1 Numbers and Fundamental Arithmetic Hey! Let s order some pizzas for a party! How many pizzas should we order? There will be 1 people in the party. Each people will enjoy 3 slices of pizza. Each pizza is cut into 8 slices. Benny Anthony 1 3 = 36 slices of pizza are required. So, the total number of pizzas = 36 8 = 4 Thus, they should order 5 pizzas. 1. Hint We should consider an integer which is greater than the mixed number. Types of numbers 1. (a) Integers (E.g. 0, 10, 153) Positive integers can be categorized into (i) odd numbers (e.g. 1, 3, 5, ) and even numbers (e.g., 4, ); or (ii) 1, prime numbers (e.g., 3, 5, 7, ) and composite numbers (e.g. 4, 6, 8, 9, ). (b) Decimal numbers (E.g. 1.45, 10.7) Mathematics Tips 1 is neither a prime number nor a composite number.
1. average 平均值. bar chart 棒形圖 3. broken line graph 折線圖 4. pictogram 象形圖 5. pie chart 圓形圖 6. statistical graph 統計圖 7. statistics 統計學 Fill in the Blanks 1. A uses rectangular bars to represent data.. A uses a circle divided into parts to represent data. 3. A is used to show the trend of data over a period of time. 4. A uses symbols or pictures to represent data. Multiple-choice Questions 5. Which of the following groups of data has an average not equal to 35? A. 40, 50, 0, 30, 35 B. 1, 19, 14, 50, 80 C. 0, 35, 35, 35, 35 count 0 as one of the data D. 88, 18, 10, 4 Referring to the following pictogram, answer questions 6 7. The number of colour pens Sarah owns Each represents pens Red Blue Green Black 6. What is the total number of colour pens that Sarah has? A. 15 B. 0 C. 30 D. 40 7. What is the difference between the numbers of green pens and black pens that Sarah has? A. B. 3 C. 4 D. 6 Basic Statistics 33
14. Complete the following table with the given angles. 175, 88, 360, 340, 10, 50, 190, 18, 180, 95, 90 Acute angles Right angles Obtuse angles Straight angles Reflex angles Round angles 15. Measure the following angles by using a protractor. (a) A (b) B C x ABC = x = Draw the following angles (16-18) in the space provided using a protractor. 16. 45 17. 100 18. 160 19. Referring to the figure, write down the types of angles for all the marked angles. e a d b c 0. In the figure, QRS is a straight line. Use suitable notation to name all the line segments and triangles in the figure. P Q R S 60
1. Measure the following angles in the figure by using a protractor. S (a) y = y (b) PQR = P Q R Draw the following angles ( - 4) in the space provided using a protractor.. 00 3. 65 4. 30 5. The figure shows a parallelogram ACDF. It is given that B and E are the mid-points of AC and DF respectively and AB = AF. A B C (a) Join BE and name the type of quadrilateral of ABEF. (b) Two students A and B are then asked to divide the above diagram into 4 identical parts. The following are the methods adopted by the two students. F E D Student A A B C Student B A B C G H I F E D F E D (i) Name all the triangles in student A s diagram. (ii) Name all the parallelograms in student B s diagram. Introduction to Geometry 61
8. In a shooting game, Peter and Mary finished first. When Susan finished the game, she told Peter that her score was the sum of Mary s score and his score. (a) Suppose Peter, Mary and Susan got x points, y points and z points respectively. Express z in terms of x and y. (b) It is known that Susan s score is 300 more than Peter s score, and Mary s score is twice Peter s score. What score did Susan get? Scoring Tips 1 EYA 9. In the figure, the 1st pattern consists of 1 row with dots, the nd pattern consists of rows with 3 dots in each row, the 3rd pattern consists of 3 rows with 4 dots in each row, and so on. 1st pattern nd pattern 3rd pattern 4th pattern 5th pattern (a) Express the number of dots in the nth pattern in terms of n. Scoring Tips (b) Now, a triangular pattern is obtained by removing half of the dots from the original pattern. 1st pattern nd pattern 3rd pattern 4th pattern 5th pattern (i) Using the result of (a), or otherwise, write down the number of black dots in the nth triangular pattern in terms of n. (ii) How many black dots are there in the 10th triangular pattern? (iii) Is there a triangular pattern with 50 black dots? Explain your answer. Scoring Tips 1 : Set up an equation involving x first. Scoring Tips : Consider the number of dots as the product of length and width in the pattern. 76
When a number is multiplied by itself several times, we usually express the result using index notation, such as = 5. The small number 5 represents the number of s multiplying together. Here are two more examples: (1) The area of a square = a a l () The volume of a cube = l 3 a l l Furthermore, we also use index notation in multiplication and division, such as r 3 r = (r r r) (r r) and k 4 k = (k k k k) k = r 5 = k 3 How can we simplify 3x + 7y 3 + 5x - y 3? Solution: 3x + 7y 3 + 5x - y 3 = 3x + 5x + 7y 3 - y 3 = 8x + 6y 3 Scoring Tips Group and combine the like terms. Follow-up 30. Simplify 5a + 3b - a - 5b. 31. Simplify 8k 3 k + 5x 3-7k + x 3. Let s see the following website to study the classical game of guessing a playing card. http://www.hkep.com/misc/summer/samnd_e/samnd_foundation_chapter10e.pdf Introduction to Algebra 77
Revision Test Marks: 71 Section A (16 marks, each question carries 1 mark) 3 5. Convert 1% into a fraction. 1. + = 4 3 1 1 A. B. 1 1 5 A. B. 3 17 3 4 C. D. 3 17 5 5 C. D. 1. It is given that Y is a factor of 10. Which of the 6. x Solve = 8. following number(s) must be the common factor of Y and 10? A. x = 3 C. x = 1 B. x = 5 D. x = 0 I. II. 60 7. Which of the following is a negative number? III. Y A. (-) + (-3) B. (-) - (-3) A. I only B. III only - C. (-)(-3) D. C. I and II only D. II and III only -3 3. In the figure, the radius of the circle is 5 cm. Find the circumference of the circle. (Take π = 3.14.) 8. In the figure, the marked angle is 5 cm A. an acute angle. B. a right angle. C. an obtuse angle. D. a reflex angle. A. 15.7 cm B. 31.4 cm C. 47.1 cm D. 6.8 cm 4. Find the average of 3, 7, 9 and 5. A. 3 B. 5 C. 4 D. 6 9. Which of the following points lies on the y-axis? A. (-, 0) B. (1, 1) C. (0, 3) D. (, -) 10. Simplify 3x - x + y. A. x + y B. x C. y D. x + y 78
數學科常用指令 Question Commands in Mathematics 1. Calculate / Evaluate / Find( 計算 / 求 ) E.g. (Calculate / Evaluate / Find) the values of a and b. ( 求 a 及 b 的值 ). Construct / Draw / Plot( 繪畫 ) E.g. (Construct / Draw / Plot) a graph using the data given. ( 利用已知的數據, 繪畫一圖表 ) 3. Estimate( 估算 ) E.g. Estimate the length of the pencil. ( 估算鉛筆的長度 ) 4. List( 列出 ) E.g. List all the possible values of a. ( 列出 a 的所有可能值 ) 5. Name / Write down( 寫出 ) E.g. (Name / Write down) all the right angles in the figure. ( 寫出圖中所有直角的名稱 ) 6. Prove / Show( 證明 ) E.g. (Prove / Show) that triangles ABC and PQR are congruent. ( 證明三角形 ABC 及 PQR 為全等 ) 7. Solve( 解 ) E.g. Solve the following equations. ( 解下列各方程 ) 8. Satisfy( 滿足 ) E.g. Find the value of x that satisfies the equation. ( 求滿足方程的 x 的值 ) 9. Simplify( 化簡 ) E.g. Simplify the following expressions. ( 化簡下列數式 ) 10. Sketch( 繪畫 的略圖 ) E.g. Sketch the graph of y = x. ( 繪畫 y = x 的略圖 ) 11. Which( 哪些 / 哪種 / 哪個 ) E.g. Which of the following numbers are even numbers? ( 下列哪些數為偶數?) 1.... if necessary.( 如需要時 ) E.g. Give the answer correct to 1 decimal place if necessary. ( 如需要時, 答案須準確至一位小數 ) 84