Special Numbers, Factors and Multiples

Transcription

1 Specil s, nd Student Book - Series H = 9 = 3 Mthletics Instnt Workooks Copyright

2 Student Book - Series H Contents Topics Topic - Odd, even, prime nd composite numers Topic - Divisiility tests Topic 3 - Squre numers Topic 4 - Tringulr numers Topic 5 - Topic - The highest common fctor (HCF) Topic 7 - Topic 8 - Lowest common multiple (LCM) Topic 9 - Index nottion, squre roots nd cue roots Topic 0 - Prolem solving with specil numers, fctors Dte completed Prctice Tests Topic - Topic test A Topic - Topic test B Author of The Topics nd Topic Tests: AS Klr

3 Topic : Odd, even, prime nd composite numers QUESTION c d List the first five even numers. How do you know tht numer is even? List the first five odd numers. How do know tht numer is odd? QUESTION Complete the following. The sum of two even numers is n numer. The sum of two odd numers is n numer. c The sum of n odd nd even numer is n numer. d The product of ny odd numer nd is n numer. e The product of n odd numer nd n even numer is n numer. Which is the only even prime numer? List ll the prime numers less thn 5. c List the prime numers etween 30 nd 40. QUESTION 4 All even numers end in one of five digits. List them. All odd numers end in one of five digits. List them. c Wht is the next odd numer fter 999? d Wht is the next even numer fter 9999? e The product of two odd numers is n numer. f The product of two even numers is n numer. g The squre of n odd numer is n numer. h The squre of n even numer is n numer. i The difference etween two different odd numers is n numer. j The difference etween two different even numers is n numer.

4 Topic - Divisiility tests QUESTION Complete the following sttements c d e f g h If the numer is even it is lwys divisile y If the sum of the digits of numer is divisile y 3 then the whole numer is divisile y If the lst digits of numer is divisile y 4 then the whole numer is divisile y If the lst digit is 5 or 0 then the whole numer is divisile y If the numer is divisile y nd 3 then the whole numer is divisile y If the lst 3 digits re divisile y 8 then the whole numer is divisile y If the sum of the digits is divisile y 9 then the whole numer is divisile y If the numer ends in 0 then the whole numer is divisile y QUESTION List the numers tht re divisile y 84 4 c 83 d 98 e 385 List the numers tht re divisile y c 38 d 93 e 57 QUESTION 4 List the numers tht re divisile y c 94 d 0 e 357 QUESTION 5 List the numers tht re divisile y c 998 d 350 e 90 QUESTION List the numers tht re divisile y c 853 d 9 e 584 QUESTION 7 List the numers tht re divisile y c 38 d 49 e 33 QUESTION 8 List the numers tht re divisile y c 5 d 399 e 584 QUESTION 9 List the numers tht re divisile y c 95 d 5008 e 990

5 Topic 3: Squre numers QUESTION c d Why re these clled squre numers? Extend this pttern y two more terms. Wht is the 7 th squre numer? Wht numers re shown y the squres ove? QUESTION = = + 3 = 4 = = 9 = 3 Drw nother digrm to show = 5 Write three more lines of the ptterns given elow. i = = ii = + 3 = 4 = + + = = 9 = = = = = 4 Write ech of the following in the expnded form. 3 = = c 8 = d 4 = e 0 = f = g 3 = h 9 = i 4 = j = k 5 = l 0 = QUESTION 4 Write ech of the following in the index form. 3 3 = 7 7 = c = d = e 5 5 = f = g 9 9 = h = i 8 8 = j 0 0 = k = l 5 5 = m = n 5 5 = o 4 4 = p 0 0 = 3

6 Topic 4: Tringulr numers QUESTION c d e Why re these clled tringulr numers? Extend this pttern y two more terms. Wht is the 7 th tringulr numer? Wht numers re shown y the tringles ove? If the 3 rd tringulr numer is + + 3, write n expression for the 4 th tringulr numer. QUESTION Write four more lines of the pttern given elow. = + = = = 0 List the first eight tringulr numers. Add the first two tringulr numers. Wht type of numer do you get? c Add the next two tringulr numers. Wht type of numer do you get? d Add ny two consecutive tringulr numers. Wht type of numer do you get? e Find two numers tht re oth tringulr nd squre nd less thn 40. QUESTION 4 A dot digrm for the first three tringulr numers is drwn for you. Drw similr dot digrm for the first five tringulr numers. 4 4

7 Topic 5: QUESTION Is the first numer fctor of the second? Write True or Flse. 3, 5, 5 c 8, 3 d 5, 4 e 4, 8 f, 9 g, h 3, i 7, 3 j, 3 k 7, 37 l 4, 0 m 9, 30 n, 30 o 9, 3 p 7, 8 QUESTION Find ll possile fctors of ech of the following numers. 8 g 4 9 h 0 c 48 i 44 d 3 j 9 e 5 k 9 f 00 l 84 Find the vlue of the missing fctor. 3 = 5 = 5 c 3 = 33 d 7 = 3 e 4 = 3 f = 4 g 5 = 30 h = 48 i 9 = 45 j 3 = 7 k 3 = 30 l 7 = 49 QUESTION 4 c Wht numer is fctor of every numer? Write the next three numers greter thn 4 tht hve only two fctors. Complete the sttement A prime numer hs only fctors. QUESTION 5 Use fctor tree to fctorise ech of the following numers. 30 c 8 d 7 e 00 f 0 5

8 Topic : The highest common fctor (HCF) QUESTION Find the fctors for ech pir of numers nd underline the common fctors. c QUESTION Find the fctors for ech set of numers nd underline the common fctors. c List ll the fctors of 8. List ll the fctors of. c List the common fctors of 8 nd. d Wht is the highest common fctor (HCF) of 8 nd. QUESTION 4 Complete the following, underline the common fctors nd find the HCF. c HCF = HCF = HCF = d e f HCF = HCF = HCF = 44 EXCEL ESSENTIAL SKILLS: YEAR 7 MATHEMATICS REVISION AND EXAM WORKBOOK

9 Topic 7: QUESTION List the next three multiples of ech of the following numers.,,, 4,,, c 8,,, d 3,,, e 7,,, f 5,,, g,,, h 9,,, i,,, QUESTION Which of the following numers re multiples of 3? 8, 4, 8, 3, 0, 5, 8, 3,, 4, 90 Are ll whole numers multiples of? c Are ll even whole numers multiples of? d If 3 is fctor of, is multiple of 3? e Is it possile to find the lrgest multiple of ny whole numer? Is the first numer multiple of the second? Write True or Flse., 3 3, 9 c 48, d 8, 7 e 8, f 5, 5 g 5, 3 h 7, i 8, j, 8 k 7, 8 l 35, 5 m 3, 4 n, o 5, 8 p 3, 7 QUESTION 4 List ll the multiples of 3 less thn 4. List ll the common multiples of nd 5 etween nd 4. c List ll the multiples of 7 etween nd 34. QUESTION 5 List the first five multiples of the following numers. 5 d 0 0 e 40 c 5 f 7

10 Topic 8: Lowest common multiple (LCM) QUESTION List the first eight multiples of 4. List the first eight multiples of. c List the common multiples of 4 nd in prts nd. d Wht is the lowest common multiple (LCM) of 4 nd? QUESTION List the first eight multiples for ech pir of numers nd underline the common multiples. 3 5 c d Find the first eight multiples for ech set of numers nd underline the common multiples QUESTION 4 Find the first five multiples for ech set of numers, underline the common multiples nd find the LCM. 8 0 LCM = LCM = c s Multiple d s Multiple LCM = LCM = 4 8

11 Topic 9: Index nottion, squre roots nd cue roots QUESTION Write ech of the following in index form. = = c = d = e = f = QUESTION Write ech of the following in the expnded form nd evlute. 3 = 3 = c 4 3 = d 5 3 = e 3 = f 7 = Complete the following tles. QUESTION 4 If = then = Complete the following. If = 4 then 4 = c If 3 = 9 then 9 = d If 4 = then = e If 5 = 5 then 5 = f If = 3 then 3 = g 3 3 If = then = h 3 3 If = 8 then 8 = i 3 3 If 3 = 7 then 7 = Evlute the following. e i m q = 8 = 3 8 = 5 = ( 3) = 49 = c 4 = d 4 = f 3 = g 00 = h 9 = j 3 4 = k 3 5 = l 3 7 = n 3 = o = p = r ( 4) = s ( 5) = t ( ) = 9

12 Topic 0: Prolem solving with specil numers, fctors Write ll one-digit odd numers. Write ll one-digit even numers. 3 Are there ny even prime numers? If so, write these. 4 Write ll one-digit prime numers. 5 Is fctor of 48? 7 is one fctor of 5; wht is the mtching fctor? 7 Write ll fctors of 8. 8 List four prime numers etween 30 nd Wht re the common fctors of nd 30? 0 Find the highest common fctor of 8 nd. Write the first three common multiples of nd 9. Find the lowest common multiple of nd 9. 3 Which of these 9, 9, 9, 39, 49, 59 re prime numers? 4 Write the first prime numer greter thn 0. 5 Is prime numer? Write the first two numers tht re oth tringulr nd squre. 7 Which of the following numers re fctors of 4?,, 3, 4, 5,, 7, 8, 9, 0 8 Find the sum of the first four tringulr numers. 9 Find the product of the first three squre numers. 0 Write the smllest prime numer. 0

13 Unit Test PART A Instructions This prt consists of multiple-choice questions Ech question is worth mrk Fill in only ONE CIRCLE for ech question Clcultors re NOT llowed Time llowed: 5 minutes Totl mrks = The sum of the ll the prime numers etween nd 0 is A 5 B C 8 D 7 The sum of two consecutive odd numers is. The smller numer is A 5 B 7 C 9 D 3 3 The squre root of 5 is A 3 B 4 C 5 D 4 The sum of three consecutive even numers is 4. The smllest is A 4 B C 8 D 0 5 The highest common fctor (HCF) of 8 nd is A B 4 C 8 D The product of the first three tringulr numers is A B 8 C 4 D 30 7 The sum of the first three squre numers is A 0 B C 4 D 8 The sum of the first four prime numers greter thn 3 is A B 3 C 4 D 53 9 The first prime numer greter thn 5 is A B 7 C 8 D 9 0 The numer of fctors prime numer hs is A B C 3 D 4 The lowest common multiple (LCM) of 4 nd is A 4 B C 8 D If 7 is one fctor of 3 then the mtching fctor is A 7 B 8 C 9 D 3 Mrks Totl mrks chieved for PART A

14 Unit Test PART B Instructions This prt consists of 5 questions Ech question is worth mrk Write nswers in the nswers-only column Time llowed: 0 minutes Totl mrks = 5 Questions Answers only Mrks List the first three even numers. How do you know tht numer is odd? 3 Which is the only even prime numer? 4 Write the first prime numer greter thn 0. 5 Wht is the th squre numer? Write 7 3 in expnded form. 7 List the first four tringulr numers. 8 Write the next three numers greter thn 0 tht hve only two fctors. 9 Which of the following numers re multiples of 4?, 4,, 8, 0,, 4,, 8, 0 0 List the common fctors of 8 nd 0. Write in the index form. If 7 3 = 343 then find 3 Write the product of the second tringulr numer nd the second squre numer. 4 Find the sum of the first five squre numers. 5 Find the sum of the first six tringulr numers. Totl mrks chieved for PART B 5