Maths Flashcards
How do you calculate the area of a rectangle?
Length x width
How do you calculate the area of a parallelogram?
Base x height
How do you calculate area of a trapezium?
1/2 (a+b)h
How do you calculate area of a triangle?
1/2 x base x height
How do you calculate the circumference of a circle?
pi x diameter
How do you calculate circumference of a circle?
2 x pi x radius
How do you calculate the area of a circle?
Pi x radius^2
How do you calculate the volume of a cuboid?
Length x width x height
How do you calculate the volume of a prism?
area of cross section x length
How do you calculate the volume of a cylinder?
pi x radius^2 x height
How do you calculate the volume of a pyramid?
1/3 x area of base x height
What’s the general quadratic equation?
ax^2 + bx + c = 0
Whats the quadratic formula
x = −b± b^2−4ac
➗
2a
How do you calculate speed?
Speed = distance ➗ time
How do you calculate density?
Density = mass ➗ volume
How do you calculate pressure?
Pressure = force ➗ area
How do you calculate the hypotenuse in Pythagoras’ theorem?
A^2 + b^2 = c^2
What’s the mneumonic for trigonometry?
SohCahToa
How do you calculate sine?
SOH
Sine = opposite ➗hypotenuse
How do you calculate consine?
CAH
Cos = Adjacent ➗ hypotenuse
How do you calculate tangent?
TOA
Tan = opposite ➗adjacent
If you’re finding a side length what do you tick from sohcahtoa?
The thing you know and the thing you want to know
If you’re finding an angle in sohcahtoa what do you tick?
The two things you know
How do you change the decimal number to angle size in trigonometry?
Use the inverse sin, tan or cos button
What is the modal class?
The class with the highest frequency
How do you calculate the median class?
N+1 ➗ 2 = class position Median is value in that position
How do you estimate the mean in a grouped frequency chart?
Sum of fx ➗ sum of frequency
What does the range show?
How spread out the data is
How do you work out the position of the lower quartile?
N+1➗4
How do you work out the position of the upper quartile
3(n+1) ➗ 4
How do you calculate the inter quartile range?
Upper quartile - lower quartile
What the plan view?
View from above
What’s the side elevation?
View from the side
What’s the front elevation?
View from the front
What is the formula linking the number of faces, edges and vertices of a polyhedron?
Vertices + faces - edges = 2
How do you calculate the total surface area of a cylinder?
2 x pi x r x h + 2 x pi x r^2
How do you calculate the curved surface area of a cone?
Pi x radius x slant height
How do you calculate the surface area of a sphere?
4 x pi x radius^2
How do you calculate volume of a cone?
1/3 x pi x radius^2 x perpendicular height
How do you calculate the volume of a sphere?
4/3 x pi x radius^3
What does the gradient on a distance time graph show?
Represents speed
Gradient = distance ➗ time
What is a stationary object represented as on a distance time graph?
A horizontal line
What does the gradient on a velocity time graph show?
Acceleration
What does a horizontal line represent on a velocity time graph?
A constant speed
In a velocity time graph, how is acceleration calculated?
By the gradient. Velocity ➗ time
How do you calculate gradient on straight line graphs?
Gradient = change in y coordinate ➗ change in x coordinate Gradient = m
How many factors does a prime number have?
2
What does bidmas stand for?
Brackets, indices, division, multiplication, addition, subtraction
What is the least common multiple?
The smallest number that will divide by all the numbers in the question. Multiply all the factors of each number to get LCM. or list al the multiples and the LCM is the smallest one
What’s the Highest common factor?
The biggest number that will divide into all the numbers in the question. Multiply all the prime factors that appear in both numbers together to get HCF or list and the HCF is the biggest factor
How do you calculate a fraction into a decimal?
Divide numerator by the denominator
How do you calculate a decimal as a percentage?
X 100
In multiplication what do you do with the powers?
Add them
In division what do you do with the powers?
Subtract them
In a distance time graph, the steeper the graph…?
The faster the object is moving
In a distance time graph, if the gradients negative…?
The object is coming back
In a velocity time graph the area under the graph is?
The distance travelled
A negative slope of a velocity time graph shows?
Deceleration
How do you calculate percentage change?
Change ➗original X 100
What do angles In a triangle add up to?
180 degrees
What do angles on a straight line add up to?
180 degrees
What do angles in a quadrilateral add up to?
360 degrees
What do angles around a point add up to?
360 degrees
What are alternate angles?
Alternate angles are the same. They’re found in a z shape
What are allied angles?
Allied angles add up to 180 degrees. They’re found in a C or U shape
What are corresponding angles?
Corresponding angles are the same. They’re found in an F shape
What’s the sum of exterior angles?
360 degrees. Exterior angle = 360 ➗ n
What’s the sum of interior angles?
(N-2) x 180 degrees or 180 - exterior angle
What’s an isosceles Triangle?
2 sides the same, 2 angles the same, 1 line of symmetry
What’s a scalene triangle?
All three sides different, all three angles different, no symmetry
What’s an equilateral triangle?
3 equal sides, 3 equal angles, 3 lines of symmetry
What’s a right angled triangled?
1 right angle (90 degrees) , no lines of symmetry
What does SSS stand for when proving triangles are congruent?
Three sides are the same
What does AAS stand for when proving triangles are congruent?
Two angles and a corresponding side match up
What does SAS stand for when proving triangles are congruent?
Two sides and the angle between them match up
What does RHS stand for when proving triangles are congruent?
A right angle, the hypotenuse and one other side all match up
When are shapes similar?
if they have The same angles, all three sides are proportional any two sides are proportional and the angle between them is the same
What’s a translation?
Movement of the shape. Given as a vector - written x over y. Shapes are congruent under translation
What is rotation?
To describe rotation - angle of rotation - direction of rotation - centre of rotation Shapes are congruent under rotation
What are reflections?
For a reflection you must give the equation of the mirror line. Shapes are congruent under reflection
What is enlargement?
For enlargement you must specify
- the scale factor
- the centre of enlargement
What’s the scale factor?
If the scale factor is bigger than 1 the shape gets bigger. If the scare factor is smaller than 1 it gets smaller. If the scale factor is negative then the shape pops out he other side of the enlargement centre
How do you calculate the area of a sector?
Area of sector = x(angle) ➗ 360 X area of full circle
How do you calculate the length of the arc?
X(angle) ➗360 X circumference of full circle
What are probabilities?
A probability at 0 means something will never happen. A probability of one means it definitely will.
How do you calculate probability?
Probability = number of ways for something to happen ➗ total number of possible outcomes
What do probabilities always add up to?
1
How do you calculate relative frequency in probability experiments?
Relative frequency = frequency ➗ number of times you tried the experiment
The more times you do the experiment…?
The more accurate your estimate of the probability
How do you calculate expected frequency of a result?
Probability x number of trials
In histogram, how do you calculate frequency?
Frequency = frequency density X class width Frequency is area of the bar
How do you calculate Standard form?
A x 10^n Where A is a number between 1 and 10 and N is the number of places the decimal point would move if you wrote the number out in decimal form
What is Pythagorus’ Theorem?
a^2 + b^2 = c^2
What is Sine?
Sine = opposite / hypotenuse
What is Cosine?
Cosine = adjacent / hypotenuse
What is Tangent?
Tangent = opposite / adjacent
When do you use SOHCAHTOA?
if you have a right angled triangle
To find a side in sohcahtoa what do you do?
Tick the thing you know and the thing you want to know