Maths Flashcards
What is the formula for the cosine rule?
a² = b² + c² - 2bc cos(A)
What is the formula for the sine rule?
a / sin(A) = b / sin(B) = c / sin(C)
How are sides in a non right angled triangle labelled?
With a lower case ‘a’, ‘b’ or ‘c’. They are always opposite to the angle/vertice with the same letter.
How are angles in a non right angled triangle labelled?
With a capital ‘A’, ‘B’ or ‘C’, but all with a ‘^’ above them. They are always opposite to the side with the same letter.
(Often written as just ‘A’, ‘B’ and ‘C’ in equations.)
What is (a² - b²) factorised?
(a + b) (a - b)
What is (a + b) (a - b) expanded?
a² - b²
What is the quadratic formula?
x = -b ± √(b² - 4ac) /
2a
What is a:
1) Mean
2) Median
3) Mode
4) Range
Mean: Average of all values
Median: Middle number in an ordered list
Mode: Number that appears most
Range: Difference between highest and lowest value.
What is the equation for a straight line on a graph?
y = mx + c
What does ‘m’ and ‘c’ mean in the following equation?
y = mx + c
m = gradient
c = y-intercept
What is the equation for gradient?
Change in y / Change in x
sin (30) =
1 / 2
cos (30) =
√3 / 2
tan (30) =
1 / √3
sin (60) =
√3 / 2
cos (60) =
1 / 2
tan (60) =
√3
sin (90) =
1
cos (90) =
0
What is the equation for proportion?
y = kx
What is the equation for inverse proportion?
y = k/x
What is the equation for percentage change?
(Change / Original) x 100
How can triangles be proved to be congruent?
- SSS (3 equal sides)
- ASA (2 equal angles and 1 equal side)
- SAS (1 equal angle and 2 equal sides)
- RHS (Right angle, equal hypotenuse and 1 other equal side)
What is the formula for the area of a triangle?
(base x height) / 2
What is the formula for the area of a parallelogram?
base x height
What is the formula for the area of a trapezium?
1/2 x (sum of parallel sides) x height
What is the formula for the area of a circle?
π r²
What is the formula for the circumference of a circle?
2 π r
What is the formula for the area of a sector?
(θ / 360) π r²
What is the formula for the length of an arc?
(θ / 360) 2 π r
What is formula for the surface area of a sphere?
4 π r²
What is the formula for the surface area of a cone?
πrl + πr²
What is the formula for the surface area of a cylinder?
2πrh + 2πr²
What is the formula for the volume of a prism?
(Cross-section area) x (length)
What is the formula for the volume of a sphere?
(4/3) πr³
What is the formula for the volume of a pyramid?
(1/3) x (base area) x (vertical height)
What is the formula for the volume of a cone?
(1/3) πr²h
What is the Pythagoras Theorem?
a² + b² = c²
What is:
1) an upper quartile
2) a lower quartile
Upper quartile: Median of upper half of a data set.
Lower quartile: Median of lower half of a data set.
What is the formula for frequency density?
Frequency density =
Frequency / Class width
What is the formula for frequency density?
Freq. density = Frequency / Class width
What is the Area Sine Rule?
(1/2) ab sin(C)
