Page 29 - 新思维数学学生用书9 样章

2 Expressions and formulae

a Read what Sofia says.

I use a different
method to write the
expression for the
perimeter. I work out
perimeter = 2(x + 5) + 2(2x),
then I expand the brackets
and simplify.

Show that Sofia’s method will give the correct expression for the perimeter.
b Critique each method. Whose method do you prefer to use to write the expression for the
perimeter? Explain why.
c When x = 3, copy and complete these workings:

length of rectangle = x + 5 = 3 + 5 =
width of rectangle = 2x = 2 × 3 =
perimeter = 2 × length + 2 × width = 2 × + 2 × =
area = length × width = × =

d When x = 3, copy and complete these workings:
perimeter = 6x + 10 = 6 × 3 + 10 =

area = 2x + 10x = 2 × 3 + 10 × 3 = + =
2
2
e What do you notice about your answers for the perimeter and area in parts c and d?
Do you think this is a good method to use to check your expressions are correct?
Explain your answer.
5 Write an expression for i the perimeter and ii the area of each rectangle.

Write each expression in its simplest form.
iii Then use the values given, and the method from Question 4, to check your expressions

are correct.
a x + 2 b y – 6
3
4
x = 4
y = 10
c n + 4 d p 2

4p
n
p = 2

n = 6

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