Oxford Mathematics for the New Century
© Oxford University Press 2020 Final Exam Paper S1 (2020-2021) P.9
Long Questions (53 marks)
Answer ALL questions and give your solutions in the spaces provided.
13. The figure shows a piece of rectangular glass. The perimeter P cm of the glass
can be calculated by the formula P = 2(a + b), where a cm and b cm are the
length and the width of the glass respectively.
(a) If P = 56 and b = 12, find the length of the glass.
(b) It is given that the cost $C of making the glass can be calculated by the
formula C = 3ab + 50. Johnny has $600. Does he have enough money to
make a piece of rectangular glass of perimeter 56 cm and width 12 cm?
Explain your answer.
(7
marks)
a cm
b cm
- 9
牛津數學新世代
© 牛津大學出版社 2020 期終考試卷 中一 (2020-2021 年度) 第 18 頁
多項選擇題 (90 分)
選出每題最佳的答案。
1. 240 =
A. 23 3 5
B. 23 52
C. 24 3 5
D. 24 52
2. 參看以下數線。下列何者正確?
I. A > 0
II. B > A
III. AB > 0
A. 只有 I
B. 只有 III
C. 只有 I 及 II
D. 只有 II 及 III
3. 秀怡買了 5 盒朱古力,每盒有 x 粒朱古力。若她把朱古力平均分給 8 名小
朋友,每名小朋友可分得多少粒朱古力?
A.
8
5x
B. 8 5x
C. 5x + 8
D. 5x 8
4. 考慮公式 P = 2(a + r)。若 P = 20 和 r = 3,則 a =
A. 7。
B. 13。
C. 15。
D. 21。
A B 0
- 18
Oxford Mathematics for the New Century
© Oxford University Press 2020 Final Exam Paper S1 (2020-2021) P.1
Name of School
Final Exam Paper S1 (2020-2021)
Name: ( ) Time allowed: 1 hour 30 minutes
Class: Full marks: 200
Date:
Short Questions (57 marks)
Answer ALL questions and give your solutions in the spaces provided.
1. Calculate the following expressions.
(a)
5
4 + 3
7 2 (b) 2.8 + 5.2 4.5
(4 marks)
2. Evaluate the following expressions.
(a) 3 + (4)(5) (b)
62
)2(6
(4 marks)
- 1 © 牛津大學出版社
2020 1B
第 8 章 程度一 第 3 頁
解:
(a) R(5 , 3) 和 S(1 , 4) 屬於象限 I。 1A+1A
(b) T(-4 , -2) 屬於象限 III。 1A
<end>
<code=10250971>
<bk=1A><ch=8><ex=8A><lvl=L1><cat=F,TSA><mark=2><title=10250971><content>
在下列各直角坐標平面上,標出指定的點。
(a) P(2 , 3) (b) P(1 , 2)
(2 分)
解:
(a)
1A
(b)
1A
<end>
y
x
0
3 2 1 1
2
1
1
2P
y
x
0 1 2 3
3
2
1
P
y
x
0 1 2 3
3
2
1
y
x
0
3 2 1 1
2
1
1
2
- 290 © OXFORD
UNIVERSITY PRESS 2020 1A Chapter 5 Level 2 P.54
<code=10235340>
<bk=1A><ch=5><ex=5B><lvl=L2><cat=F,EYA><mark=5><title=10235340><content>
Carol has 300 stamps. The number of stamps owned by Betty is 40% less than that owned by
Carol.
(a) Find the number of stamps owned by Betty.
(b) If Betty gives some of her stamps to Carol, is it possible that the number of stamps owned by
Betty is exactly half of that owned by Carol? Explain your answer.
(5 marks)
Solution:
(a) Number of stamps owned by Betty
= 300 (1 40%) 1M
= 300 0.6
= 180 1A
(b) ∵
3 300180
= 160, which is an integer. 1M+1A
∴ It is possible that the number of stamps owned by Betty is exactly half of that owned by
Carol. 1A
Alternative
Suppose Betty gives x stamps to Carol so that the number of stamps owned by Betty is half
of that owned by Carol.
Then the number of stamps owned by Carol is 300 + x. 1M
2
1 (300 + x) = 180 x 1A
300 + x = 2 (180 x)
300 + x = 360 2x
3x = 60
x = 60 3
= 20
∴ It is possible that the number of stamps owned by Betty is exactly half of that owned by
Carol. 1A
<end>
<code=10235398>
<bk=1A><ch=5><ex=5B><lvl=L2><cat=F><mark=4><title=10235398><content>
There were 750 newborn babies in a hospital last year. The number of newborn babies decreases
by 12% this year. Find
(a) the difference in the number of newborn babies between this year and last year,
(b) the number of newborn babies this year.
(4 marks)
- 188 © OXFORD
UNIVERSITY PRESS 2020 1B Chapter 8 Level 2 P.78
<code=10261515>
<bk=1B><ch=8><ex=8B><lvl=L2><cat=F,CT><mark=5><title=10261515><content>
S(2 , 4) and T(2 , 6) are two points in a rectangular coordinate plane.
(a) Find the length of ST.
(b) The y-coordinate of S is increased, and the x-coordinate of S and the coordinates of T remain
unchanged. If the new length of ST is 11 units, find the percentage increase in the y-coordinate
of S.
(5 marks)
Solution:
(a) ST = [4 (6)] units 1M
= 10 units 1A
(b) Let u be the new y-coordinate of S.
u (6) = 11 1M
u = 5
∴ The new y-coordinate of S is 5.
The required percentage increase
= 4
45 100% 1M
= 4
1 100%
= 25% 1A
<end>
<code=10261529>
<bk=1B><ch=8><ex=8C><lvl=L2><cat=F,EYA><mark=6><title=10261529><content>
D(5 , 5), E(5 , 3) and F are three points in a rectangular coordinate plane, where F lies on the
y-axis. Jerry claims that the area of △DEF can be equal to 20 sq. units. Do you agree? Explain
your answer.
(6 marks)
Solution:
∵ F lies on the y-axis.
∴ x-coordinate of F = 0 1M
∵ D and E have the same x-coordinate.
∴ DE is a vertical line. 1M
Height of DEF with base DE
= (5 - 0) units 1M
= 5 units
DE = [5 - (-3)] units 1M
= 8 units
Area of DEF
- 365 牛津數學新世代
© 牛津大學出版社 2020 學期考試卷 1A (2020-2021 年度) 第 1 頁
學校名稱
學期考試卷 1A (2020-2021年度)
姓名: ( ) 時間: 1小時30分鐘
班別: 總分: 200分
日期:
短題目 (57 分)
各題均須作答,題解須寫在預留的空位內。
1. (a) 用指數記數法把下列各數寫成質因數連乘積。
(i) 18
(ii) 24
(b) 由此,求 18 和 24 的 H.C.F.和 L.C.M.。
(5 分)
2. 比較下列各組數的大小,並以「>」或「<」來表示。
(a) +5 _______ 15
(b) 0.3 _______ 0
(c) 2 020 _______ 2 021
(3 分)
牛津數學新世代
© 牛津大學出版社 2020 學期考試卷 1A (2020-2021 年度) 第 13 頁
多項選擇題 (90 分)
選出每題最佳的答案。
1. 下列哪個數是合成數?
A. 71
B. 79
C. 81
D. 89
2. 下列哪個數不可以被 9 整除?
A. 2 169
B. 3 897
C. 5 601
D. 7 020
3. 下列何者正確?
I.
6
5
8
7 =
68
57
II.
9
2
4 =
9
249
III.
3
1
5 = 16 5
A. 只有 I
B. 只有 II
C. 只有 I 及 III
D. 只有 II 及 III
4. 參看以下的數線。哪一點代表 +4?
A. P
B. Q
C. R
D. S
0 +2
8 P QRS
Oxford Mathematics for the New Century
© Oxford University Press 2020 Term Exam Paper 1A (2020-2021) P.7
Long Questions (53 marks)
Answer ALL questions and give your solutions in the spaces provided.
14. A piece of metal at 10C is heated by a burner. It is given that the temperature
of the metal increases by xC every second by heating. Suppose that the
temperature of the metal is 38C after it is heated for 24 seconds.
(a) Find the value of x.
(b) Find the time required to increase the temperature of the metal to 230C by
heating.
(c) Jacky claims that the temperature of the metal is over 500 C after it is
heated for 4 minutes. Do you agree? Explain your answer.
(8 marks)
k = 5
60
= 12
<end>
<code=10216890>
<bk=1A><ch=3><ex=3E><lvl=mcL1><cat=F,DSE><mark=2><title=10216890><content>
Andy spends $x on a gift. The amount of money spent by Sharon on a gift is $20 less than that
spent by Andy. If they spend $100 in total, find the amount of money spent by Sharon on the gift.
A. $40
B. $50
C. $60
D. $80
Solution:
The answer is A.
x + (x 20) = 100
2x = 100 + 20
2x = 120
x = 2
120
= 60
Amount of money spent by Sharon on the gift
= $(60 20)
= $40
<end>
<code=10216970>
<bk=1A><ch=3><ex=3A><lvl=mcL1><cat=F><mark=2><title=10216970><content>
Represent the word phrase 'divide x by y, and then subtract 4 from the quotient' by an algebraic
expression.
A.
x
y
4
B. 4
x
y
C.
y
x
4
D. 4
y
x
Solution:
The answer is D.
<end>
29
學期考試卷
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