编制数学模型

1、 DEAR GCSE WLc STUDENT Youll want to be sure of your best grade in the limited time thats available for practice and revision. Thats what this book provides. - Tightly focussed on the syllabus you dont have to revise anything you wont be assessed on. - The work is set around worked examples which highlight key skills and real exam questions - so all your practice leads to performance where it counts: on coursework, in mocks and on the exam. - The first 10 units revise all the topics examined - l

2、eading to the all-important grade e“. - Take Progress Tests 1. 2 and 3 and see how youre doing on the way to grade He“ and beyond: the answers tell you what you need to work at. - Polish your higher grade skills on Units 11-14 and check your progress in Test 4. -If you are taking a Mental Arithmetic test, unit 15 helps with these skills and gives you practice. Per- suade a friend to read them out With practice youll achieve the high scores that are important in these tests. I hU)lL L+ b, I .1 J,

3、O)k 00V . l( fetJ MMe. CtM-Adt M. fo.J, J , 13 . . A pfLoMe. fVWoer QCWCM be. cMlfd4d b . OAcl eJj. (, lS f() RuLe.s. (W s,JCUQ bq(, .I;. b.15 . (iv) tratOL .Iftcts l. 3. E 10 . , . . . . . , . . 1l,“Q OfOti . WOA.O To .AA.N. fo.c.c:rC“: 0 tbr t cJ.i.Nid.at UQ.t. o Utc.t, 8 ,“ 0. f 1-7 = 4 remainder 2. The day of the week is 2 days after Saturday, i.e. it is Monday. Topic: BODMAS _ EJlAIIIU 3 Find the value of: (i) 6 x (18 -;-2) - 3; (ii) (3 x 6) -;-(2 x 6 -3) .“. These questions need the BODMAS

4、 rule. (i) Brackets first, so 6 X (18 -;-2) -3 = 6 X 9 -3 Of and divide do not appear, so Multiply next gives 54 -3. Add does not appear. Subtract gives the answer 51. Hence, 6 X (18 -;-2) -3 = 6 X 9 -3 = 54 -3 = 51. (ii) There are two sets of brackets here, so each one is worked out separately. First bracket = 3 X 6 = 18 Second bracket = 2 X 6 -3 (Multiply) = 12 -3 (Subtract) = 9 Hence we have (3 X 6) -;-(2 X 6 -3) = 18 -;-9 = 2. 10 Number Topic: types of number WDIIICED EXAMPLE 4 Look at this

5、list of numbers 2.5.8. II. 14. I20 (a) Which of these numbers are prime? (b) Which of these numbers is the cube of another number in the list? (c) The numbers form a pattern. Write down the next two numbers in the pattern. (MEG) (a) Referring to a prime number list. the answer is 2.5.11.17. (b) The cube numbers would be given by I x I x 1 = 1; 2 x 2 x 2 = 8; 3 x 3 x 3 = 27 . You can see that the answer is 8. because it is the cube of 2. (c) The numbers increase by 3 each time. and so the next tw

6、o numbers will be 23. 26. Questions to try 1. Janet is trying to discover the factors of 570 using a calculator. She has already discovered that 15 is a factor. To test whether the number 16 is a factor of 570. she does the calculation 570 -:-16 Her calculator shows 35.625 (a) Write this calculator answer to the nearest whole number. (b) Is 16 a factor of 570? Give a reason for your answer. (c) Janet continues to look for factors. She tests the numbers 17. 18 onwards. What is the next factor she

7、 will find? 2. Using each of the figures 2.3.5 and 8 only once. write down: (i) the largest possible four figure number; (ii) a mUltiple of 4; (iii) a pair of 2 digit numbers that differ by 47. (NEA) 3. There were 67 people on a bus. At the first stop. 29 people got off and 18 people got on. At the next stop. 7 people got off and II people got on. How many people are now on the bus? Tl)e ten tiles shown above are used in a game to make words. and the scores shown on the tiles are added together.

8、 For example. scores 2 + 7 + 6 + 4 = 19. 5. Working with numbers II (a) Calculate the score for: ItL1 L:1cl 2 (b) A player makes the word ABODE. Calculate the score for this word. (c) Another player makes a five-letter word and scores a total of 23. Four of the letters in the word are A, E, Land N. What is the fifth letter? (d) A third player makes a six-letter word using the letters A, E, L, Nand two others. All the letters in the word are different and the score for the word is 34. What are th

9、e other two letters? (MEG) 12 14 7 2 15 9 8 15 9 14 3 5 12 13 8 11 7 10 16 1 16 10 11 6 4 13 (i) (ii) (i) The numbers in each row, each column, and both diagonals of this number square add up to 34. The numbers 1,2,3,4,5 and 6 have been left out. Put them in their correct places. (ii) The number square in this part also contains many sets of four numbers which add up to 34. Nineteen of these sets contain the number I. For example, I + 4 + 14 + 15. Find, and write down, as many sets of four numbers from this number square, which contain the number 1 and add up to 34, as you can. (MEG) Using the digits I, 5, 7 and 8 no more than once, write down: (i) a prime number between 10 and 30; (ii) a multiple of 7; (iii) two numbers whose difference is 24; (iv) a number divisible by the square of 5. 12 Number , a/s t ns and declm Frac 10 Fract

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