Page 6 - 新思维数学学生用书8 样章

5 Angles and constructions
11 Show that the sum of the angles of triangle XYZ must be 180°.
X
Tip
Y
Use your answer
to Question 10 as
How to use this book
a guide.
9 Sequences and functions
Z
4 Think like a mathematician
Copy these sequences and fill in the missing terms.
12 ABCD is a trapezium. 1 b 5, 8 , 11 , , , 22 ,
1
6
a
3
3
1
2, 4 ,
, 8 ,
,13, 15
5
5
5
Two sides are extended to make the triangle AXB. 7 7 7
1
1
1
3
c a 25, 24 , , , 24, , 23 1 2 d 100, 89 , , 68 , , 47 X ,
Show that the angles of triangles ABX and DCX are the same size.
2
4
2
2
e b 8, Show that angles A and D of the trapezium , , 24, 23.6, , , 22.4
f
,
, 8.9, 9.2,
,
add up to 180°.
These investigations, to be carried Think like a mathematician D C D C 2.6 Inequalities
What can you say about angles
c
B and C of the trapezium?
Give a reason for your answer.
out with a partner or in a group, 5 How can you answer these questions without working out more of the terms
B
B
A
A
in the sequences?
Read Zara’s comments.
a
In the sequence 0.4, 0.8, 1.2, 1.6, 2, 2.4, …, what is the first term
will help develop skills of thinking 13 ABCD is a parallelogram. The method I am going Tip
A
a
Show that opposite angles of the
greater than 10?
Is 45 a term in the sequence 5, 7 , 10, 12 , 15, ...?
to use is to identify the smallest
and working mathematically. b b parallelogram are equal. D 2 1 1 2 B Extend the
sides of the
integer for each inequality first. Then I’ll
Compare your answer to part a
Is 5 a term in the sequence 30, 26 , 23 , 20, ...?
1
c with a partner’s answer. Can you 2 3 1 3 parallelogram.
identify the largest integer for each
3
Discuss your answers. C
inequality. Then I’ll work out the list of
improve his or her answer? Can you
improve your own answer?
integers for each inequality.
6 Write the first three terms of each of these sequences.
Questions to help you think Imagine you have to explain corresponding angles to someone who does
The first one has been started for you.
a
What do you think of Zara’s method? Can you improve
a
first term is 8
about how you learn. not know about them. How can you convince him or her that corresponding
her method, or suggest a better one?

angles are equal?
term-to-term rule is: multiply by 2 then subtract 5
b Use what you think is the best method to answer
the question.
first term = 8
Summary checklist
second term = 8 × 2 − 5 = 16 − 5 = 11
This is what you have Summary checklist − 5 =
I can recognise vertically opposite angles and I know that they are equal.
third term = 11 × 2 − 5 =
I can identify corresponding angles and alternate angles between parallel lines.

learned in the unit. I can understand inequalities.
b
I can draw inequalities.
first term is 15, term-to-term rule is: subtract 9 then multiply by 3
c
2 Expressions, formulae and equations
first term is 12, term-to-term rule is: divide by 2 then add 5
108 7 The first three terms of a sequence are 8, 10, 14, …
a Which of these cards, A, B or C, shows the correct term-to-term rule?
Questions that cover what you Check your progress
A
multiply by 3 then subtract 14
have learned in the unit. 1 Jin thinks of a number, x.

Write an expression for the number Jin gets when he divides the number by 2
B
then adds 5. divide by 2 then add 6
2 a Use the formula K = mg to work out K when m = 12 and g = 4 .
b C subtract 3 then multiply by 2
Rearrange the formula K = mg to make m the subject.
c Use your formula in part b to work out m when K = 75 and g = 10.
3 b Expand Which is the first term in this sequence greater than 50?
a x(x + 3)
b 5y(7y − 4w)
4 Factorise
200 a 6x + 9
b
Project 6 Biggest cuboid
2y 2 − 12y
At the end of several units, 5 Work out the value of x and y in this diagram.

All measurements are in centimetres.
6(x + 1)
there is a project for you to Project 6
y
3 + 16 20
carry out, using what you Biggest cuboid

3x + 21
Start with a 12 cm by 12 cm square of paper.
6
Write the inequality shown by this number line. Use the letter x.
have learned. You might make Draw six rectangles that can be cut out and fitted together to make a cuboid.

5
0
For example, these six rectangles could be joined to make this 2 cm by 3 cm
10
25
20
15
something or solve a problem. by 5 cm cuboid:

61
62
There are lots of gaps between the rectangles, so perhaps we could have
made a cuboid with a bigger surface area and a bigger volume.
Can you find a cuboid that uses more of the paper?
What is the volume of your cuboid?
What different volumes of cuboid can you make from a 12 cm by 12 cm square?
Can you find any cuboids that use the whole square of paper?
What is the biggest volume of cuboid you can make? 5
350