Maths Flashcards
What’s the rule for angles on a straight line?
They add up to 180*
What’s the rule for angles around a point?
They add up to 360*
What’s the rule for vertically opposite angles?
They’re equal
What’s the rule for angles in a triangle
They add up to 180*
What does an isosceles triangle have?
Two equal sides/lengths and two equal base angles
What’s a quadrilateral?
Shape with 4 sides
What’s the rule for angles on a quadrilateral?
They add up to 360*
What’s the rule for alternative angles and how do you recognise them?
Alternative angles are equal
They’re an s or z shape with parallel arms
What’s the rule for corresponding angles and how do you recognise them?
Corresponding angles are equal
F shape with parallel arms.
What’s the rule for co-interior angles and how do you recognise them?
They add up to 180*
Look for c shape with parallel arms
When’s a shape regular?
When all sides are the same shape and all angles are the same size
What’s equation for sum of interior angles in any polygon?
(n-2)x180*
An interior angle + an exterior angle =?
180*
What’s the rule for Exterior angles of a polygon?
They add up to 360*
What’s a polygon?
Shape with at least 3 sides and angles
What’s a tangent?
Line that touches the edge of a curve at one point
What’s the rule for circle theorem for tangent and radius?
A tangent and radius meet to make a 90* angle
What’s the circle theorem for two tangents?
Tangents from the same extended point to the circumference of the circle are equal in length
What’s the circle theorem for angle at circumference and angle at centre? What do you look for to apply this?
Angle at the centre is twice the size of the angle at the circumference
One angle must be at centre and other three must be touching circumference
What’s the circle theorem for angles in the same segment? What do you look for to apply this?
Angles in the same segment are equal
Look for a ‘bowtie’ shape. All points will be touching the circumference
What’s the circle theorem for angle in a semicircle? What do you look for to apply this?
Angle in a semicircle is 90*. One length of triangle must go through centre of circle, all vertices touching circumference
What’s the circle theorem for a cyclic quadrilateral? What do you look for to apply this?
Opposite angles (diagonally opposite) in a cyclic quadrilateral add up to 180*. All points of quadrilateral must be touching circumference
What are the two rules for bearings?
Always measured clockwise from north, must always have 3 digits
How do you work out HCF from a Venn diagram?
Multiply together numbers in middle
How do you work out LCF from a Venn diagram?
Multiply all numbers in diagram together
X^4 x X^3 =?
= X^7
P^8 / p^2 = ?
P^6
(X^4)^3 =?
X^12
X^4/X^4 = ?
X^0 = 1
9 ^ 1/2 = ?
(Little 2) (Square Root of 9)
16 ^ 3/2 = ?
(Little 2) (Square Root of 16^3 ) = 4^3 = 64
4^-2 = ?
1/(4^2) = 1/16
When asked to evaluate, what does it want you to do?
Work out
When using bus stop method, which number needs to be an integer?
The number inside the bus stop
How do you multiply two numbers that are both in standard form?
Time the first integers, add the indices. Write answer in standard form
When do you factorise into double brackets?
When expanding quadratics
When do you use smiley face method to factorise?
When the quadratic has an integer before it
What’s the rule of difference of two squares?
a^2-b^2= (a-b)(a+b)
What’s a surd?
A square root of an integer that doesn’t give you an integer answer
What’s the surd law?
(Square Root of a b) = (Square Root of a) (Square Root of b)
What does it mean to rationalise the denominator?
Getting rid of the surd on the denominator
What’s the first signification figure of a number?
The first non zero digit of a number when reading from the left
How do you estimate.
Round each number to 1sf, then work out the calculation
How do you convert from a percentage to a decimal?
Divide by 100
How do you convert from a percentage to a fraction?
Write it over 100
How do you convert from decimal to percentage.
Times by 100
How do you convert from decimal to fraction
Multiply by 100 and write over 100
How do you convert from fraction into decimal
Try writing it over 100, or divide numerator by denominator
How do you convert from fraction to percentage?
Write it over 100
Speed equation?
Speed = distance / time
Density equation?
Density (g/cm^3) = mass / volume
Pressure equation?
Pressure = force / area
Pressure is measured in N/m^2
1m^2 = ?^2 cm^2 = ? Cm?
1m^2 = 100^2 cm^2 = 10000cm^2
What does an expression have?
No equal sign
How do you solve fractional equations?
Make a common denominator (put numerator into foil brackets) Expand brackets. Solve.
What’s the basic equation of a line? And what do the parts mean
Y = mx +/- c
m is gradient
Y and x are coordinates
+/- c is the y intercept (where line crosses y axis)
What’s the rule for gradient of lines that are parallel?
They have the same gradient
What’s the rule for gradient of lines that are perpendicular?
Lines a and b are perpendicular
Gradient of line b will be the negative reciprocal of line a
Equation of gradient of a line between two points?
Difference in ys / difference in xs
How do you work out midpoint of two coordinates
( (x1 + x2)/2 , (y1+y2)/2 )
What’s Pythagoras theorem?
a^2 + b^2 = c^2
Only works on right angle triangles. C = hypotenuse, the line opposite the right angle
In trigonometry, what are the opposite and adjacent, what is theta.
Opposite = the length opposite theta Adjacent = the side adjacent to theta, but not the hypotenuse Theta = an angle that’s not the right angle
Sin theta = ?
Sin theta = opposite / hypotenuse
Cos theta = ?
Cos theta = adjacent / hypotenuse
Tan theta = ?
Tan theta = opposite / hypotenuse
If you end up with 10 x sin 60 = x, what do you enter into your calculator?
Sin (60) x 10
Sin 0* = ?
0
Sin 30* = ?
1/2
Sin 45* = ?
(Square root of 2) / 2
Sin 60* = ?
(Square root of 3) / 2
Sin 90* = ?
1
Cos 0* = ?
1
Cos 30* = ?
(Square root of 3) / 2
Cos 45* = ?
(Square root of 2)/2
Cos 60* = ?
1/2
Cos 90* = ?
0
Tan 0* = ?
0
Tan 30* = ?
(Square root of 3)/3
Tan 45* = ?
1
Tan 60* = ?
Square root of 3
Tan 90* = ?
Error
If you have cos theta = 6/12, how would you work out theta?
Cos -1
Theta = cos -1 (6/12)
What’s the perimeter?
Total length around the outside of a shape