NCSSM PLACEMENT TEST Questions And Answers
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Angles - ANSWER -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 - ANSWER -share a common vertex, a common side, but not
common interior points.
Complementary angles - ANSWER -2 angles when added together that equal 90
degrees.
They do not have to be adjacent angles.
Supplementary angles - ANSWER -2 angles when added together that equal 180
degrees.They do not have to be adjacent angles.
Vertical angles - ANSWER -vertical angles are congruent.
Alternate interior angles - ANSWER -alternate interior angles are congruent.
Corresponding angles - ANSWER -corresponding angles are congruent.
Sum of the angles in a triangle - ANSWER -the 3 angles of a triangle add up to
180 degrees.
Triangles classified by sides - ANSWER -scalene triangles have no equal sides.
isosceles triangles have at least 2 equal sides.
equilateral triangles have 3 equal sides.
Triangles classified by angles - ANSWER -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 - ANSWER -the exterior angle of a triangle equals the
sum of the 2 opposite interior angles.
Isosceles triangles - ANSWER -sides opposite congruent angles are congruent.
angles opposite congruent sides are congruent.
,Triangle inequality theorem - ANSWER -the sum of 2 sides of a triangle must be
greater than the 3rd side.
Mid segment of a triangle - ANSWER -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 - ANSWER -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 - ANSWER -bisects an angle into 2 congruent angles.
they meet in a triangle at a point called the incenter.
Altitude - ANSWER -makes a right angle with the opposite side.
they meet in a triangle at a point called the orthocenter.
Perpendicular bisector - ANSWER -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 - ANSWER -angles in similar (∼) triangles are congruent.
sides are in proportion.
angles are in a proportion of one to one. (1:1)
Proving triangles similar - ANSWER -need only 2 angles to be congruent to probe
2 triangles similar.
Proving triangles congruent - ANSWER -can not be angle angle side (A.S.S.) or
side side angle(S.S.A.).
C.P.C.T.C. - ANSWER -corresponding parts of congruent triangles are congruent.
Pythagorean theorem - ANSWER -a squared plus b squared equals c squared.
the hypotenuse is always c.
Proving right triangles congruent - ANSWER -hypotenuse leg.
Right triangle ratios - ANSWER -
, Slope - ANSWER -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 - ANSWER -y minus y one equals slope (m) times x
minus x one.
Slope intercept form of a line - ANSWER -y equals slope (m) times x plus the y
intercept (b)
Slope formula - ANSWER -y two minus y one divided by x two minus x one.
rise over run.
Distance formula - ANSWER -the square root of x two minus x one squared plus
y two minus y one squared.
Midpoint formula - ANSWER -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 - ANSWER
-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 - ANSWER -y must be positive and
isolated on one side of the equation.
Slopes of parallel lines - ANSWER -have the same slope and a different y
intercept.
Slopes of perpendicular lines - ANSWER -the slopes are negative reciprocals.
to find the negative reciprocal make the slope a fraction, flip it, and change the
sign.
Parallel and perpendicular lines - ANSWER -
Axis of symmetry - ANSWER -the equation for axis of symmetry is x equals
negative b divided by two times a.
, Surface area of a cylinder - ANSWER -2 times pi times radius times the sum of
the height and radius.
Volume of a cylinder - ANSWER -pi times radius squared times the height.
Surface area of a rectangular prism - ANSWER -2 times the sum of the length
times the width, the length times the height. and the width times the height.
Volume of a rectangular prism - ANSWER -length times width times height.
Volume of a cone - ANSWER -one third times pi times the radius squared times
the height.
Volume of a pyramid - ANSWER -one third times the area of the base times the
height.
the base could be a triangle, rectangle, or square
Surface area of a sphere - ANSWER -4 times pi times the radius squared.
Volume of a sphere - ANSWER -four thirds times pi times the radius to the thrid
power.
Lateral surface area of a cylinder - ANSWER -2 times pi times the radius times
the height.
Lateral surface area of a cone - ANSWER -pi times the radius times the slant
height.
Polygons - ANSWER -a triangle has 3 sides. a quadrilateral has 4 sides. a
pentagon has 5 sides. a hexagon has 6 sides. a octagon has 8 sides. a decagon has
10 sides.
Formula for angles of polygons - ANSWER -the sum of the interior angles equals
the number of sides minus 2 times 180 degrees.
the sum of the exterior angles equal 360 degrees.
Perimeter - ANSWER -distance around the outside of a polygon.
Parallelograms - ANSWER -opposite sides are parallel.
opposite sides and angles are congruent.
Verified 100% Correct|latest updates| Graded A+
Angles - ANSWER -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 - ANSWER -share a common vertex, a common side, but not
common interior points.
Complementary angles - ANSWER -2 angles when added together that equal 90
degrees.
They do not have to be adjacent angles.
Supplementary angles - ANSWER -2 angles when added together that equal 180
degrees.They do not have to be adjacent angles.
Vertical angles - ANSWER -vertical angles are congruent.
Alternate interior angles - ANSWER -alternate interior angles are congruent.
Corresponding angles - ANSWER -corresponding angles are congruent.
Sum of the angles in a triangle - ANSWER -the 3 angles of a triangle add up to
180 degrees.
Triangles classified by sides - ANSWER -scalene triangles have no equal sides.
isosceles triangles have at least 2 equal sides.
equilateral triangles have 3 equal sides.
Triangles classified by angles - ANSWER -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 - ANSWER -the exterior angle of a triangle equals the
sum of the 2 opposite interior angles.
Isosceles triangles - ANSWER -sides opposite congruent angles are congruent.
angles opposite congruent sides are congruent.
,Triangle inequality theorem - ANSWER -the sum of 2 sides of a triangle must be
greater than the 3rd side.
Mid segment of a triangle - ANSWER -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 - ANSWER -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 - ANSWER -bisects an angle into 2 congruent angles.
they meet in a triangle at a point called the incenter.
Altitude - ANSWER -makes a right angle with the opposite side.
they meet in a triangle at a point called the orthocenter.
Perpendicular bisector - ANSWER -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 - ANSWER -angles in similar (∼) triangles are congruent.
sides are in proportion.
angles are in a proportion of one to one. (1:1)
Proving triangles similar - ANSWER -need only 2 angles to be congruent to probe
2 triangles similar.
Proving triangles congruent - ANSWER -can not be angle angle side (A.S.S.) or
side side angle(S.S.A.).
C.P.C.T.C. - ANSWER -corresponding parts of congruent triangles are congruent.
Pythagorean theorem - ANSWER -a squared plus b squared equals c squared.
the hypotenuse is always c.
Proving right triangles congruent - ANSWER -hypotenuse leg.
Right triangle ratios - ANSWER -
, Slope - ANSWER -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 - ANSWER -y minus y one equals slope (m) times x
minus x one.
Slope intercept form of a line - ANSWER -y equals slope (m) times x plus the y
intercept (b)
Slope formula - ANSWER -y two minus y one divided by x two minus x one.
rise over run.
Distance formula - ANSWER -the square root of x two minus x one squared plus
y two minus y one squared.
Midpoint formula - ANSWER -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 - ANSWER
-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 - ANSWER -y must be positive and
isolated on one side of the equation.
Slopes of parallel lines - ANSWER -have the same slope and a different y
intercept.
Slopes of perpendicular lines - ANSWER -the slopes are negative reciprocals.
to find the negative reciprocal make the slope a fraction, flip it, and change the
sign.
Parallel and perpendicular lines - ANSWER -
Axis of symmetry - ANSWER -the equation for axis of symmetry is x equals
negative b divided by two times a.
, Surface area of a cylinder - ANSWER -2 times pi times radius times the sum of
the height and radius.
Volume of a cylinder - ANSWER -pi times radius squared times the height.
Surface area of a rectangular prism - ANSWER -2 times the sum of the length
times the width, the length times the height. and the width times the height.
Volume of a rectangular prism - ANSWER -length times width times height.
Volume of a cone - ANSWER -one third times pi times the radius squared times
the height.
Volume of a pyramid - ANSWER -one third times the area of the base times the
height.
the base could be a triangle, rectangle, or square
Surface area of a sphere - ANSWER -4 times pi times the radius squared.
Volume of a sphere - ANSWER -four thirds times pi times the radius to the thrid
power.
Lateral surface area of a cylinder - ANSWER -2 times pi times the radius times
the height.
Lateral surface area of a cone - ANSWER -pi times the radius times the slant
height.
Polygons - ANSWER -a triangle has 3 sides. a quadrilateral has 4 sides. a
pentagon has 5 sides. a hexagon has 6 sides. a octagon has 8 sides. a decagon has
10 sides.
Formula for angles of polygons - ANSWER -the sum of the interior angles equals
the number of sides minus 2 times 180 degrees.
the sum of the exterior angles equal 360 degrees.
Perimeter - ANSWER -distance around the outside of a polygon.
Parallelograms - ANSWER -opposite sides are parallel.
opposite sides and angles are congruent.
