Page 27 - 新思维数学学生用书9 样章

2 Expressions and formulae

Worked example 2.2

a Ahmad thinks of a number, n.
Write an expression, in terms of n, for the number Ahmad gets when he

i divides the number by 3, then subtracts 6
ii adds 3 to the number, then multiplies the result by 4
iii multiplies the number by itself, then halves the result
iv square roots the number then adds 5.

b The diagram shows a rectangle. Write an expression in terms of x for x 2
i the perimeter 3x + 4
ii the area.
Write each expression in its simplest form.

Answer

n
a i n − 6 Divide n by 3, then subtract 6. Write n ÷ 3 as .
3 3
ii 4(n + 3) Add 3 to n, then multiply the result by 4. Write n + 3 inside
brackets to show this must be done before multiplying by 4.
2
iii n 2 Multiply n by itself to give n × n; write this as n .
2
n
2 Then divide the result by 2. Write n ÷ 2 as .
2
2
iv n + 5 Square root n. Then add 5.
b i 3x + 4 + 3x + 4 + x + x 2 Add together the lengths of the four sides to work out
2
the perimeter.
= 2x + 6x + 8 Simplify the expression by collecting like terms.
2
ii x (3x + 4) Multiply the length by the width to work out the area.
2
= 3x + 4x 2 Simplify the expression by multiplying out the bracket.
3

Exercise 2.2

1 Kara thinks of a number, n.
Write the correct expression from the cloud for the number Kara gets when she:
a adds five to the number
b multiplies the number by five, then subtracts five 5 – n 5(n + 5)

c divides the number by five, then adds five 5n – 5 n − 5
d adds five to the number, then multiplies by five 5
e subtracts five from the number, then divides by five n + 5 n + 5
5
f subtracts the number from five.

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