General memory for maths MCQ Flashcards
equation for binomial coefficient nCr + definition
n!/r!(n-r)! the number of ways of choosing r objects from n objects
Sum of angles and single angle of a regular triangle
180, 60
Sum of angles and single angle of a regular square
350, 90
Sum of angles and single angle of a regular pentagon
540, 108
Sum of angles and single angle of a regular hexagon
720, 120
Sum of angles and single angle of a regular heptagon
900, 128.571
Sum of angles and single angle of a regular octagon
1080, 135
Sum of angles and single angle of a regular nonagon
1260, 140
Sum of angles and single angle of a regular decagon
1440, 144
exterior angle equation
360/n
interior angle equation
180(n-2)
area of a parallelogram
base x height
features of a parallelogram
opposite angles are equal, angles next to each other add up to 180 degrees, the diagonals bisect the angles, diagonals bisect into 2 congruent triangles
features of a rhombus
the diagonals are perpendicular, opposite angles are equal, angles adjacent add up to 180 degrees, diagonals bisect the angles and also the rhombus into 2 isosceles triangles/4 congruent right angled triangles
area of a trapezium and angle features
0.5(sum of parallel sides) x height - the interior angles of the parallel sides sum to 180 degrees
features of a kite
diagonals meet at 90 degrees, 2 sides of the same length, the angle made at the point 2 different length sides are made is equal to the opposite side.
Area of a kite
(diagonal x diagonal)/2
define congruence
2 shapes are congruent is they are exactly the same. I.e same shape and size, or if one has the same shape and size as the mirror image of the other
What are the conditions of congruence
FOUR CONDITIONS: SSS, SAS, ASA and RHS (right angle, hypotenuse, side) - have to occur next to each other
What are similar triangles
Similar triangles have the same size angles (congruent angles) and corresponding SIDES in PROPORTION.
what are sectors, segments and arcs (minor vs. major)
a sector is pizza, a segment is a straight slice and an arc is from one point on the perimeter to another. Longer/larger is the major shorter/smaller is the minor,
angle between radius and tangent
90 degrees
circumference and area of a circle
πr^2 and 2πr // πd
opposite angles in a cyclic quadrilateral
add to 180 degrees, the exterior angle of one of these angles is equal to the opposite angle in the cyclic quadrilateral
the angle subtended by two points to the centre is
twice the angle subtended by those 2 points at the circumference
Alternate segment theorem
the angle between a chord and a tangent through on the end points is equal to the angle in alternate segment
angle in a triangle semicircle
90 degrees when the hypotenuse is the diameter
volume and surface area of a cube
volume is a^3 and surface area is 6a^2
volume and surface area of a cuboid dimensions x, y, and z
volume = xyz, SA = 2(xy+xz+yz)
volume of a right angles prism
area of face x length
volume of right angles circular cylinder
πr^2 x height, SA = 2πr^2 + 2πrl
Area of a triangle
1/2absinC // 1/2base x height where height is perpendicular to height
volume and surface area of a sphere
volume 4/3πr^3 and SA 4πr^2
pyramids and cones volume
1/3 x base x perpendicular height
arc length
r x theta when theta is in radians, otherwise π(r)theta/180
convert radians to degrees
Radians to degrees x180/π … Degreens to radians xπ/180
area of a sector
Degrees: πr^2 x theta/360 … Radians: 1/2r^2 theta
sin 30
1/2
sin 60
root3/2
sin 45
root2/2
cos 30
root3/2
cos 60
1/2
cos 45
root2/2
tan 1/2
root3/3
tan 60
root3
tan 45
1
cos 90
0
sin 90
1
tan 90
undefined
sin 0
0
cos 0
1
tan 0
0
