Page 15 - 新思维数学活动用书9 样章

2 Expressions and formulae

Use a counter-example to show that each of these statements is not true (x ≠ 0, y ≠ 0).

a 10x = (10x) 2 b (2y) = 2y 3 c 3x − 3y = 3(y − x)
2
3
10 Here are two expressions that you can use to estimate the mass, in kg, of a child aged between
one and five years old. A is the age, in years, of the child.

Expression 1 Expression 2
5A + 8 2(A + 4)
2

a Use expression 1 to estimate the mass, in kg, of a 4-year-old child.
b Use expression 2 to estimate the mass, in kg, of a 3-year-old child.
c Copy and complete the table showing the estimates of the mass of a child using both
expressions.

Age (A years) 1 2 3 4 5

Mass using expression 1
Mass using expression 2

d Fasil is 3 years old and has a mass of 13.5 kg.

Which expression would give the best estimate for his mass?
Explain your answer.
11 Work out the value of each expression.

a 5(x − ) x + 5x 2 − 12x when x = 3
3
3
y
b 3y+ 16 +    4 − 20 when y = 4
4  2 y

3c
+
−
−
12 Show that 4d − 100 − 3cdc cd = d + 8c 2 () 2 − −− c 2
)
)
(
(4
2
3
c 2 ( cd ) d
+
when c = 5 and d = −3.

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