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Mathematics Year 08 > Maths Y08 Spr1 > Flashcards

Maths Y08 Spr1 Flashcards

1
Q

1.0 Degree

A

Unit of angle measurement. Symbol is °

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2
Q

1.1 Acute

A

Refers to an angle less than 90°

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3
Q

1.2 Right Angle

A

An angle of 90°. Corresponding to a quarter turn

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4
Q

1.3 Obtuse

A

An angle more than 90° but less than 180°

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5
Q

1.4 Straight Line

A

An angle of 180°. Corresponding to half a turn

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6
Q

1.5 Reflex

A

An angle greater than 180° and less than 360°

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7
Q

1.6 Full Turn (Circle)

A

Entire rotation is 360°. Corresponding to a full turn

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8
Q

1.7 Vertically opposite

A

Angles opposite each other when two lines cross – they are equal in size.

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9
Q

2 Parallel Lines

A

Two straight lines that never meet and stay the same distance away from each other throughout their entire length

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10
Q

2.1 Transversal

A

The third line which crosses the two parallel lines

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11
Q

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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12
Q

2.3 Corresponding

A

The angles in matching corners made when the transversal crosses the two parallel lines corresponding angles are equal size

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13
Q

2.4 Co-Interior

A

Angles that lie between the two parallel lines on the same side of the transversal. The two angles sum to 180°

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14
Q

3.0 Polygon

A

A 2D shape having more than three straight sides

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15
Q

3.1 Regular Polygon

A

A polygon with all equal side lengths and all equal size interior and exterior angles

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16
Q

3.2 Interior Angle

A

Is an angle on the inside of the shape, made between two of the sides

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17
Q

3.3 Exterior Angle

A

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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18
Q

3.4 Sum of interior Angles

A

(n – 2) x 180° where n is the number of sides

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19
Q

3.5 Individual Interior Angle

A

((n – 2) x 180°)/2 where n is the number of sides. Each individual interior angle is the same size

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20
Q

3.6 Sum of exterior Angle

A

All the exterior angles total 360°

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21
Q

3.01 3 Sides

A

Equilateral Triangle

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22
Q

3.02 4 Sides

A

Square

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23
Q

3.03 5 Sides

A

Pentagon

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24
Q

3.04 6 Sides

A

Hexagon

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25
Q

3.05 7 Sides

A

Heptagon

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26
Q

3.06 8 Sides

A

Octagon

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27
Q

3.07 9 Sides

A

Nonagon

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28
Q

3.08 10 Sides

A

Decagon

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29
Q

4.0 Net

A

A model of a solid shape opened up and flatten

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30
Q

4.1 Plan

A

A drawing of something as viewed from above

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31
Q

4.2 Elevation

A

The upwards angle from the horizontal to a line of sight from the observer of an object

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32
Q

4.3 Quadrilateral

A

A closed, two-dimensional shape which has four straight sides and four vertices

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33
Q

4.4 Square

A

Has four straight sides – all equal in length and has four right angles

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34
Q

4.5 Rectangle

A

A quadrilateral where all interior angles are right angles. Opposite sides are parallel and of equal length.

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35
Q

4.6 Rhombus

A

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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36
Q

4.7 Parallelogram

A

A quadrilateral whose opposite sides are parallel and equal in length. Opposite angles are equal.

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37
Q

4.8 Kite

A

A quadrilateral whose adjacent sides are of equal length. The kite’s diagonal bisect at right angle

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38
Q

5.0 Prism

A

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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39
Q

5.1 Face

A

A flat surface of a three-dimensional shape

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40
Q

5.2 Edge

A

The side of a polygon or a line segment where two faces meet

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41
Q

5.3 Vertex (Vertices)

A

The point where the edges of a solid meet. Vertices is the plural of a single vertex

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42
Q

5.4 Cube

A

Is a three-dimensional solid that has six identical square faces

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43
Q

5.5 Cuboid

A

Is a three-dimensional solid that has six rectangular faces. Cubes are a special type of cuboid

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44
Q

5.6 Cylinder

A

A circular prism.

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45
Q

5.7 Cone

A

Is a three-dimensional solid with a circular base and a curved surface that tapers to a point (vertex)

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46
Q

5.8 Pyramid

A

Is a three-dimensional solid which has a polygon base and triangular faces that taper to a point (vertex)

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47
Q

5.9 Sphere

A

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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48
Q

7.0

A

Sphere

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49
Q

7.1

A

Cube

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50
Q

7.2

A

Cuboid

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51
Q

7.3

A

Cylinder

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52
Q

7.4

A

Cone

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53
Q

7.5

A

Square Based Pyramid

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54
Q

7.6

A

Triangular Based Pyramid

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55
Q

7.7

A

Triangular Prism

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56
Q

6 Compass (Cardinal Points)

A

A navigational instrument that shows direction.

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57
Q

6.1 Bearing

A

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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58
Q

6.2 Clockwise

A

the same direction as the way hands on the clock go.

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59
Q

6.3 Reverse Bearing (back bearing)

A

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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60
Q

6.4 Scale (in scale drawings)

A

the ratio of the measurement on the drawing compared to the measurement of the original subject.

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61
Q

7 Ratio

A

Ratio compares the size of one part to another part.

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62
Q

7.1 Proportion

A

Proportion compares the size of one part to the size of the whole. (Usually written as a fraction)

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63
Q

7.2 Simplifying ratios

A

Divide all parts of the ratio by a common factor.

64
Q

7.3 Sharing in a ratio

A
  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.
65
Q

7.4 Direct Proportion. Graphs showing direct proportion pass through the origin and are straight.

A

When one variable increases as the other increases.

66
Q

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!

A

When one variable decreases as the other increases.

67
Q

8 Algebra

A

Numbers and quantities called variables are represented by letter and symbols in expressions and equations

68
Q

8.1 Term

A

One part of an algebraic expression which may be a number, a variable or a product of both

69
Q

8.2 Expression

A

A mathematical statement containing a minimum of two numbers and at least one maths operation (addition, subtraction, multiplication, and division)

70
Q

8.3 Formula/ Formulae

A

a mathematical rule written using symbols, usually as an equation describing a certain relationship between quantities
E = mc2 A = r2

71
Q

8.4 Simplify Algebra

A

To simplify an expression: to remove brackets, unnecessary terms and numbers and leave an expression in its simplest form

72
Q

8.5 Expanding Bracket

A

Means to multiply each term in the bracket by the term/expression outside the bracket

73
Q

Single brackets

A

2(3x-5)=6x-10

74
Q

Double brackets

A

(x+25)(x-10)=x^2+15x-250

75
Q

8.6 Factorising

A

The reverse of expanding brackets.

76
Q

E.g.

A

15x+20=5(3x+4)

77
Q

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

A

(x+2)(x+5) expands to give…
x^2+7x+10
10 = 2 x 5
7 = 2 + 5

78
Q

8.7 Identities

A

Expressions that are ALWAYS equal to each other for all values of the variables involved.

79
Q

8.8 Equation

A

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.

80
Q

8.9 Forming equations

A

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°

81
Q

9 Substitution
Substitute a=3

A

Where a variable is replaced by a number
5a=5(3)=5x3=15

82
Q

9.1 Inequality

A

An inequality makes a statement about non-equal comparisons between two, or more, expressions

83
Q

10 Line segment

A

A line segment has a start and end point.

84
Q

10.1 Axis

A

A Reference grid, showing position

85
Q

10.2 Coordinates

A

Written in pairs. The first term is the x-coordinate (movement across). The second term is the y-coordinate (movement up or down)

86
Q

10.3 Gradient

A

The steepness of a line is called the gradient.
The change in y coordinates, divided by the change in x coordinates.

87
Q

10.4 Y-Intercept

A

Where a line crosses the y axes of a graph.

88
Q

10.5 Substitute

A

To replace letters in a formula with numbers.

89
Q

10.6 Table of values

A

Used to generate coordinates to draw the graph of an equation.

90
Q

10.7 Midpoint

A

The midpoint of a line segment is the point exactly in the middle.

91
Q

10.8 Quadratic

A

A quadratic equation contains a term in x2 but no higher power of x.

92
Q

10.9 Linear graph

A

Straight line graph. The equation of a linear graph can contain an x-term, a y-term and a number.

93
Q

11.0 y = mx + c

A

The general equation of a straight line.

94
Q

11.1 Horizontal

A

The equation of a horizontal line is y = c
It has a gradient of 0
A line parallel to the horizon.

95
Q

11.2 Vertical

A

A line at right angle to the horizontal
The equation of a vertical line is x = a
It has an undefined gradient

96
Q

12 Distance – Time Graph

A

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

97
Q

12.1 Average Speed

A

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

98
Q

12.2 Conversion Graph

A

Is a graph used to change units from one form to another. E.g. Miles to kilometre, pounds to a foreign currency.

99
Q

12.3 Fixed Charge

A

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.

100
Q

12.4 Constant

A

A value that remains unchanged (e.g. fixed charge). It is independent of variations in charges

101
Q

12.5 Variable

A

Is a quantity that may change within the context of the maths problem or experiment in science.

102
Q

12.6 Rate of change

A

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)

103
Q

13 Sequence

A

Ordered sets of numbers or shapes arranged according to a rule

104
Q

13.1 Term

A

One of the numbers in a sequence

105
Q

13.2 Term-to-term rule

A

A rule that defines the value of each term in a sequence
if the previous terms are known

106
Q

13.3 Nth term rule

A

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.

107
Q

13.4 Triangular Number Sequence

A

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

108
Q

13.5 Fibonacci Sequence

A

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, …

109
Q

13.6 Arithmetic

A

A sequence where terms have the same value added each time

110
Q

13.7 Linear

A

Where the first line of difference in an arithmetic sequence is constant

111
Q

13.8 Quadratic

A

Where the second line of difference in an arithmetic sequence is constant

112
Q

13.9 Geometric

A

A sequence where terms are multiplied by the same value each time. This is known as a common ratio.

113
Q

14 0.1 as a percentage

A

10%

114
Q

14.1 0.25 as a percentage

A

25%

115
Q

14.2 0.5 as a percentage

A

50%

116
Q

14.3 0.75 as a percentage

A

75%

117
Q

14.4 1 as a percentage

A

100%

118
Q

14.5 0.2 as a percentage

A

20%

119
Q

14.6 0.4 as a percentage

A

40%

120
Q

14.7 0.6 as a percentage

A

60%

121
Q

14.8 0.8 as a percentage

A

80%

122
Q

15 statistics

A

The collection, organisation, presentation, interpretation and analysis of data

123
Q

15.1 Data

A

data is a collection of information gathered by observation, questioning or measurement

124
Q

15.2 Qualitative Data

A

Data in words, describing qualities, characteristics or categories

125
Q

15.3 Quantitative Data

A

Numerical data which can be counted or measured

126
Q

15.4 Discrete Data

A

A type of quantitative data that has a finite number value e.g. number of siblings

127
Q

15.5 Continuous Data

A

A type of quantitative data that has a infinite value – a numerical value that is measured e.g. length, weight, time

128
Q

15.6 Average

A

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

129
Q

15.6a Mean

A

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.

130
Q

15.6b Median

A

A type of average which is the middle value of an ordered set of data values

131
Q

15.6c Mode

A

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

132
Q

15.6d Range

A

The difference between the lowest and highest values in a data set

133
Q

15.7 Interquartile Range

A

a measure of spread equal to the upper quartile (Q3) minus the lower quartile (Q1) in a data set.
IQR = Q3 - Q1

134
Q

15.8 Grouped frequency table

A

Data that has been ordered and sorted into groups called classes, often displayed in a frequency table

135
Q

15.9 Estimate mean

A

When a midpoint has been used to represent a grouped set of data when calculating the mean

136
Q

16 Midpoint

A

The middle value of a group of data. To calculate add together the upper and lower value of the group and divide by two.

137
Q

16.1 ∑ f

A

∑ is the symbol for Sigma, this means ‘sum of’ so this would mean the sum of all frequency (f) values

138
Q

16.2 ∑ fx

A

∑ 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

139
Q

16.3 n

A

’n’ is the number of data points there are

140
Q

17 Stem and leaf diagram

A

Data value is split into a ‘leaf’ and a stem
e.g. ‘32’ is split into ‘3’ stem and a ‘2’ as the leaf

141
Q

17.1 Stem

A

The first digit/ digits

142
Q

17.2 Leaf

A

The last digit of the data value

143
Q

17.3 Quartiles

A

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

144
Q

18 Frequency Polygon

A

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).

145
Q

19 Box Plot

A

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

146
Q

20.1 Scatter graphs

A

Used to represent and compare two sets of data.

147
Q

20.2 Correlation

A

The mathematical definition for the type of relationship.

148
Q

20.3 Line of best fit

A

A straight line on a graph that represents the data on a scatter graph.

149
Q

20.4 Interpolation

A

Interpolation is using the line of best fit to estimate values inside our data point.

150
Q

20.5 Extrapolation

A

Extrapolation is where we use the line of best fit to make predictions outside of our data.

151
Q

20.6 Outlier

A

A point that lies outside the trend of the graph.

152
Q

20.7 No Correlation

A

There is no linear relationship between the two.

153
Q

20.8 Strong Correlation

A

When two sets of data are closely linked.

154
Q

20.9 Weak Correlation

A

When two sets of data have correlation, but are not closely linked.

155
Q

21 Pie Chart

A

a type of graph in which a circle is divided into sectors that each represent a proportion of the whole

Mathematics Year 08 (3 decks)

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