angle (perpendicular), the diameter divides the chord into 2
equal parts.
Lengths of 2 intersecting secants
the whole length of the first secant times the outside length of the first secant equals the whole
length of the second secant times the outside length of the second secant.
Lengths of an instersecting secant and tangent
the whole length of the first secant times the outside length of the first secant equals the length of
the tangent squared.
Lengths of intersecting tangents
Tangents to a circle sharing a common vertex are equal.
Angles
acute angles are less than 90 degrees. Right angles are 90 degrees. obtuse angles are between 90 and
180 degrees. Straight angles are 180 degrees and reflex angles are greater than 180 degrees.
Adjacent angles
share a common vertex, a common side, but not common interior points.
Complementary angles
2 angles when added together that equal 90 degrees.
They do not have to be adjacent angles.
Supplementary angles
2 angles when added together that equal 180 degrees.They do not have to be adjacent angles.
Vertical angles
vertical angles are congruent.
Alternate interior angles
alternate interior angles are congruent.
Corresponding angles
corresponding angles are congruent.
Sum of the angles in a triangle
the 3 angles of a triangle add up to 180 degrees.
Triangles classified by sides
scalene triangles have no equal sides.
isosceles triangles have at least 2 equal sides.
equilateral triangles have 3 equal sides.
,Triangles classified by angles
acute triangles have 3 acute angles.
right triangles have a 90 degree and 2 acute angles.
obtuse triangles have an obtuse and 2 acute angles.
Exterior angle of a triangle
the exterior angle of a triangle equals the sum of the 2 opposite interior angles.
Isosceles triangles
sides opposite congruent angles are congruent.
angles opposite congruent sides are congruent.
Triangle inequality theorem
the sum of 2 sides of a triangle must be greater than the 3rd side.
Mid segment of a triangle
a mid segment connects the midpoint of 2 sides of a triangle and is equal to ½ the side not containing
the 2 midpoints.
Median
bisects the opposite side into 2 congruent line segments.
they meet in a triangle at a point called the centroid.
median segments are in a ratio of 2 to 1.
Angle bisector
bisects an angle into 2 congruent angles.
they meet in a triangle at a point called the incenter.
Altitude
makes a right angle with the opposite side.
they meet in a triangle at a point called the orthocenter.
Perpendicular bisector
bisects and makes a right angle with a side of a triangle.They meet in a triangle at a point called the
circumcenter.
Similar triangles
angles in similar (∼) triangles are congruent.
sides are in proportion.
angles are in a proportion of one to one. (1:1)
Proving triangles similar
need only 2 angles to be congruent to probe 2 triangles similar.
Proving triangles congruent
, can not be angle angle side (A.S.S.) or side side angle(S.S.A.).
C.P.C.T.C.
corresponding parts of congruent triangles are congruent.
Pythagorean theorem
a squared plus b squared equals c squared.
the hypotenuse is always c.
Proving right triangles congruent
hypotenuse leg.
Right triangle ratios
Slope
from left to right. up the hill is positive slope. down the hill is negative slope. a horizontal line has 0
slope and a verical line as an undefined slope.
Point slope form of a line
y minus y one equals slope (m) times x minus x one.
Slope intercept form of a line
y equals slope (m) times x plus the y intercept (b)
Slope formula
y two minus y one divided by x two minus x one.
rise over run.
Distance formula
the square root of x two minus x one squared plus y two minus y one squared.
Midpoint formula
x one plus x two divided by two is the x coordinate.
y one plus y two divided by two is the y coordinate.
Find the endpoint of a line given the midpoint and the other endpoint
the integers added to the coordinates of C to get the coordinates of M are added to the coordinates
of M to get the coordinates of D.
Finding the slope and y intercept of a line
y must be positive and isolated on one side of the equation.
Slopes of parallel lines
have the same slope and a different y intercept.
