Exercise 1
1 Write down the names of four different quadrilaterals that have opposite sides that are equal in length.
2 Tick the properties of each quadrilateral. Rectangle Kite Rhombus
One of more lines of symmetry
All angles equal
All sides equal
Perpendicular diagonals
3 Lucy is describing a quadrilateral:
The diagonals are perpendicular and equal in length. She asks five of her friends to draw the quadrilateral she is thinking of.
a) Freddie draws this shape.
Explain why he is wrong.
b) Here are the shapes her other four friends draw.
Zak Pete Pria Amy
Which friend has drawn the shape that Lucy described?………………...
5 Write down the size of each lettered angle.
6 Theo looked at this diagram and said, ‘Angle b is 70° and angle f is 100°.’ Is he correct? Explain your answer.
6.2 Angles of a triangle
Summary of key points
The angles inside a shape are called interior angles. The angles outside a shape are called the exterior angles.
Angle w is one of the exterior angles of triangle ABC.
Remember that the angles in a triangle add up to 180°.
3 Join the parts to make four correct sentences.
Multiplying by 0.1 is the same as dividing by 1 100 or multiplying by 10.
Multiplying by 0.01 is the same as multiplying by 1 100 or dividing by 100.
Dividing by 0.1 is the same as dividing by 1 10 or dividing by 10.
Dividing by 0.01 is the same as multiplying by 1 10 or multiplying by 100.
4 Complete each statement by writing in one of these signs: < or > or =.
a) 28 × 0.01 ………. 28
b) 0.069 ÷ 0.01 ………. 6.9
c) 4.2 ÷ 0.01 ………. 4200 × 0.1
d) 0.048 × 0.01 ………. 0.048 ÷ 0.1
5 Complete the calculations by writing in one of these signs: × or ÷.
6 Arrange these six cards to make two correct number statements. Each card should be used only once.
8 Presenting and interpreting data 1
You will practice how to:
• Record, organise and represent categorical, discrete and continuous data. Choose and explain which representation to use in a given situation:
o tally charts, frequency tables and two-way tables
o dual and compound bar charts
o frequency diagrams for continuous data
o stem-and-leaf diagrams.
• Interpret data, identifying patterns, trends and relationships, within and between data sets, to answer statistical questions. Discuss conclusions, considering the sources of variation, including sampling, and check predictions.
8.1 Frequency tables and diagrams
Summary of key points
Class intervals are used to group data in a frequency table. The modal class is the class interval that is most frequent.
Discrete data
Examples of grouped intervals for discrete data are:
1–4, 5–8, 9–12…
Notice that all intervals have the same width.
Continuous data
It is important to make sure there are no overlaps or gaps when choosing intervals for continuous data.
Such intervals are usually written using inequality signs, for example:
Notice that all intervals have the same width.
A set of grouped data can be represented in a frequency diagram.
For grouped discrete data:
• The bars are equal width.
• There are gaps between the bars.
• Each interval is written below the corresponding bar
The group 20 ≤ x < 30 includes any values that are at least 20 but less than 30.
For grouped continuous data:
• The bars are equal width.
• A continuous scale is used.
• There are no gaps between the bars.