Maths Y08 Spr1 Flashcards
1
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1.0 Degree
A
Unit of angle measurement. Symbol is °
2
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1.1 Acute
A
Refers to an angle less than 90°
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1.2 Right Angle
A
An angle of 90°. Corresponding to a quarter turn
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1.3 Obtuse
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An angle more than 90° but less than 180°
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1.4 Straight Line
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An angle of 180°. Corresponding to half a turn
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1.5 Reflex
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An angle greater than 180° and less than 360°
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1.6 Full Turn (Circle)
A
Entire rotation is 360°. Corresponding to a full turn
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1.7 Vertically opposite
A
Angles opposite each other when two lines cross – they are equal in size.
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2 Parallel Lines
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Two straight lines that never meet and stay the same distance away from each other throughout their entire length
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2.1 Transversal
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The third line which crosses the two parallel lines
11
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2.2 Alternate
A
A pair of angles on the inner side of each of the parallel line and the transversal, but on opposite sides of the transversal are equal
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2.3 Corresponding
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The angles in matching corners made when the transversal crosses the two parallel lines corresponding angles are equal size
13
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2.4 Co-Interior
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Angles that lie between the two parallel lines on the same side of the transversal. The two angles sum to 180°
14
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3.0 Polygon
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A 2D shape having more than three straight sides
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3.1 Regular Polygon
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A polygon with all equal side lengths and all equal size interior and exterior angles
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3.2 Interior Angle
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Is an angle on the inside of the shape, made between two of the sides
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3.3 Exterior Angle
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Is an angle on the outside of the shape when the side lines are extended (360 ÷ n where n is the number of sizes)
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3.4 Sum of interior Angles
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(n – 2) x 180° where n is the number of sides
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3.5 Individual Interior Angle
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((n – 2) x 180°)/2 where n is the number of sides. Each individual interior angle is the same size
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3.6 Sum of exterior Angle
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All the exterior angles total 360°
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3.01 3 Sides
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Equilateral Triangle
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3.02 4 Sides
A
Square
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3.03 5 Sides
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Pentagon
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3.04 6 Sides
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Hexagon
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3.05 7 Sides
Heptagon
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3.06 8 Sides
Octagon
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3.07 9 Sides
Nonagon
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3.08 10 Sides
Decagon
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4.0 Net
A model of a solid shape opened up and flatten
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4.1 Plan
A drawing of something as viewed from above
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4.2 Elevation
The upwards angle from the horizontal to a line of sight from the observer of an object
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4.3 Quadrilateral
A closed, two-dimensional shape which has four straight sides and four vertices
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4.4 Square
Has four straight sides – all equal in length and has four right angles
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4.5 Rectangle
A quadrilateral where all interior angles are right angles. Opposite sides are parallel and of equal length.
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4.6 Rhombus
A quadrilateral with all sides equal in length. Also opposite sides are parallel and opposite angles are equal. The shapes diagonals bisect at right angle
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4.7 Parallelogram
A quadrilateral whose opposite sides are parallel and equal in length. Opposite angles are equal.
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4.8 Kite
A quadrilateral whose adjacent sides are of equal length. The kite’s diagonal bisect at right angle
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5.0 Prism
A three-dimensional shape that has the same cross-sectional shape throughout. It’s two end faces are identical. A prism takes its name from the shape of its base
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5.1 Face
A flat surface of a three-dimensional shape
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5.2 Edge
The side of a polygon or a line segment where two faces meet
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5.3 Vertex (Vertices)
The point where the edges of a solid meet. Vertices is the plural of a single vertex
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5.4 Cube
Is a three-dimensional solid that has six identical square faces
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5.5 Cuboid
Is a three-dimensional solid that has six rectangular faces. Cubes are a special type of cuboid
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5.6 Cylinder
A circular prism.
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5.7 Cone
Is a three-dimensional solid with a circular base and a curved surface that tapers to a point (vertex)
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5.8 Pyramid
Is a three-dimensional solid which has a polygon base and triangular faces that taper to a point (vertex)
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5.9 Sphere
Is a three-dimensional solid that is perfectly round, like a ball. Every point on the surface is the same distance from the centre
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7.0
Sphere
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7.1
Cube
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7.2
Cuboid
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7.3
Cylinder
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7.4
Cone
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7.5
Square Based Pyramid
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7.6
Triangular Based Pyramid
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7.7
Triangular Prism
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6 Compass (Cardinal Points)
A navigational instrument that shows direction.
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6.1 Bearing
The angle of direction in relation to a north line. Measured in degrees from the north in a clockwise direction. Given as a 3 digits
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6.2 Clockwise
the same direction as the way hands on the clock go.
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6.3 Reverse Bearing (back bearing)
The bearing of a line measured in direction backward to the direction of the original object. Back bearing is a line bearing ta`
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6.4 Scale (in scale drawings)
the ratio of the measurement on the drawing compared to the measurement of the original subject.
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7 Ratio
Ratio compares the size of one part to another part.
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7.1 Proportion
Proportion compares the size of one part to the size of the whole. (Usually written as a fraction)
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7.2 Simplifying ratios
Divide all parts of the ratio by a common factor.
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7.3 Sharing in a ratio
1. Add the total parts of the ratio. 2. Divide the amount to be shared by this value to find the value of one part. 3. Multiply this value by each part of the ratio.
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7.4 Direct Proportion. Graphs showing direct proportion pass through the origin and are straight.
When one variable increases as the other increases.
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7.6 Inverse Proportion E.g. Graphs showing inverse proportion are curved, and get close to the x and y axis – but do not touch them!
When one variable decreases as the other increases.
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8 Algebra
Numbers and quantities called variables are represented by letter and symbols in expressions and equations
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8.1 Term
One part of an algebraic expression which may be a number, a variable or a product of both
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8.2 Expression
A mathematical statement containing a minimum of two numbers and at least one maths operation (addition, subtraction, multiplication, and division)
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8.3 Formula/ Formulae
a mathematical rule written using symbols, usually as an equation describing a certain relationship between quantities
E = mc2 A = r2
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8.4 Simplify Algebra
To simplify an expression: to remove brackets, unnecessary terms and numbers and leave an expression in its simplest form
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8.5 Expanding Bracket
Means to multiply each term in the bracket by the term/expression outside the bracket
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Single brackets
2(3x-5)=6x-10
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Double brackets
(x+25)(x-10)=x^2+15x-250
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8.6 Factorising
The reverse of expanding brackets.
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E.g.
15x+20=5(3x+4)
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E.g. For double brackets, you are looking for two numbers with a product that gives the constant term, and a sum that gives the ‘x’ coefficient
(x+2)(x+5) expands to give…
x^2+7x+10
10 = 2 x 5
7 = 2 + 5
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8.7 Identities
Expressions that are ALWAYS equal to each other for all values of the variables involved.
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8.8 Equation
A mathematical statement containing an equals sign, to show that two expressions are equal. 7x+2=6x+5
Is true when x=3 but not for any other values.
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8.9 Forming equations
Setting up an equation using your knowledge and other information given in a question.
Find the value of x.
Knowledge: “Angles in a pentagon sum to 540°”.
Form the equation, by adding the angles: x+10 + 2x+10 +x+10 + 2x +x+20=540.
And then solve!
7x+50=540
7x=490
x=70°
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9 Substitution
Substitute a=3
Where a variable is replaced by a number
5a=5(3)=5x3=15
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9.1 Inequality
An inequality makes a statement about non-equal comparisons between two, or more, expressions
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10 Line segment
A line segment has a start and end point.
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10.1 Axis
A Reference grid, showing position
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10.2 Coordinates
Written in pairs. The first term is the x-coordinate (movement across). The second term is the y-coordinate (movement up or down)
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10.3 Gradient
The steepness of a line is called the gradient.
The change in y coordinates, divided by the change in x coordinates.
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10.4 Y-Intercept
Where a line crosses the y axes of a graph.
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10.5 Substitute
To replace letters in a formula with numbers.
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10.6 Table of values
Used to generate coordinates to draw the graph of an equation.
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10.7 Midpoint
The midpoint of a line segment is the point exactly in the middle.
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10.8 Quadratic
A quadratic equation contains a term in x2 but no higher power of x.
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10.9 Linear graph
Straight line graph. The equation of a linear graph can contain an x-term, a y-term and a number.
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11.0 y = mx + c
The general equation of a straight line.
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11.1 Horizontal
The equation of a horizontal line is y = c
It has a gradient of 0
A line parallel to the horizon.
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11.2 Vertical
A line at right angle to the horizontal
The equation of a vertical line is x = a
It has an undefined gradient
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12 Distance – Time Graph
The distance travelled by an object can be represented by a distance-time graph. Time is plotted along the x-axis and the distance is plotted along the y-axis.
The gradient of the line indicated the speed of the object – the steeper the line the faster the object is moving. A flat line indicates non-movement
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12.1 Average Speed
The average speed of an object is the total distance travelled by the object divided by the total time.
D = S x T
S = D / T
T = D / S
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12.2 Conversion Graph
Is a graph used to change units from one form to another. E.g. Miles to kilometre, pounds to a foreign currency.
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12.3 Fixed Charge
Is a standard charge paid before any variable aspect of the asset is used. E.g. line rental on a broadband deal, hire charge, before hours hired for.
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12.4 Constant
A value that remains unchanged (e.g. fixed charge). It is independent of variations in charges
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12.5 Variable
Is a quantity that may change within the context of the maths problem or experiment in science.
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12.6 Rate of change
Is the rate that describes how one quantity changes in relation to another. On a graph the rate of change is shown by the line – this can increase or decrease (i.e. Go up or down)
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13 Sequence
Ordered sets of numbers or shapes arranged according to a rule
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13.1 Term
One of the numbers in a sequence
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13.2 Term-to-term rule
A rule that defines the value of each term in a sequence
if the previous terms are known
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13.3 Nth term rule
Is the general rule for the formula which enables the finding of any term in the sequence by using the position term number as the ‘n’ value.
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13.4 Triangular Number Sequence
A number that can be represented in the shape of a triangle
e.g. 3, 6, 10, 15, 21…..
Triangular numbers have the formula (n(n+1))/2
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13.5 Fibonacci Sequence
Named after Leonardo Fibonacci, an Italian mathematician. In a Fibonacci sequence each number is the sum of the two numbers before it n1 + n2 = n3.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …
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13.6 Arithmetic
A sequence where terms have the same value added each time
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13.7 Linear
Where the first line of difference in an arithmetic sequence is constant
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13.8 Quadratic
Where the second line of difference in an arithmetic sequence is constant
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13.9 Geometric
A sequence where terms are multiplied by the same value each time. This is known as a common ratio.
113
14 0.1 as a percentage
10%
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14.1 0.25 as a percentage
25%
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14.2 0.5 as a percentage
50%
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14.3 0.75 as a percentage
75%
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14.4 1 as a percentage
100%
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14.5 0.2 as a percentage
20%
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14.6 0.4 as a percentage
40%
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14.7 0.6 as a percentage
60%
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14.8 0.8 as a percentage
80%
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15 statistics
The collection, organisation, presentation, interpretation and analysis of data
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15.1 Data
data is a collection of information gathered by observation, questioning or measurement
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15.2 Qualitative Data
Data in words, describing qualities, characteristics or categories
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15.3 Quantitative Data
Numerical data which can be counted or measured
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15.4 Discrete Data
A type of quantitative data that has a finite number value e.g. number of siblings
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15.5 Continuous Data
A type of quantitative data that has a infinite value – a numerical value that is measured e.g. length, weight, time
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15.6 Average
An average is a measure used to find the location of the middle (central tendency) of a data set.
• Mean, median and mode are all types of averages.
• Often the word average refers to the mean
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15.6a Mean
Usually called the average and may be called the arithmetic mean.
The mean is the total of all the scores or amounts, divided by, how many scores or amounts there were.
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15.6b Median
A type of average which is the middle value of an ordered set of data values
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15.6c Mode
In a set of scores, values or numbers the mode is the one that occurs the most. Known as Modal class when working with frequency tables
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15.6d Range
The difference between the lowest and highest values in a data set
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15.7 Interquartile Range
a measure of spread equal to the upper quartile (Q3) minus the lower quartile (Q1) in a data set.
IQR = Q3 - Q1
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15.8 Grouped frequency table
Data that has been ordered and sorted into groups called classes, often displayed in a frequency table
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15.9 Estimate mean
When a midpoint has been used to represent a grouped set of data when calculating the mean
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16 Midpoint
The middle value of a group of data. To calculate add together the upper and lower value of the group and divide by two.
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16.1 ∑ f
∑ is the symbol for Sigma, this means 'sum of' so this would mean the sum of all frequency (f) values
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16.2 ∑ fx
∑ is the symbol for Sigma, this means 'sum of' so this would mean the sum of all the frequency multiplied by the category value/or midpoint (f x x) values
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16.3 n
’n’ is the number of data points there are
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17 Stem and leaf diagram
Data value is split into a ‘leaf’ and a stem
e.g. ‘32’ is split into ‘3’ stem and a ‘2’ as the leaf
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17.1 Stem
The first digit/ digits
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17.2 Leaf
The last digit of the data value
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17.3 Quartiles
Data divided into quarters
• Quartile 1 (Q1) is the median of the lower half of the values.
• Quartile 3 (Q3) is the median of the upper half of the values
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18 Frequency Polygon
Is a graphical form of representing data. It is used to show the shape of the data distribution, and shows trends. It is constructed by plotting the midpoint (x-axis) against the frequency (y-axis).
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19 Box Plot
a simple way of representing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, usually with a vertical line inside to indicate the median value
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20.1 Scatter graphs
Used to represent and compare two sets of data.
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20.2 Correlation
The mathematical definition for the type of relationship.
148
20.3 Line of best fit
A straight line on a graph that represents the data on a scatter graph.
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20.4 Interpolation
Interpolation is using the line of best fit to estimate values inside our data point.
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20.5 Extrapolation
Extrapolation is where we use the line of best fit to make predictions outside of our data.
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20.6 Outlier
A point that lies outside the trend of the graph.
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20.7 No Correlation
There is no linear relationship between the two.
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20.8 Strong Correlation
When two sets of data are closely linked.
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20.9 Weak Correlation
When two sets of data have correlation, but are not closely linked.
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21 Pie Chart
a type of graph in which a circle is divided into sectors that each represent a proportion of the whole
