Chapter 3 Use of Formula
3.17
OPEN-ENDED QUESTION ZONE
1
If A  bh , write down two sets of values of b and h such that A is greater than 20.
2
4 marks: 2 marks for correct answer; 2 marks for clear explanation.
S UGGESTED SOLUTION
[ Analysis: We may substitute different values of b and h by trial and error. ]
Let b  2 and h  41.
1
A  (2)(41)
2
 41
 20
Let b  4 and h  13.
1
A  ( 4)(13)
2
 26
 20
 b  2, h  41 and b  4, h  13 are two sets of required values.
S OLUTION
OF A STUDENT
1
bh
2
 bh  2A
 A
When A  20
i . e . b . h  40
 b  5, h  9 and
b  6, h  8
 
(Translated from a Student's Solution in Chinese)
Comments
This student can give correct answers and explain clearly.
3.18
New Trend Mathematics S2A — Junior Form Supplementary Exercises
Explain how to find two algebraic fractions such that their sum is a polynomial.
5 marks: 2 marks for correct answer; 3 marks for clear explanation.
S UGGESTED SOLUTION
[ Analysis: Since the difference of two identical algebraic fractions is 0, i.e. a polynomial, we can make use of
this property to obtain the required algebraic fractions. ]
1
1

0
x 1 x 1
1
1
 (x 
)  (
)x
x 1
x 1
1
x( x  1)  1
 x

x 1
x 1



x2  x 1
x 1
x2  x 1
1
and 
are two required algebraic fractions.
x 1
x 1
S OLUTION
OF A STUDENT
x  4 x 2x  4
 
x 2
2
2
2
(polynomial)
 
(Translated from a Student's Solution in Chinese)
Comments
This student does not know the meaning of algebraic fractions.
Exercise of Open-ended Questions 3
Level 1
1
1. If A  (a  b)h , write down two sets of values of a, b and h such that A is smaller than
2
15.
4 marks: 2 marks for correct answer; 2 marks for clear explanation .
Chapter 3 Use of Formula
3.19
2. The figure shows rectangle ABCD. Let P cm be its perimeter. Find two values of x such
that P is greater than 30.
A
(x  1) cm
B
(x  3) cm
D
C
4 marks: 2 marks for correct answer; 2 marks for clear explanation.
Level 2
3. Explain how to find three algebraic fractions whose sum is a constant.
5 marks: 3 marks for correct answer; 2 marks for clear explanation.
4. Write down the values of a, b, c, d and x to make the following equality holds.
a
c
19


7 marks: 5 marks for correct answer; 2 marks for clear explanation.
b( x  1) d (1  x) 12
3.20
New Trend Mathematics S2A — Junior Form Supplementary Exercises
This is a blank page.