1. x + 2 = 10 2. 3y = -33 3. 6h + 7 = 19
4. -4 = 10 - 2k 5. 2 = y 5 1- 6. 5d + 2d = 42
7. 9 - 5e = -8e 8. r - 2 = 5r - 6 9. 4 + 6s + 9 = 2s - 3
習 題 3C
程度一
解下列各方程。[第 1-21 題]
1. x + 3 = 15 2. y - 8 = 12 3. 3z = 27
4. 5a = -65 5. u
6 = -11 6. w
3
2
- = -12
7. 2b - 7 = 15 8. 6 + 3c = -9 9. 32 = 5 + 9d
10. 20 = -16 - 6F 11. r 4 5- = 7 12. 13 = S
4
12 13.
3(p + 4) = 12 14. -18 = 6(Q - 2) 15. h
3 + 9 = 8
16. 11 - k
4 = -5 17. 2m + 6
1 = 6
5 18.
8
3- - 5n = 8
7
19. 12 + 7a - 6 = -15 20. 24 - 4b + 9 = 17 21. 16 = 2 - 3c - 10
解下列各方程。[第 22-31 題]
22. 2u + 8u = 30 23. 12 = 3w - 9w
24. 5x + 8 = 3x 25. -7y = 15 - 4y
26. 4z + 5z + 6 = 15 27. 2a - 6 - 5a = -27
28. 3B + 8 = 4B + 2 29. 8c + 27 = 3c - 18
30. 25 - 4d = 6d + 35 31. -8 - 7T = 4 - 3T
程度二
解下列各方程。[第 32-49 題]
32. 0.5a + 6 = 8 33. 7.4 - 3b = 0.2
34. x4
91+ = 7 35.
y2
35- = -4
➥ 例 9
➥ 例 10
➥ 例 11
程度 0
程度 0
程度 0
程度 0
程度 0
程度 0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
2
2
2
2
2
1
1 習題目標
1 利用移項和/或轉移乘除
運算的技巧解方程。
2 合併同類項以解方程。
考試題型 參考
TSA Q13,Q14,
Q28-Q31,
Q34,Q35 2019 (MC1) Q28,
2017 (MC2) Q27,
2014 (MC2) Q29
鞏固練習 3C
1
3
1
8
7
-3
-11
11
1
2 6
-4
12
3
-4
6 -1
4
3
-13
11
-6
0
-3
64
20
-2
-5 -9
-3
2.4
-1
7
-66-5
33
-1
4
9
18
3
-40
-3
-8
4
1
8.12
Chapter 8
27. The figure shows the graph for Keith running along a
straight road. It is given that Keith runs from city P to city Q
at a speed of 6 km/h.
(a) Find the distance between city P and city Q.
(b) How long does Keith stay at city Q?
(c) If Keith runs back from city Q to city P along the same
road at a speed of 5 km/h, when will he arrive at city P?
28. The figure shows the graph for a car travelling from city P
to city R via city Q along a straight road.
(a) Find the speed of the car travelling from city P to city Q
in km/h.
(b) If the car travels from city Q to city R at a speed of
72 km/h,
(i) find the distance between city P and city R,
(ii) find the average speed of the car travelling from
city P to city R.
Level 3
29. There are two types of tea leaves, packs A and B, in a shop. Each pack
A weighs 50 g and costs $180, whereas each pack B weighs 40 g and
costs $160.
(a) Which pack of tea leaves has a higher cost rate?
(b) The shopkeeper mixes one pack A and one pack B of tea leaves
together to form a new pack C. He claims that the cost of pack
C is $ 2
50
180
40
160+
/g, i.e. $3.8/g. Do you agree? Explain your
answer.
30. Towns A, B, C and D are on the same straight
road. The figure shows the graphs for Terry and
Sarah running along the road.
(a) Find the speed of Terry.
(b) When do Terry and Sarah meet?
(c) Who is faster? Explain your answer.
8:15
0
7:00 7:30
city Q
Distance from city P (km)
city P
Time
➥ Example 5
8:45
75
0
6:00 7:30
city Q
city R
Distance from city P (km)
city P
Time
Explain
6:00
6
10.5
16
0
4:00
town B
town C
town D
Distance from town A (km)
town A
Time
Terry
Sarah
Explain
三角比的關係 11.29
✔ 課後評估
[在本習題中,不得使用計算機。]
1. 把左右兩欄配對起來。
1 - sin2 i •
cos2 (90c - i) • • sin2 i
cos
sin i
i • • cos2 i
1 - sin2 (90c - i) • • tan i
()
tan90
1
c i •
判斷下列各題是「對」還是「錯」。「對」的在 內 加「 ✓」;「 錯 」的 加「 ✗」。 [第 2-8 題]
2. sin 45c = cos 45c
3. sin 30c + cos 60c = tan 45c
4. tan 60c = 3 tan 30c
5. 已知 sin i = 5
4 ,其中 i 是一個銳角。我們可以
繪畫圖中的三角形,從而求得 tan i = 4
3 。
6. (sin 24c + cos 24c)2 = 1
7. cos
cos 40
50c
c = tan 40c
8. tan 10c + tan 80c = 1
完成下列各題。[第 9-10 題]
9. sin2 63c + sin2 ( ) = 1
10. tan 30c tan 40c tan 60c =
()
tan 1
5
4 3
11.62 Chapter 11
Cross-topic Questions
52. The figure shows a 3ABC in a rectangular coordinate plane, where
BC = 5 units.
(a) Find the distance between A and B.
(b) Find the coordinates of C.
53. If (x + A)(x + 8 ) / x2 + Bx - 4, find the constants A and B.
54. In the figure, ABC, CDE and BDF are straight lines, and AC # EF.
(a) Is 3CDB a right-angled triangle? Explain your answer.
(b) If DE : DC = 1 : 2 and CD = EF = 2 cm, find the sum of
the perimeters of 3BCD and 3DEF.
(Leave the radical sign ' ' in the answer.)
Multiple-choice Questions
55. Find the value of ()3 44 - .
A. 3
B. -3
C. 3 or -3
D. 4
58. In the figure, hexagon BCDEFG is obtained
by cutting out square AGFE from square
ABCD. The areas of ABCD is 81 cm2. Find
the perimeter of hexagon BCDEFG.
A. 20 cm
y
x
O
C
B(-1,-1)
A(-1,2)
✂
✂
150°
60°
C
A
E F
D
B
Explain
A G B
13
1A 冊 第3章 • 第3.25頁
3B 冊 第 11 章 • 第11.29頁
Book 2B Ch.11 • P.11.63
Book 2B Ch.8 • P.8.12
習題 Exercise
保底 少辣
保底 少辣
程度0習題
課後評估
拔尖 加辣
拔尖 加辣
跨課綜合題
程度3習題