Page 21 - 新思维数学学生用书8 样章

1 Integers

10 a Show that 3 + 4 = 5 2
2
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b Are these statements true or false? Give a reason for your answer each time.
i (−3) + (−4) = (−5) 2
2
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ii (−13) = 12 + (−5) 2
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iii 8 = −10 − 6 2
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c Show your work to a partner.
Do they find your explanation clear?

Think like a mathematician

11 a Here is an equation: x + x = 6
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i Show that x = 2 is a solution of the equation.
ii Show that x = −3 is a solution of the equation.
b Here is another equation: x + x = 12
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i Show that x = 3 is a solution of the equation.
ii Find a second solution to the equation.
c Find two solutions to this equation: x + x = 20
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d What patterns can you see in the answers to a, b and c?

Find some more equations like this and write down the solutions.
e Compare your answers with a partner’s.

12 a Copy and complete this table.
x x − 1 x − 1 x + x + 1
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3
2 1 7
3 2 13
4
5

b What pattern can you see in your answers?
c Add another row to see if the pattern is still the same.
d Add three rows where x is a negative integer.

Is the pattern still the same if x is a negative integer?
e Compare your answers with a partner’s.

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