Maths Yr09 Sum1 Flashcards
1 Distance-Time Graphs
You can find the speed from the gradient of the line (Distance ÷ Time)
1.1 Real Life Graphs
Graphs that model a real-life situation
1.2 Pythagoras’ theorem
For any right angled triangle:
1.3 Hypotenuse
The longest side of a right-angled triangle. It is always opposite the right angle. For Pythagoras’ theorem, this is represented by ‘c’. For trigonometry we label it ‘H’
1.4 Adjacent
The side next to the angle.
1.5 Opposite
The side opposite the given or asked for angle.
1.6 Trigonometric Formulae
Use SOH CAH TOA to remember the formula:
1.7 Acute angle
An angle less than 90°
1.8 Right angle
An angle of 90°
1.9 Obtuse angle
An angle between 90° and 180°
2 Reflex angle
An angle greater than 180° but less than 360°
2.1 Angles on a straight line
Angles on a straight line sum to 180°
2.2 Angles in a triangle
Angles in a triangle sum to 180°
2.3 Angles around a point
Angles around a point sum to 360°
2.4 Parallel lines
Two lines that are always the same distance apart (equidistant)
2.5 Alternate angles
Alternate angles are equal. (‘Z’ shape)
2.6 Corresponding angles
Corresponding angles are equal. (‘F’ shape)
2.7 Co-interior angles
Co-interior angles sum to 180 (‘C’ shape)
2.8 Vertically opposite
Vertically opposite angles are equal
2.9 Bearing
An angle, measured clockwise from north line, has 3 digits.
3 Perimeter
The total distance around the outside of a shape
3.1 Area
The amount of space inside a shape.
3.2 Area of a Rectangle
Length x Width
3.3 Area of a Parallelogram
Base x Perpendicular Height
Not the slant height.
3.4 Area of a Triangle
Base x Height ÷ 2
3.5 Area of a Trapezium
1/2 (a+b)h, where a and b are the lengths of the parallel sides, and h the perpendicular height
3.6 Volume of a Cylinder
For a cylinder of heighthwith radiusr, the volume of a cylinder can be calculated using the formula:
3.7 Volume of a Cone
The formula for calculating the volume of a cone, where r is the radius and h is the perpendicular height is:
3.8 Volume of a Pyramid
The volume of a pyramid can be calculated using the formula:
3.9 Volume of a Sphere
The volume of a sphere be calculated using the formula
4 Pi (π)
The ratio of a circle’s circumference to its diameter
4.1 Radius
A line that goes from the centre to the circumference. It is half the length of the diameter
4.2 Diameter
A line that passes through the centre of the circle. It is double the length of the radius
4.3 Circumference of a circle
The outside of the circle. The perimeter of the circle C=2πr=πd
4.4 Area of a circle
A=πr^2
4.5 Chord
A line segment connecting two points on a circle
4.6 Sector
An AREA within a circle bounded by a chord and an arc
Area of a sector= angle/(360°)×πr^2
4.7 Segment
An AREA within a circle bounded by a chord and an arc The smaller area is the minor segment and the
4.8 Arc
Part of the circumference between two points. Arc length= angle/(360°)×πd
4.9 Tangent
A straight line that touches the circle at one point.
5 Qualitative Data
Non-numerical, descriptive data E.g. Eye colour, gender
5.1 Quantitative Data
Numerical data E.g. Shoe size, weight
5.2 Continuous Data
Data that can take any numerical value within a given range. E.g. weight, voltage
5.3 Discrete Data
Data that can take only specific values within a given range. E.g. number of children, shoe size
5.4 Grouped data
Data that has been grouped into categories
5.5 Primary data
Data that has been collected by yourself for a specific purpose E.g. Survey
5.6 Secondary data
Data that has been collected by someone else for another purpose E.g. Websites
5.7 Mean
To calculate the mean add up the values and divide by how many values there are
5.8 Median
The middle value from a set of ordered data
5.9 Mode/Modal Value
MOst frequent piece of data
6 Range
The difference between the lowest and highest values in a data set
6.1 Positive Correlation
As one value increases the other value Increases. E.g. Height and weight – taller people tend to be heavier
6.2 Negative Correlation
As one value increases the other value Decreases. E.g. The number of weeks a song has been in the Top 40 and sales of the single for that week.
6.6 Compound Shape
A shape made up of a combination of other known shapes put together.
6.7 Net
A pattern that you can fold to make a model of a 3D shape.
6.8 Volume
The amount of 3D space inside a shape. The capacity of that object, measured in cubic units
6.9 Prism
A prism has across-sectionwhich is exactly the same shape and size throughout its length.
7 Cross section
A cross section is the shape made by cutting straight across an object.
7.1 Volume of a prism
Volume of a prism = Area of the cross section x Length
7.2 Volume of a Cube/Cuboid
Volume of a cube/cuboid = length x width x depth
7.3 Surface area a Cube/Cuboid
The total area of all the faces of a cube/cuboid
6.3 Speed, Distance, Time
Speed = Distance ÷ Time Distance = Speed x Time Time = Distance ÷ Speed
6.4 Density, Mass, Volume
Density = Mass ÷ Volume Mass = Density x Volume Volume = Mass ÷ Density
6.5 Pressure,Force, Area
Pressure = Force ÷ Area Force = Pressure x Area Area = Force ÷ Pressure
