Equations etc Flashcards
Area of a Circle
πr²
Circumference of a circle
2πr
Arc length
(Beta)
——- x 2πr
(360)
Area of a parallelogram
base x perpendicular height
Area of a trapezium
1/2(a+b)h
volume of a prism
area x cross section x length
volume of a pyramid
1
— x area of base x h
3
volume of a sphere
4
—- x πr³
3
curved surface area
πrl
volume of a cone
1
— x πr ² x h
3
Area of a triangle
1/2 x base x height
Area of a triangle (when c is between a and b)
1/2 x a x b x sin(C)
Cosine rule (When to use)
find an angle when given 3 sides or when given 2 sides and 1 angle
Sine rule (when to use)
find a length given 2 sides and 1 side or find an angle given 2 sides and 1 angle
interior angle + exterior angle
180 Degrees
Exterior angle
360
——
n
speed
speed= distance
————
Time
Density
Density= Mass
———
Volume
Pressure
pressure= Force
———
Area
Area of a sector of a circle
(BÊTA/360)xPI x rSQUARED
Circle theorem for angle at centre or circumference
«The angle si tended at the centre is twice that sub tended at the circumference by the same arc/chord”
Angle at circumference with Diameter
“Angle subtended at circumference by the diameter is 90 degrees”
Angles at circumference by arc or chord
“Angles subtended at the circumference by the same arc/cord are equal”
Opposite angles in a cyclic quadrilateral
“Opposite angles in a cyclic quadrilateral add up to 180”
Alternate segment Theorem
“Angle between a chord and tangent is the same as an angle subtended by that chord at the circumference in an alternate segment”
Radius and tangent rule
“Radius is perpendicular to the tangent”
Radius perpendicular to the chord rule
“When the radius is perpendicular to the chord, it bisects that chord”
Perpendicular bisector of a chord and the diameter
“The perpendicular bisector of a chord is the diameter of the circle”
Tangents at the same point
“Two tangents drawn from the same point are equal in length”
Angles around a point…
Sum up to 360 degrees
Angles on a straight line…
Sum to 180 degrees
Opposite angles are…
Equal
Parallel lines: alternate angles are..
Equal
Parallel lines: corresponding angles are..
Equal
Parallel lines: co interior angles…
Add up to 180
2D shapes: Polygons
Interior angle + exterior angle =
180 degrees
2D shapes: Polygons
Total exterior angles of an N-sided polygon =
360 degrees
2D shapes: Polygons
Total interior angles of an n sided polygon =
180(n-2)
2D shapes: Polygons
One exterior angle of a regular n sided polygon =
360/n
2D shapes: Polygons
One interior angle of a regular n sided polygon =
180(n-2)
————-
n
ASF =
LSFsquared
VSF=
LSFcubed
Reflection transformation
State “reflection” and the line of symmetry
Rotation transformation
State “rotation” and the centre, angle and direction of rotation
Translation transformation
State “translation” and the VECTOR it’s shifted by
Enlargement transformation
State “enlargement” and the centre of enlargement and scale factor
F(x + t) + s
Becomes..
Translation by vector
-t
(S)
Af(x)
Stretch by scale factor a in the y direction
F(ax)
Stretch by scale factor 1/a in the x direction
-f(x)
Reflection in the x axis
F(-x)
Reflection in the y axis
