數學新里程(第二版) 附加練習 - 樣章

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第 1 章有向數第 8 章代數不等式第章基礎代數第 9 章代數分式及公式第章基礎幾何第 10 章面積和體積第 4 章一元一次方程第 11 章三角比的認識第章百分法第 1 章多邊形第 6 章統計與生活第 1 章集中趨勢的量度第 7 章代數式與多項式第 1 章整數指數定律第 8 章對稱與變換第章續因式分解第 9 章坐標簡介第

1 第 1 章有向數第 8 章代數不等式第章基礎代數第 9 章代數分式及公式第章基礎幾何第 10 章面積和體積第 4 章一元一次方程第 11 章三角比的認識第章百分法第 1 章多邊形第 6 章統計與生活第 1 章集中趨勢的量度第 7 章代數式與多項式第 1 章整數指數定律第 8 章對稱與變換第章續因式分解第 9 章坐標簡介第章立體圖形的探究第 10 章統計圖第 4 章求積法第 11 章二元一次方程第章與三角形相關的定理第 1 章比和率第 6 章概率的認識第 1 章直線圖形中的角第 1 章第章第章第 4 章第章第 6 章估算與近似量度與誤差恆等式與因式分解聯立方程全等與相似三角形平方根與畢氏定理第 7 章第 8 章第 9 章第 10 章第 11 章續百分法四邊形的特性直角坐標幾何三角學的應用統計的應用與誤用第 7 章續統計圖 010 中大出版社版權所有

2 1. 試不用計算機, 求下列各數的平方根 Without using a calculator, find the square roots of the following numbers. a 89 b c d 9. 下列各式是否不盡根? Is each of the following a surd? 是 Yes 否 No a b 484 c. 6 d 試不用計算機, 判斷下列各平方根在哪兩個連續數之間 Without using a calculator, find two consecutive numbers between which each of the following lies. a 中大出版社版權所有

3 即 i.e. 0 0 在和之間 0 lies between and. b 即 i.e 在和之間 180 lies between and. 4. 求下列各數的值如有需要, 答案準確至三位有效數字 Find the values of the following numbers. Give your answers correct to significant figures if necessary. a 80 b 1 04 c. 6 d 4 1 e 10 f 中大出版社版權所有

4 1. 求下列各圖中未知數的值如有需要, 答案準確至三位有效數字 Find the value of the unknown in each of the following figures. Give your answers correct to significant figures if necessary. a Q 4 P 18 p R p 畢氏定理 Pyth. theorem p b 1 1 a 中大出版社版權所有

6 . 右圖中,S 是 QR 的中點且 PS QR 求 p 的值 In the figure, S is the mid-point of QR and PS QR. Find the value of p. 1 p P Q S 18 R. 求右圖中長方形 D 的面積 In the figure, find the area of rectangle D. 17 cm 1 cm D 中大出版社版權所有

8 . 下圖所示為菱形 D 對角線和 D 的長度分別是 10 cm 和 8 cm 兩條對角線互相垂直, 且平分於 F 求菱形 D 的周界答案須準確至三位有效數字 The figure shows rhombus D. The lengths of the diagonals and D are 10 cm and 8 cm respectively. The diagonals are perpendicular to each other and bisect each other at F. Find the perimeter of rhombus D. Give your answer correct to significant figures. F D 中大出版社版權所有

9 6. 下圖中,D 是上的點使 D D In the figure, D is a point on such that D D. 19 m D 6 m a 求的長度答案須準確至三位有效數字 Find the length of. Give your answer correct to significant figures. b 求的長度答案須準確至三位有效數字 Find the length of. Give your answer correct to significant figures 中大出版社版權所有

14 1. 在正午十二時, 飛機位於機場正西方 800 km, 而飛機則位於該機場的正北方 km 若飛機和飛機在同一水平線上, 問該兩架飛機的距離是多少? 答案須準確至最接近的 km t 1:00 noon, aeroplane is 800 km due west of the airport, while aeroplane is km due north of the airport. If aeroplane and aeroplane are on the same horizontal line, what is the distance between these two aeroplanes? Give your answer correct to the nearest km. 北 /N km 800 km 機場 irport 設該兩架飛機的距離為 x km Let x km be the distance between these two aeroplanes 中大出版社版權所有

15 . 已知一塊正方形木板的周界為 60 cm, 求該木板對角線的長度答案須準確至三位有效數字 Given that the perimeter of a square wooden board is 60 cm, find the length of the diagonal of the board. Give your answer correct to significant figures. 對角線 Diagonal 周界 Perimeter 60 cm. 求右圖中 O 的周界 Find the perimeter of O in the figure. y 0, 0 1, 0 O x 中大出版社版權所有

16 4. 汽車和巴士同時由點出發, 並分別以 80 km/h 的速率向東和以 70 km/h 的速率向南行駛問兩小時後汽車與巴士的距離是多少? 答案須準確至最接近的 km car and a bus travel at the speeds of 80 km/h due east and 70 km/h due south respectively from point at the same time. What is the distance between the car and the bus after two hours? Give your answer correct to the nearest km. 80 km/h 70 km/h 北 / N 009 中大出版社版權所有 6.1

17 . 一根長. m 的竹竿靠在一堵直立的牆壁上, 竹竿的頂部距離地面 1.8 m 若竹竿的頂部下滑 0. m, 問竹竿底部移動的距離是多少? 答案須準確至三位有效數字 pole of. m long leans against a vertical wall and its upper end is 1.8 m above the ground. If the upper end of the pole slides down by 0. m, how far will the lower end of the pole move from its original position? Give your answer correct to significant figures. 0. m. m 1.8 m 中大出版社版權所有

22 1. 判斷下列各數是否完全平方若是, 求該數的平方根 a 4 b 6 c 110 d 40 e 784 f Determine whether each of the following numbers is a perfect square. If yes, find the square roots of the number. a 4 b 6 c 110 d 40 e 784 f 判斷下列各式是否不盡根 a 4 b 10 c d e f Determine whether each of the following is a surd. a 4 b 10 c d e f 試不用計算機, 求下列各數的平方根 a 81 b 196 c d e 4 11 f 100. Without using a calculator, find the square roots of the following numbers. a 81 b 196 c d e 4 11 f 中大出版社版權所有

23 4. 求下列各數的值答案須準確至三位有效數字 a 1 b 10 c 90 d 0. 7 e f Find the values of the following numbers. Give your answers correct to significant figures. a 1 b 10 c 90 d 0. 7 e f 6 7. 試不用計算機, 判斷下列各平方根在哪兩個連續數之間 a b c 60 d 140 e 80 f 480. Without using a calculator, find two consecutive numbers between which each of the following lies. a b c 60 d 140 e 80 f 試不用計算機, 求下列各數的平方根 61 a b 79 6 c 4 d.89 e 4.84 f Without using a calculator, find the square roots of the following numbers. 61 a b 79 6 c 4 d.89 e 4.84 f 中大出版社版權所有

24 7. 求下列各式的值答案須準確至三位有效數字 a b c d e f Find the values of the following expressions. Give your answers correct to significant figures. a b c d e f 求下列各圖中未知數的值答案須準確至三位有效數字 8. Find the values of the unknowns in the following. Give your answers correct to significant figures. a b P c 6 a 7 Q 8 b R 11 c 9 9. 求下列各圖中未知數的值答案須準確至三位有效數字 9. Find the values of the unknowns in the following. Give your answers correct to significant figures. a p b Q P 11 q R c Q r 0 P 14 R 中大出版社版權所有

25 10. 下圖中,D 是直線求 c 的值答案須準確至三位有效數字 10. In the figure, D is a straight line. Find the value of c. Give your answer correct to significant figures. c 16 D 11. 求下圖中正方形 D 的邊長答案須準確至三位有效數字 11. In the figure, find the length of each side of square D. Give your answer correct to significant figures. D 10 cm 1. 下圖中, 的面積是 64 cm 求的長度答案須準確至三位有效數字 1. In the figure, the area of is 64 cm. Find the length of. Give your answer correct to significant figures. 6 cm 中大出版社版權所有

26 1. 下圖中, 4 cm 及 : 8 : 1 求的長度 1. In the figure, 4 cm and : 8 : 1. Find the length of. 4 cm 14. 求下圖中梯形 D 的周界 14. In the figure, find the perimeter of trapezium D. 1 cm D 1 cm E 8 cm 1. 下圖所示為平行四邊形 D E 是上的一點使 E : E 1: 4 若 D 0 cm 及 D 1 cm, 求平行四邊形 D 的面積答案須準確至三位有效數字 1. The figure shows parallelogram D. E is a point on such that E : E 1: 4. If D 0 cm and D 1 cm, find the area of parallelogram D. Give your answer correct to significant figures. D 0 cm 1 cm E 中大出版社版權所有

27 16. 下圖中, PQ 18 cm, QR 1 cm 及 PS 10 cm 16. In the figure, PQ 18 cm, QR 1 cm and PS 10 cm. P 10 cm S 18 cm Q 1 cm R a 求 QS 的長度 b 求 RS 的長度答案須準確至三位有效數字 a Find the length of QS. b Find the length of RS. Give your answers correct to significant figures. 17. 求下圖中四邊形 D 的周界答案須準確至三位有效數字 17. In the figure, find the perimeter of quadrilateral D. Give your answer correct to significant figures. 7 cm cm 1 cm D 18. 下圖中, WX 47, XY 40 及 YZ 18. In the figure, WX 47, XY 40 and YZ. Z Y q W p X 中大出版社版權所有

28 a 求 p 的值 b 求 q 的值 c 求四邊形 WXYZ 的面積答案須準確至三位有效數字 a Find the value of p. b Find the value of q. c Find the area of quadrilateral WXYZ. Give your answers correct to significant figures. 19. 求下圖中五邊形 PQRST 的周界答案須準確至三位有效數字 19. In the figure, find the perimeter of pentagon PQRST. Give your answer correct to significant figures. T P S cm 0 cm Q R 7 cm 0. 判斷下列各三角形是否直角三角形若是, 試指出直角 0. Determine whether each of the following triangles is a right-angled triangle. If yes, indicate the right angle. a b 1 c 中大出版社版權所有

29 1. 下圖中, 正方形 D DPQR 和 RST 的面積分別為 6 cm 90 cm 和 1 cm 判斷 DR 是否直角 1. In the figure, the areas of squares D, DPQR and RST are 6 cm, 90 cm and 1 cm respectively. Determine whether DR is a right angle. 面積 rea 90 cm P Q R S D 面積 rea 1 cm T 面積 rea 6 cm. a 求證下圖中 PQR 是直角 b 求 PQR 的面積. a Prove that PQR in the figure is a right angle. b Find the area of PQR. P 4 Q R. 下圖中,D 是上的一點, 且 D D. In the figure, D is a point on and D D. 1 h 9 a 求證是直角三角形 b 求 h 的值答案須準確至三位有效數字 D 6 a Prove that is a right-angled triangle. b Find the value of h. Give your answer correct to significant figures 中大出版社版權所有

30 4. a 求證下圖中是直角三角形 b 若 PQ 4PR, 求證 ~ PQR 4. a Prove that in the figure is a right-angled triangle. b If PQ 4PR, prove that ~ PQR. P 1.. Q R. 下圖中, D D. In the figure, D D. 7 D 74 a 求證 D ~ D b 求四邊形 D 的周界答案須準確至三位有效數字 a Prove that D ~ D. b Find the perimeter of quadrilateral D. Give your answer correct to significant figures. 6. 下圖中, 與 D 相交於 E 6. In the figure, and D intersect at E. D E 中大出版社版權所有

31 a 求證 D b 求和 D 的長度 c D 是否直角三角形? 試解釋 a Prove that D. b Find the lengths of and D. c Is D a right-angled triangle? Explain briefly. 7. 一隻手錶的時針和分針分別長 8 mm 和 1 mm 問在九時正, 兩針尖端的距離是多少? 7. The lengths of the hour hand and minute hand of a watch are 8 mm and 1 mm respectively. What is the distance between the tips of these two hands when it is 9 o clock? 1 1 mm 9 8 mm 6 8. 一把長 m 的梯子靠在一堵直立的牆壁上若梯子的頂部距離地面. m, 問梯子的底部距離牆壁多遠? 答案須準確至三位有效數字 8. ladder of m long leans against a vertical wall. If the upper end of the ladder is. m above the ground, what is the distance between the lower end of the ladder and the wall? Give your answer correct to significant figures. m. m 中大出版社版權所有

32 9. 求下列各圖中的坐標及 O 的長度 9. In each of the following figures, find the coordinates of and the length of O. a y 1, 16 b y O x O x 1, 9 0. 一條長 6.4 m 的繩子, 一端固定在地面的 D 點, 另一端固定在燈柱的點燈柱的頂部和底部與點的距離相等若 D.6 m, 求燈柱的高度答案須準確至小數點後一個位 0. One end of a rope of 6.4 m long is fixed at point D on the ground, while the other end is at point on a lamp post. The distances from point to top and to bottom of the lamp post are the same. If D.6 m, find the height of the lamp post. Give your answer correct to 1 decimal place. 6.4 m D.6 m 1. 下圖中, 兩根垂直於地面的木柱相距 m, 較矮一根木柱的高度為 m 若兩根木柱的頂端相距 7 m, 問較高木柱的高度是多少? 答案須準確至三位有效數字 1. In the figure, two vertical poles are m apart and the height of the shorter pole is m. If the distance between the tops of the poles is 7 m, what is the height of the longer pole? Give your answer correct to significant figures. 7 m m m 中大出版社版權所有

33 . 求下圖中的周界. In the figure, find the perimeter of. y 9, 6, 6 O x,. 下圖所示為一座高 0 m 的燈塔, 兩根鋼纜連接塔頂和地面上的和 D 兩點, 其中 D 成一直線若 D 0 m, 求和 D 的距離答案須準確至三位有效數字. In the figure, the lighthouse is 0 m high. The top of the lighthouse is connected to points and D on the ground by two wires, where D is a straight line. If D 0 m, find the distance between and D. Give your answer correct to significant figures. 0 m 0 m 0 m D 4. 下圖所示為長方形桌面 D 若 D 的面積為 0.98 m 及, 求對角線的長度答案須準確至三位有效數字 4. The figure shows a rectangular top D of a desk. If the area of D is 0.98 m and, find the length of diagonal. Give your answer correct to significant figures. D 中大出版社版權所有

34 . 某草地球場之長度和闊度分別是 10 m 和 74 m. The length and width of a field are 10 m and 74 m respectively. D 74 m 草地球場 Field 以下是從點步行往點的其中兩條路徑 : 路徑一..沿草地球場的邊緣行走即路徑二..沿草地球場的對角線行走即問以上兩條路徑的長度相差多少? 答案須準確至三位有效數字 10 m The following are two routes to walk from point to point. Route 1: Walking along the sides of the field i.e.. Route : Walking diagonally across the field i.e.. What is the difference in length between the above two routes? Give your answer correct to significant figures. 6. 已知一塊正方形木板的面積是 1 cm, 求木板對角線的長度答案須準確至三位有效數字 6. Given that the area of a square wooden board is 1 cm, find the length of the diagonal of the board. Give your answer correct to significant figures. 對角線 Diagonal 面積 rea 1 cm 7. 樂恆由點出發, 以 60 m / 分鐘的速率向西步行他步行分鐘後到達點一棵大樹與點和點的距離分別為 4 m 和 8 m 7. Oscar walked due west from point at a speed of 60 m/min. fter minutes, he reached point. tree is 4 m and 8 m away from points and respectively. 北 / N 8 m 4 m 中大出版社版權所有

35 a 求證點在該樹的北面 b 若樂恆在點以相同速率繼續向西步行分鐘, 最終到達點求點與該樹的距離答案須準確至三位有效數字 a Prove that point is due north of the tree. b If Oscar continued to walk due west from point at the same speed for minutes, he reached point finally. Find the distance between point and the tree. Give your answer correct to significant figures. 8. 求下圖中 PR 的長度答案須準確至三位有效數字 8. In the figure, find the length of PR. Give your answer correct to significant figures. y P, 4 Q 4, 4 O x S 4, R, 9. 求下圖中多邊形的面積答案須準確至三位有效數字 9. Find the area of the polygon in the figure. Give your answer correct to significant figures. 4 cm cm 1 cm cm 40. 化簡下列各式 a b c d e f Simplify the following. a b c d e f 中大出版社版權所有

36 41. 化簡下列各式 a 8 b 99 c 104 d 140 e 64 f Simplify the following. a 8 b 99 c 104 d 140 e 64 f 化簡下列各式 a b c d e f Simplify the following. a b c d e f 化簡下列各式 a 6 4 b 10 4 c 60 4 d e f Simplify the following. a 6 4 b 10 4 c 60 4 d e f 中大出版社版權所有

38 46. 把下列各數的分母有理化 46. Rationalize the denominators of the following. a 1 a 1 b 6 10 b 6 10 c c d 108 d 108 e 4 e 4 f f 把下列各數的分母有理化 47. Rationalize the denominators of the following. a 64 7 a 64 7 b 1 b 1 c c d 18 d 18 e 1 7 e 1 7 f f 中大出版社版權所有

40 工作紙頁 1. a 17 或 or 17 b 0 或 0 0 or 0 c 0.0 或 or d 或 or. a 是 Yes b 否 No c 是 Yes d 否 No. a 和 6 之間 etween and 6 b 1 和 14 之間 etween 1 and a 8.94 b c 1.90 d 0.16 e 10.4 f 14. 工作紙 6 6. 頁 1. a 0 b 1. c 17. d cm cm..6 cm 6. a 18.0 m b 1.7 m 工作紙頁 1. a 否 No b 是,PRQ Yes, PRQ. b 7.. a 84 h b 面積 rea ; h b 108 工作紙 6D 6.1 頁 km. 1. cm. 70 單位 70 units 4. 1 km m 工作紙 6E 6.17 頁 1. a 9 b 8 c 4 7 d 6. a 11 b 7 c 1 d 6 7. a 1 7 b c 6 4. a 8 b c 工作紙 6F 6.19 頁 1. a. a b b c c d d d d. a 7 b 4 14 c 7 1 d a b 1 6 c 18 d 7 7 強化練習頁 1. a 否 No b 是 ;6 或 6 Yes, 6 or 6 c 否 No d 否 No e 是 ;8 或 8 Yes, 8 or 8 f 是 ; 或 Yes, or. a 是 Yes b 是 Yes c 否 No d 是 Yes e 否 No f 是 Yes. a 9 或 9 9 or 9 b 14 或 or 14 c 或 or 1 d 或 or e 或 or 11 f 或 or a 4.8 b 11.0 c 0.8 d 0.87 e.0 f a 4 和之間 etween 4 and b 和 6 之間 etween and 6 c 7 和 8 之間 etween 7 and 8 d 11 和 1 之間 etween 11 and 1 e 19 和 0 之間 etween 19 and 0 f 1 和之間 etween 1 and a 或 or b 或 or 中大出版社版權所有

41 c 或 or d 1.7 或 or 1.7 e. 或.. or. f 0.0 或 or a 1.8 b 7.0 c 7. d 6. e 9. f 1. 強化練習 6 6. 頁 8. a 11.4 b 8.4 c a 9.80 b 9.80 c cm cm 1. 0 cm cm 1. 6 cm 16. a 1.0 cm b 19. cm cm 18. a 1. b 0.4 c cm 強化練習頁 0. a 是, Yes, b 否 No c 是, Yes, 1. 是 Yes. b 7.. b.4. b b 0, D 4 c 否 No 強化練習 6D 6.0 頁 mm 8..7 m 9. a 1, 0, O 0 單位 1, 0, O 0 units b 0, 9, O 1 單位 0, 9, O 1 units m m. 6 單位 6 units m m. 4.4 m cm 7. b 488 m 單位 7.1 units cm 強化練習 6E 6.4 頁 40. a 8 b c d e 11 f a 7 b 11 c 6 4. a d e 66 f 6 1 d 8 b e 10 6 c f a 18 b 1 c 6 70 d e f 44. a 10 b d 1 0 強化練習 6F 6.6 頁 4. a d 46. a d 47. a d b e b 10 e b e c c f 9 c f c f 48. a 17 b 10 7 c d 11 e 11 f a 1 b 6 1 c 7 7 d e 18 f 中大出版社版權所有

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Microsoft Word - 0.5bh.doc 198 FG7. 199 HG8 E 圖中,DE 為一正方形, = 及為一邊長 1 cm 的等邊三角形, 而為此 = 90 若 DE 的面積為 10 cm, 三角形內的任意一點 ( 如圖所示 ) 若至三邊求的面積及的垂直距離的總和為 x cm, 求 x 的值 In the figure shown, DE is a square and is an equilateral triangle