Maths Higher Flashcards
Alternate angles
In a Z SHAPE and are equal
Corresponding angles
In an F SHAPE and are equal
Co-interior angles
In a C SHAPE and add to 180
Vertically opposite angles
Opposite angles are always equal
Angles in a triangle
Add to 180
Angles in a quadrilateral
Add to 360
Shapes with more than 4 sides
You can always find triangles within them
Sum of interior angles
(Number of sides - 2) x 180
Sum of exterior angles of ANY POLYGON
360 degrees
If the shape was a pentagon
360 divided by 5 (no of sides) = 72
Interior angles + exterior angle =..
180
Arc length =
Angles divided by 360 x pi x diameter of circle
Area of circle
Pi x radius squared
Area of a sector=
Angle divided by 360 x pi x radius squared
Always include the correct units
Area of a trapezium =
1/2 (a+b) x height
A+b are the values shown on the trapezium
Always use bidmas
Area of a triangle
1/2 x a x b x sin(c)
A and B are the two sides
c= the enclosed angle
Units whilst finding the area
Cm squared
Mm squared
Whatever unit it is ALWAYS has to be squared
How do you find bearings
Join the two areas together Draw a north line Measure the angle CLOCKWISE from north Bearings will always have 3 figures 95 degrees = 095 degrees
What are bearings
Bearings are a direction of travel
How do you change the subject
If x= 4w+h and you were making W the subject X=4w-h -h -h X-h = 4w Divide 4 Divide 4 X-h Over = W 4 DO BIDMAS BACKWARDS
Circle theorems
1-5
- The angle in a semi circle is 90 degrees
- The angle at the circumference is half the angle at the centre
- The angles in the same segment from a common chord are equal
- The opposite angles in a cyclic quadrilateral always add to 180
- The angle between the radius and tangent is 90
ALTERNATE CIRCLE THEOREMS
- The angle between the chord and the tangent is equal to opposite angle inside the triangle
- The tangents to a circle from the same point will be equal
- The radius through the midpoint of a chord will bisect the chord at 90 degrees
Iteration
FORMULA= Xn+1 = 3/5 - Xn^3 /5
Replace (n) with the given x0 to find x1
Xo =0 So x1 = 3/5 -0^3 /5 X1 = 0.6 So x2 = 3/5 - 0.6^3 /5 X2 =0.5568 So x3 = 3/5 - 0.5568^3 / 5
Circumference =
Pi x diameter
If asked in terms of n = (ans)n
Density mass and volume
FORMULA= density = mass divided by volume Mass = density x volume Volume = mass divided by density
Ans will always be (ans)unit/cm cubed
Pressure force and area
FORMULA = pressure = force divide by area
Force= pressure x area
Area = force divided by pressure
1m squared = 10000 cm squared
Speed distance time
Speed = distance divided by time distance = speed x time Time = distance divided by speed
Congruent triangles
SSS - side-side-side
When a triangle is shown as 3 sides
ASA- angle side angle
When a triangle has an angle then a side and a angle again
SAS - side angle side
When an triangle is shown with a side angle then a side
RHS - right angle hypotenuse side
When a triangle has a right angle then the hypotenuse then the side again
