Chapter 1 - hkscmaths.files.wordpress.com€¦ · Web viewUnit 1 Laws of Indices 1. Simplify and express your answer with positive index. 2. Simplify and express your answer with

Unit 1 Laws of Indices

1. Simplify and express your answer with positive index.

2. Simplify and express your answer with positive indices.







Solution

MULTIPLE CHOICE QUESTIONS

1. A.B.C.D.

2. A.B.C.D.

3. A.B.C.D.

4. If , then

A. .B. .C. .D. .

5.

A. 0B.C.D.

Unit 2 Formulas

1. Make a the subject of the formula .

2. Make k the subject of the formula .

3. Make x the subject of the formula .

4. Make n the subject of the formula .

5. Make a the subject of the formula .

6. Make k the subject of the formula .

7. Make x the subject of the formula .

8. Make n the subject of the formula .

9. Consider the formula .

(a) Make q the subject of the above formula.(b) If p is increased by 2, what is the change in the value of q?

10. Consider two formulas and .

(a) Express b in terms of x and y.

(b) If x and y are both increased by 4, what is the change in the value of b?


1. If , then q =

A. .

B. .

C. .

D. .

2. If , then k =

A. .

B. .

C. .

D. .

3. If , then r =

A. .

B. .

C. .

D. .

4. Consider the formula . Find the value of x when y = 9.

A. 24B. 21C. 12D. 8

5. Consider the formula . If v is increased by 3, what is the change in the value of u?

A. Decreased by 6

B. Decreased by 3

C. Increased by 3

D. Increased by 6

Unit 3 Identities and Factorization

1. Factorize(a) ,(b) .















Section A1.

A.B.C.D.

2. A.B.C.D.

3. A.B.C.D.

4. A.B.C.D.

5. A.B.C.

D.

6. A.B.C.D.

7. If p and q are constants such that , then A. .B. .C. .D. .

8. If h and k are constants such that , then A. .B. .C. .D. .

9. If a, b and c are non-zero constants such that , then

A. .B. .C. .D. .

Unit 4 Percentages1. Tom earns $12 000 a month and spends 60% of his salary on rent.

(a) How much does he spend on rent per month?(b) If the monthly rent is increased by $1500, what percentage of his salary is spent on rent?

2. It is known that Henry is 162 cm tall and Henry is shorter than Peter by 10%.(a) Find the height of Peter.(b) If John is taller than Henry by 10%, are John and Peter of the same height? Explain

your answer.

3 A packet of candies is shared among three children Ada, Betty and Cindy. The number of Ada’s candies is 25% more than that of Betty while the number of Betty’s candies is 10% more than that of Cindy. It is given that Cindy has 240 candies.(a) Find the total number of candies in the packet at the beginning.(b) By what percentage is the number of Ada’s candies more than that of Cindy’s?

4. A hawker bought 80 apples for $200. He sold 60% of the apples at $4 each, 30% of the apples at $2.5 each and the rest at $2 each.(a) Find the total amount received from selling all the apples.(b) Find the profit per cent.

5. The marked prices of two suits A and B are both $1500. If they are both sold at 10% off, the profit per cent of suits A is 50%, while the loss per cent of suit B is 50%.(a) Find the cost prices of suit A and suit B.(b) Find the profit/loss per cent from selling the two suits.

6. The marked price of a bag is $560 and it is sold at a discount of 25%.(a) Find the selling price of the bag.(b) If a loss of $60 is made by selling the bag, find the loss per cent.

7. Mr Wong deposits a sum of $200 000 in Bank A and Bank B. The simple interest rates offered by Bank A and Bank B are 3.5% p.a. and 4.5% p.a. respectively. After 2 years, the simple interests received from these 2 banks are the same. How much did Mr Wong deposit in Bank A and Bank B respectively?

8. Sally wants to deposit $9000 in a bank for 3 years. (a) If Bank A offers an interest rate of 5% p.a., compounded half-yearly, find the compound

interest obtained by Sally after 3 years. (Give your answer correct to the nearest dollar.)(b) It is known that the simple interest rate offered by Bank B is 5.5% p.a.. Which bank, A

or B, should Sally deposit the money in order to get more interest after 3 years? Explain

your answer.MULTIPLE CHOICE QUESTIONS

1. In a school, 45% of the students are female. If 80% of the male students and 60% of the female students wear glasses, then the percentage of students who wear glasses is

A. 27%.B. 29%.C. 71%.D. 73%.

2. The length and the width of a rectangle are decreased by 10% and x% respectively. If the area of the rectangle is decreased by 23.5%, then x =

A. 10.B. 13.5.C. 15.D. 18.5.

3. Gloria buys a watch for $2400. She sells the watch to Edmond at a loss of 10%. At what price should Edmond sell the watch in order to have a profit per cent of 20%?

A. $2112B. $2592C. $2727D. $3168

4. If a book is sold at its marked price, then the profit per cent is 25%. If the book is sold at a discount of 30%, a loss of $15 will be resulted. Find the cost of the book. A. $105

B. $120C. $150D. $185

5. A sum of $50 000 is deposited at an interest rate of 6% p.a. for 2 years, compounded quarterly. Find the amount correct to the nearest dollar.

A. $56 180B. $56 275C. $56 325D. $56 358

Unit 5 Simultaneous Equation

1.The total price of 6 magazines and 8 newspapers is $148, while the total price of 11 magazines and 7 newspapers is $233. Find the price of one magazine and the price of one newspaper.

2.The length of a rectangle is 3 times the width and the perimeter is 72 cm. Find the length and the width of the rectangle.

3.John is 22 cm taller than Dennis. If the sum of their heights is 176 cm, find the height of each of them.

4.David has a total of 13 coins of $10 and $2. If the coins are worth $90, what is the number of each kind of coins that David has?

5.In a convenience store, the total selling price of 3 sets of salad and 4 bottles of lemon tea is $109, while the total selling price of 9 sets of salad and 8 bottles of lemon tea is $299. Find the selling price of 1 set of salad and 1 bottle of lemon tea.

6.Three years ago, the father’s age was 8 times the son’s age. Two years later, the father’s age will be 4.5 times the son’s age. Find the present ages of the father and the son.

7.Mr Lee’s electricity bill consists of two charges, one is a flat rate of $12a, the other one is a usage charge of $b per unit. In the last two months, Mr Lee used 124 units and 76 units of electricity respectively, and the bills were $576 and $360 respectively. Find the values of a and b.

Unit 6 Symmetry, Transformation and Polar Coordinates

Section A(1)1. The coordinates of the points P and Q are (8, 2) and (15, 2) respectively. P is rotated anti-clockwise about the origin O through 90 to P. Q is translated to the right by 7 units to Q.

(a) Write down the coordinates of P and Q.(b) Does △OPQ have reflectional symmetry? Explain your answer.

2. The coordinates of the points A and B are (5, 3) and (5, 8) respectively. A is the reflection image of A with respect to the x-axis. B is translated to the left by 5 units to B.(a) Write down the coordinates of A and B.(b) Let P(0, p) be a point on the rectangular coordinate plane. Find the value of p such that

△PAB has reflectional symmetry about the straight line y = 3.

3. The coordinates of the point X are (3, 12). X is rotated clockwise about the origin O through 180 to X1, and then X1 is reflected about the x-axis to X2.

(a) Write down the coordinates of X1 and X2.(b) Does △OX1X2 have reflectional symmetry? If yes, write down the number of axes of symmetry.

4. The coordinates of the point P are (10, 5). P is reflected about the y-axis to Q, and then Q is rotated anti-clockwise about the origin O through 180 to R.(a) Write down the coordinates of Q and R.(b) Find the area of △PQR.

5. In a polar coordinate system, O is the pole. The polar coordinates of the points A, B and C are (10, 107), (12, 197) and (10, ) respectively.(a) Find the value of such that OB is the angle bisector of AOC. (b) Hence, determine whether A, O and C are collinear. Explain your answer.

6. In a polar coordinate system, O is the pole. The polar coordinates of the points P and Q are (4, 52) and (4, 112) respectively.(a) Find OPQ.(b) Find the area of △OPQ. (Leave your answer in surd form.)

Others

6. In Figure 1, ABCDEF is a L-shaped paper card. The measurements given are correct to the nearest cm.

Figure 1

(a) Write down the maximum absolute error of the measurements.(b) Simon claims that the actual area of the paper card must not be greater than 740 cm2. Do

you agree? Explain your answer.

11. The heights of seven students randomly selected from a class are as follows:169 cm, 155 cm, 167 cm, 177 cm, 166 cm, 190 cm, 159 cm

(a) Find the mean and the median of the heights of the students.(b) Two more students are randomly selected from the class.

(i) Write down the greatest possible value of the median of the heights of the nine students.

(ii) It is known that both the mean and the mode of the heights of the nine students are equal to 167 cm. Find the heights of the two newly selected students.

12. It is given that A(12, 3) and B(9, 1) are two points on the rectangular coordinate plane. C(0, c) is a point on the y-axis such that ∠BAC = 90°.(a) (i) Express the slope of AC in terms of c.

(ii) Hence, find the value of c.(b) (i) Find the area of △ABC.

(ii) D is a point on BC such that the area of △ABD is square units. Find the

coordinates of D.

14. Let a and b be non-zero numbers. If , then a : b =

A. 1 : 3.B. 2 : 3.C. 3 : 1.D. 3 : 2.

單元 1 整數指數律1. 化簡，並以正指數表示答案。

2. 化簡，並以正指數表示答案。







Solution

多項選擇題1.

A.B.C.D.

2. A.B.C.D.

3. A.B.C.D.

4. 若，則 A. 。

B. 。C. 。D. 。

5.

A. 0B.C.D.

單元 2 公式1. 令 a 成為公式的主項。2. 令 k 成為公式的主項。3. 令 x 成為公式的主項。4. 令 n 成為公式的主項。5. 令 a 成為公式的主項。6. 令 k 成為公式的主項。7. 令 x 成為公式的主項。8. 令 n 成為公式的主項。9. 考慮公式。

(a) 令 q 成為上述公式的主項。(b) 若 p 的值增加 2，寫出 q 的值的改變。

10. 考慮公式及。(a) 試以 x 及 y 表示 b。(b) 若 x 及 y 的值均增加 4，寫出 b 的值的改變。

多項選擇題

1. 若，則 q =

A. 。B. 。C. 。

D. 。2. 若，則 k =

A. 。B. 。C. 。D. 。

3. 若，則 r =

A. 。B. 。C. 。D. 。

4. 考慮公式。求當 y = 9 時 x 的值。A. 24B. 21C. 12D. 8

5. 考慮公式。若 v 的值增加 3，則 u 的值會A. 減少 6。B. 減少 3。C. 增加 3。D. 增加 6。

單元 3 恆等式與因式分解1. 因式分解

(a) ，(b) 。

2. 因式分解(a) ，(b) 。

3. 因式分解(a) ，(b) 。

4. 因式分解(a) ，(b) 。

5. 因式分解(a) ，(b) 。

6. 因式分解(a) ，(b) 。

7. 因式分解(a) ，(b) 。

8. 因式分解(a) ，(b) 。

9. 因式分解(a) ，(b) 。

10. 因式分解(a) ，(b) 。

11. 因式分解(a) ，(b) 。

12. 因式分解(a) ，(b) 。

13. 因式分解(a) ，(b) 。

14. 因式分解(a) ，(b) 。

多項選擇題甲部1.

A.B.C.D.

2. A.B.C.D.

3. A.B.C.D.

4. A.B.C.D.

5. A.B.

C.D.

6. A.B.C.D.

7. 若 p 及 q 均為常數使得，則 A. 。B. 。C. 。D. 。

8. 若 h 及 k 均為常數使得，則 A. 。B. 。C. 。D. 。

9. 若 a、 b 及 c 均為非零常數使得，則

A. 。B. 。C. 。D. 。

單元 4 百分法1. 偉明的月薪為 $12 000，他的租金開支佔其月薪的 60%。

(a) 他每月的租金開支為多少？(b) 若每月的租金增加 $1500，則租金開支佔其月薪百分之幾？

2. 已知家明的身高是 162 cm，他比偉業矮 10%。(a) 求偉業的身高。(b) 若志健比家明高 10%，問志健和偉業的身高是否相同？試解釋你的答案。

3 媽媽把一包糖果分給美兒，梓晴和思詠三位小朋友。美兒所得的糖果數目比梓晴多25%，而梓晴所得的糖果數目比思詠多 10%。已知思詠所得的糖果數目為 240。(a) 求該包糖果最初的糖果數目。(b) 美兒所得的糖果數目比思詠多百分之幾？

4. 一名小販以 $200 購入 80 個蘋果。他把其中 60% 的蘋果以每個 $4售出，30% 的蘋果以每個 $2.5 售出，餘下的蘋果以每個 $2 售出。

(a) 求售出所有蘋果所得到的總金額。(b) 求盈利百分率。

5. 西裝 A 和西裝 B 的標價均為 $1500。若兩套西裝均以九折出售，則西裝 A 的盈利百分率為 50%，而西裝 B 的虧蝕百分率為 50%。

(a) 求西裝 A 和西裝 B 的成本。(b) 求出售兩套西裝的盈利百分率或虧蝕百分率。

6. 一個手袋的標價為 $560，現以 25% 的折扣百分率出售。(a) 求該手袋的售價。(b) 若出售該手袋的虧蝕為 $60，求虧蝕百分率。

7. 黃先生把一筆總額為 $200 000 的款項存入銀行 A 和銀行 B。銀行 A 和銀行 B 所提供的年利率分別為 3.5% 和 4.5%，並以單利息計算。2 年後，黃先生從兩間銀行所得的利息相同。問黃先生分別在銀行 A 和銀行 B 存入了多少款項？8. 嘉莉打算把 $9000 存入銀行，年期 3年。

(a) 若銀行 A 的年利率為 5%，且每半年計算複利息一次，求嘉莉在 3 年後所得的複利息。(答案準確至最接近的元。)

(b) 已知銀行 B 的年利率為 5.5%，以單利息計算。嘉莉應把款項存入哪一間銀行以獲取較多的利息？試解釋你的答案。

多項選擇題1. 在某學校中，45% 的學生是女生。若 80% 的男生和 60% 的女生都有配戴眼鏡，問配戴眼鏡的學生佔全校學生的百分之幾？

A. 27%B. 29%C. 71%D. 73%

2. 某長方形的長度和闊度分別減少了 10% 和 x%。若該長方形的面積減少了 23.5%，則 x =

A. 10。B. 13.5。C. 15。D. 18.5。

3. 綺婷以 $2400 購買了一隻手錶，並以 10% 的虧蝕百分率把該手錶賣給家浩。若家浩打算獲取 20% 的盈利，則他應以多少元出售手錶？

A. $2112B. $2592C. $2727D. $3168

4. 若一本書以它的標價出售，則盈利百分率是 25%。若該本書以 30% 的折扣百分率出售，則虧蝕為 $15。求該書的成本。 A. $105

B. $120C. $150D. $185

5. 把 $50 000 存入銀行，年利率為 6%，年期 2年，每季計算複利息一次。求本利和，準確至最接近的元。

A. $56 180B. $56 275C. $56 325D. $56 358

單元 5 聯立方程1.已知 6 本雜誌和 8 份報紙的售價是 $148，而 11 本雜誌和 7 份報紙的售價是 $233。求一本雜誌和一份報紙的售價。

2.一個長方形的長度是它的闊度的三倍。如果周界是 72 cm，長方形的長度和闊度分別是多少

3.敏聰比海峯高 22 cm。如果他們的高度的和是 176 cm，求他們各自的身高。

4.沛堅有 $10 和 $2 硬幣共 13 枚。如果硬幣共值 $90，沛堅有 $10 和 $2 硬幣各多少枚？

5.在某便利店中，3 份田園沙律和 4 枝柑桔檸檬茶的售價是 $109，而 9 份田園沙律和 8 枝柑桔檸檬茶的售價則是 $299。求每份田園沙律的售價和每枝柑桔檸檬茶的售價。

6.三年前，父親的年齡是兒子的 8 倍。兩年後，父親的年齡將是兒子的四倍半。求他們現在的年齡。

7.李先生每月的電費賬單的收費由兩部分組成，其中一部分是固定收費，金額是 $12a，另一部分是按用量收費，每單位電力收費 $b。於上兩個月份，李先生分別用了 124 個及 76 個單位電力，而賬單金額分別是 $576 和 $360。求 a 和 b 的值。

單元 6 對稱、變換及極坐標

1. 點 P 及點 Q 的坐標分別為 (8, 2) 及 (15, 2)。P 繞原點 O 按逆時針方向旋轉 90 至 P。Q 向右方平移 7 單位至 Q。(a) 寫出 P 及 Q 的坐標。(b) 問 △OPQ 是否具有反射對稱性質? 試解釋你的答案。

2. 點 A 及點 B 的坐標分別為 (5, 3) 及 (5, 8)。A 為 A 沿 x 軸反射的影像。B 向左方平移 5 單位至 B。(a) 寫出 A 及 B 的坐標。(b) 設 P(0, p) 為直角坐標平面上的一點，使得 △PAB 沿直線 y = 3 反射對稱。求 p 的值。

3. 點 X 的坐標為 (3, 12)。X 繞原點 O 按順時針方向旋轉 180 至 X1，然後 X1 再沿 x 軸反射至 X2。(a) 寫出 X1 及 X2 的坐標。(b) 問 △OX1X2 是否具有反射對稱性質？若是的話，寫出其對稱軸的數目。

4. 點 P 的坐標為 (10, 5)。P 沿 y 軸反射至 Q，然後 Q 再繞原點 O 按逆時針方向旋轉 180 至 R。

(a) 寫出 Q 及 R 的坐標。(b) 求 △PQR 的面積。

5. 在某極坐標系統中，O 為極點。點 A、點 B 及點 C 的極坐標分別為 (10, 107)、(12, 197) 及 (10, )。(a) 求的值，使得 OB 是 AOC 的角平分線。(b) 由此，判斷 A、O 與 C 是否共線。試解釋你的答案。

6. 在某極坐標系統中，O 為極點。點 P 及點 Q 的極坐標分別為 (4, 52) 及 (4, 112)。(a) 求 OPQ。(b) 求 △OPQ 的面積。(答案以根式表示。)

其他6. 圖 1 中，ABCDEF 是一張 L 形卡紙，當中所標示的量度值均準確至最接近的 cm。

圖 1

(a) 寫出量度值的最大絕對誤差。(b) 志華宣稱卡紙的真確面積一定不會超過 740 cm2。你是否同意？試解釋你的答案。

11. 在某班中隨意選出 7名學生，他們的身高如下：170 cm, 155 cm, 167 cm, 177 cm, 166 cm, 190 cm, 159 cm

(c) 求該 7 名學生身高的平均數和中位數。(d) 現從該班隨意選出另外兩名學生。

(iii)寫出該 9 名學生身高的中位數的最大可能值。(iv) 已知該 9 名學生身高的平均數和眾數都是 167 cm。求兩名新選出的學生的身高。

12. 已知 A(12, 3) 和 B(9, 1) 是直角坐標平面上的兩點。C(0, c) 是 y 軸上的一點使∠BAC = 90°。(a) (i) 求 AC 的斜率，答案以 c 表示。

(ii) 由此，求 c 的值。(b) (i) 求 △ABC 的面積。

(ii) D 是 BC 上的一點，使 △ABD 的面積為平方單位。求 D 的坐標。14. 設 a 和 b 為非零常數。若，則 a : b =

A. 1 : 3。B. 2 : 3。C. 3 : 1。

D. 3 : 2。

Full SolutionsUnit 1STRUCTURAL QUESTIONS

Suggested Solutions

1.

2.

3.

4.

5.

6.

7.

8.


1. CC

2 CA

3. CB

4. CB

5. CC

Full SolutionsUnit 2

STRUCTURAL QUESTIONS

Suggested S olutions

1.

2.

3.

4.

5.

6.

7.

8.

9. (a)

(b) New value of q

∴ The value of q is increased by 5.

10. (a) ……(1)

……(2)

By substituting (1) into (2), we have

(b) New value of b

∴ The value of b is decreased by 2.


1. CC

2. CD

3. CC

4. CA

When y = 9,

5. CD

New value of u

∴ The value of u is increased by 6.

Full Solutions

Unit 3STRUCTURAL QUESTIONS


1. (a)

(b)

2. (a)

(b)

3. (a)

(b)

4. (a)

(b)

5. (a)

(b)

6. (a)

(b)

7. (a)

(b)

8. (a)

(b)

9. (a)

(b)

10. (a)

(b)

11. (a)

(b)

12. (a)

(b)

13. (a)

(b)

14. (a)

(b)


1. CC

2. CB

3. CA

4. CA

5. CC

6. CD

7. CC

By comparing the constant terms, we have

By comparing the coefficients of x, we have

8. CD



9. CA



∴

Unit 4STRUCTURAL QUESTIONS


1. (a) The amount he spend on rent per month

(b) The required percentage

2. (a) The height of Peter

(b) The height of John

∴ John and Peter are not of the same height.

3. (a) The number of Betty’s candies

The number of Ada’s candies

∴ The total number of candies in the packet at the beginning

(b) The required percentage

4. (a) The total amount received

(b) The profit percentage

5. (a) The cost price of suit A

The cost price of suit B

(b) The loss per cent

6. (a) The selling price of the bag

(b) The loss per cent

7. Let $x be the amount that Mr Wong deposits in Bank A.

∴ Mr Wong deposits $112 500 in Bank A and $87 500 in Bank B.

8. (a) The required compound interest

(b) The interest received from Bank B

∴ Sally should deposit the money in Bank B.


1. CC

Let x be the total number of students in the school.The required percentage

2 CC

Let l cm and w cm be the original length and the original width of the rectangle respectively.

The new area

∴

3. CB

The required price

4. CB

Let $x be the cost of the book.

∴ The cost of the book is $120.

5. CC

The required amount

單元 5 聯立方程1. 設一本雜誌的售價為 $x，一份報紙的售價為 $y。依題意，可得

從 (i)，6x + 8y = 148 3x + 4y = 74 3x = 74 – 4y

把 (iii) 代入 (ii)，可得

把 y = 5 代入 (iii)，可得

一本雜誌的售價是 $18 ，而一份報紙的售價是 $5 。 2. 設該長方形的長度為 x cm，闊度為 y cm。依題意，可得把 (i) 代入 (ii)，可得

2(3y + y) = 72

2(4y) = 72 8y = 72 y = 9把 y = 9 代入 (i)，可得

x = 3(9) = 27該長方形的長度是 27 cm ，闊度是 9 cm 。

3.設敏聰的身高是 x cm，海峯的身高是 y cm。依題意，可得把 (i) 代入 (ii)，可得

y + 22 + y = 176 2y + 22 = 176

2y = 154 y = 7把 y = 77 代入 (i)，可得

x = 77 + 22 = 99敏聰的身高是 99 cm ，而海峯的身高是 77 cm 。

4.設沛堅有 x 枚 $10 硬幣，有 y 枚 $2 硬幣。依題意，可得(ii) ÷ 2：

(iii) – (i)： 4x = 32 x = 8把 x = 8 代入 (i)，可得

8 + y = 13 y = 5沛堅有 8 枚 $10 硬幣，有 5 枚 $2 硬幣。

5. 設每份田園沙律的售價是 $x，每枝柑桔檸檬茶的售價是 $y。依題意，可得

(i) 3：

(iii) – (ii)： 4y = 28 y = 7把 y = 7 代入 (i)，可得

3x + 4(7) = 109

3x + 28 = 109 3x = 81 x = 27每份田園沙律的售價是 $27 ，而每枝柑桔檸檬茶的售價是 $7 。

6.設現在父親是 x 歲，而兒子是 y 歲。依題意，可得從 (i)， x – 3 = 8(y – 3)

把 (iii) 代入 (ii)，可得8y – 21 + 2 = 4.5(y + 2) 8y – 19 = 4.5y + 9 3.5y = 28 y = 8

把 y = 8 代入 (iii)，可得 x = 8(8) – 21

= 43現在父親是 43 歲，而兒子則是 8 歲。

7.依題意，可得

(i) – (ii)： 48b = 216 b = 4.5把 b = 4.5 代入 (ii)，可得

12a + 76(4.5) = 360 12a + 342 = 360

12a = 18 a = 1.5

a 的值是 1.5 ，而 b 的值是 4.5 。

Unit 5 Symmetry, Transformation and Polar Coordinates

1. (a) The coordinates of P are ((2), 8), i.e. (2, 8).The coordinates of Q are (15 + 7, 2), i.e. (8, 2).

(b)

∴ △OPQ is an isosceles triangle.∴ △OPQ has reflectional symmetry.

2. (a) The coordinates of A are (5, (3)), i.e. (5, 3).The coordinates of B are (5 5, 8), i.e. (0, 8).

(b) Let M be the mid-point of the line segment joining B and P.Since △PAB has reflectional symmetry about the straight line y = 3, M lies on the line y = 3, i.e. the coordinates of M are (0, 3).∴ By the mid-point formula, we have

3. (a) The coordinates of X1 are ((3), 12), i.e. (3, 12).The coordinates of X2 are (3, (12)), i.e. (3, 12).

(b)

∴ △OX1X2 is an isosceles triangle.∴ △OX1X2 has reflectional symmetry and it has 1 axis of symmetry.

4. (a) The coordinates of Q are (10, 5).The coordinates of R are ((10), (5)), i.e. (10, 5).

(b)

∵ PR PQ∴ The area of △PQR

5. (a)∵ OB is the angle bisector of AOC.∴∴

(b)

∴ A, O and C are collinear.

6. (a)OP = 4 units and OQ = 4 units

∴

(b) The area of △OPQ

Others

either one1A

6. (a) The maximum absolute error

1A

(b) The greatest possible area of the paper sheet1M + 1A

∴ The claim is agreed. 1A f.t.

11. (a) Mean 1A

Median 1A

(b) (i) To find the greatest possible value of the median of the heights of the nine students, we may assume that the two newly selected students are both taller than or equal to 190 cm, i.e. the greatest possible value of the median is 169 cm. 1A

(ii) ∵ The mode of the heights of the nine students is 167 cm.∴ One of them must be 167 cm. 1ALet h cm be the height of the other newly selected student.∵ The mean of the heights of the nine students is 167 cm.

∴ 1M

∴ The height of the other newly selected student is 153 cm. 1A12. (a) (i) Slope of AC

1A

(ii) Slope of AB

1A

∵ ∠BAC = 90°∴

1M

1A

(b) (i) unitsunits

∴ Area of △ABC

sq. units

1A

(ii) ∵ D lies on BC and area of △ABD area of △ABC.

∴ D is the mid-point of BC.∴ The coordinates of D

1M

1A

14. CB

∴

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Chapter 1 - hkscmaths.files.wordpress.com€¦ · Web viewUnit 1 Laws of Indices 1. Simplify and express your answer with positive index. 2. Simplify and express your answer with