Cmbridge Essentils Mthemtics Core 8 NConsolidtion Worksheet N Consolidtion Worksheet Work these out. 8 b 7 + 0 c 6 + 7 5 Use the number line to help. 2 Remember + 2 2 +2 2 2 + 2 Adding negtive number is the sme s subtrcting the number. Subtrcting negtive number is the sme s dding the number. Copy nd complete these. 6 + 8 6 8 b 7 + 7 c 5 + 5 d 2 + 8 2 8 e f 5 9 5 9 Remember 2 6 2 6 2 6 Multiplying two numbers with the sme sign gives positive nswer. Multiplying two numbers with different signs gives negtive nswer. Work these out. 5 b 5 c 6 2 d 2 e 7 2 f 5 6 Work these out. 2 b 7 2 c 5 2 2 2 d 0 2 + 6 2 2 or squred mens. Originl mteril Cmbridge University Press 2009
Cmbridge Essentils Mthemtics Core 8 NConsolidtion Worksheet 5 Work these out. 25 b 6 c d 9 6 2 2 2 2 2 8 is cubed. Complete these sttements. b 6 c 5 d 0 7 The multiples of 7 re the numbers in the 7 times tble: 7,, 2, 28 Write the first twelve multiples of. b Write the first twelve multiples of. The multiples tht re in both nd b. c Write the numbers thn re common multiples of nd. d Wht is the lowest common multiple of nd? 8 2 2 2 6 2 2, so the fctors of 2 re, 2,,, 6, 2. Write ll the fctors of these numbers. Finding fctor pirs might help you. 0 b 2 c 50 d 6 9 Write down ll the fctors of 2. b Write down ll the fctors of 56. The fctors tht re in both nd b. c Write down the fctors tht re common to 2 nd 56. d Wht is the highest common fctor of 2 nd 56? 0 Prime numbers hve only two fctors, nd the number itself. 7 is prime numbers. Its fctors re nd 7. 9 is not prime numbers s it hs more thn two fctors. The fctors of 9 re, nd 9. Which of these numbers re prime numbers? 5 2 9 2 2 7 27 Originl mteril Cmbridge University Press 2009 2
Cmbridge Essentils Mthemtics Core 8 N2 Consolidtion Worksheet N2 Consolidtion Worksheet Frctions cn be simplified by cncelling. This mens dividing numertor (top number) nd denomintor (bottom number) by the sme number. 5 5 25 25 00 5 20 or 25 00 5 5 25 When the frction cnnot be cncelled further, it is in its lowest terms. Cncel these frctions to their lowest terms. 8 0 b 8 0 c 5 6 d 5 00 e 2 9 Find multipliction tble tht contins both the numertor nd denomintor. For exmple, 8 nd 0 re both in the 6 times tble, so divide 2 0. 0 so 0. 0 2 5 8 the top nd bottom of by 6. 0 0.0 00 nd 0.00 000 so 0.65 65 2 nd 0.02 00 000 Write ech deciml s frction in its lowest terms. 0.6 b 0.8 c 0.96 d 0.055 e 0.60 5 5 2 5 5 or 0 0 2 5 0 re clled equivlent frctions. 5 5 A frction my be written s deciml by finding n equivlent frction with denomintor of 0, 00, 000 etc. 9 50 2 8 0.8 00 2 Chnges these frctions to decimls in the sme wy. b 7 0 c 20 d 2 50 e 5 Originl mteril Cmbridge University Press 2009
Cmbridge Essentils Mthemtics Core 8 N2 Consolidtion Worksheet A frction cn be chnged to deciml by dividing the numertor by the denomintor. 8 8 0.75 6 8.000 This is terminting deciml. 0. This is clled recurring deciml. b Convert ech frction below into deciml. i 5 ii 7 iii 9 iv 7 0 v Stte whether ech nswer to prt is terminting deciml or recurring deciml. 7 2 5 Frctions cn be dded or subtrcted only if they hve the sme denomintor. You cn then dd or subtrct the numertors. Never dd or subtrct denomintors. 5 + 2 5 + 2 5 5 If the frctions hve different denomintors, convert them to common denomintor before dding or substrcting. A common denomintor is multiple of ech denomintor. For exmple, 5 nd hve common multiples 5, 0, 5 nd so on. (It does not mtter which multiple you use, becuse you cn cncel the nswer t the end if necessry.) So to work out 5 + 2, we could use common deomintor of 5. 2 0 +0 + + 5 5 5 5 5 Work out these frction clcultions. Remember to show ll your working. 5 2 5 5 5 0 5 2 + 7 7 b c 5 5 2 + d 5 0 2 6 e 2 + f 2 5 5 g 6 8 5 h 9 20 6 To find frction of n mount, divide by the denomintor nd multiply by the numertor. mens. For exmple, 2 2 2 5 mens 5 then 2. For exmple, 5 2 5 (5 5) 2 2 6 Work these out. 2 5 of 20 b 9 of 5 c of 0 d of 80 kg 8 Originl mteril Cmbridge University Press 2009 2
Cmbridge Essentils Mthemtics Core 8 N2 Consolidtion Worksheet 2 N2 Consolidtion Worksheet 2 A percentge mens n mount out of 00. For exmple, 0% mens 0 out of 00. As frction, this is 0 00 0 As deciml, this is 0 00 0. Write ech percentge below s frction in its lowest terms. i 0% ii % iii 7.5% iv % v 75% b Write ech percentge in prt s deciml. 2 To find percentge of n mount, chnge the percentge to deciml then multiply by the mount. Work out 6% of 50 0.6 50 8 2% of 80 kg b 5% of 200 c 5% of 96 m d 72% of $55 e 2% of 00 cm f 70% of 60 To write one mount s percentge of nother, first write the two mounts s frction. Find n equivlent frction with denomintor of 00, then chnge to percentge. Find s percentge of 25. 25 52 52% 00 To find 50p s percentge of 5, the 5 must first be converted to pence: 50p s percentge of 500p. Find these percentges. 70 s percentge of 200 b 25 cm s percentge of 5 m c 50 g s percentge of 2 kg Alwys mke sure tht the units of both mounts re the sme. Convert one of the mounts if necessry. d 2 minutes s percentge of 2 hours Originl mteril Cmbridge University Press 2009
Cmbridge Essentils Mthemtics Core 8 N2 Consolidtion Worksheet 2 Wht is 6% of 80 kg? Work it out in esy steps. First find 0% of 80 kg: 0% of 80 kg 80 kg 0 8 kg Use your nswer to work out 0%, 5% nd % of 80 kg: 0% of 80 kg 8 kg 2 kg 5% of 80 kg 8 kg 2 kg % of 80 kg 8 kg 0 0.8 kg So 6% of 80 kg 0% + 5% + % of 80 kg 2 kg + kg + 0.8 kg 28.8 kg Complete these clcultions. i 0% of 200 0% of 200 0% of 200 So 0% of 200 ii 27% of 60 20% of 60 + 5% of 60 + % of 60 0% of 60 20% of 60 2 5% of 60 2 2% of 60 20% of 60 So 27% of 60 + + iii 89% of 500 500 0% of 500 % of 500 0% of 500 % of 500 0 So 89% of 500 b Use similr method to work these out without clcultor. i ii % of 800 kg 6% of 500 cm iii 6% of 00 litres Originl mteril Cmbridge University Press 2009 2
Cmbridge Essentils Mthemtics Core 8 N Consolidtion Worksheet N Consolidtion Worksheet 600 cn be written s 6 00 or 6 0 2. 000 cn be written s 000 or 0. Remember tht 00 0 0 0 2 nd 000 0 0 0 0 9 000 cn be written s 9 000 or 9 0. Write these numbers using powers of 0. 9000 b 5 000 c 200 d 7 000 000 e four hundred f two thousnd g eight million h twenty thousnd 2 Multiplying by 0. is the sme s dividing by 0. So 5 0. is the sme s 5 0. Dividing by 0. is the sme s multiplying by 0. Show the deciml point fter the units. 5. 0.5 All the digits move one plce to the right. So 28 0. is the sme s 28 0. Without clcultor, work these out. 7 0. b 29 0. c 0. d 28 0.0 e 2 0. f 7 0. g 2 0. h 9 0.0 Round these to the nerest 00. 20 b 780 c 65 d 26 Lies between 00 nd 00. Which is it nerest to? Round these to the nerest 0. Hint It my help to drw number line. Hlfwy rounds up. 87 b 6 c d 6 e 25 5 You cn dd or subtrct numbers in your hed by prtitioning or splitting up the numbers. 7 + 28 7 + 20 + 8 86 80 6 67 + 8 6 6 75 57 Work these out in your hed, using prtitioning. Show your working clerly. 28 + 5 b 2 + 77 c 8 6 d 5 66 Originl mteril Cmbridge University Press 2009
Cmbridge Essentils Mthemtics Core 8 N Consolidtion Worksheet 6 When multiplying by deciml in your hed, brek the clcultion into smller steps. 26 0.2 26 0. 2 2.6 2 5.2 25 0.7 (20 0.7) + (5 0.7) +.5 7.5 Now work these out in the sme wy. Remember tht 0. is the sme s 0. You could write this s 6 0.0 2. Remember 0.0 is the sme s 00. 2 0. b 9 0.2 c 5 0. d 6 0.02 7 To multiply by number tht is close to multiple of 0, multiply by the multiple of 0, then djust. 8 2 8 20 + 8 960 + 8 008 22 29 22 0 22 660 22 68 Work these out. Show your working. b 6 9 c 20 22 8 When you dd or subtrct decimls, line up the deciml points nd write the digits in the correct columns. 6. + 8.7 + 0.025 + 7 6. 8.7 0.025 + 7. Whole numbers hve deciml point t the end..795 Work these out. 2. + 2.57 + 2 + 6.05 b 2.8 + 0.07 +.72 + 6 c 9.8.6 d.5 8.62 e.72 65.8 You will need to dd zero in when you write the sum..50 8.62 Originl mteril Cmbridge University Press 2009 2
Cmbridge Essentils Mthemtics Core 8 N Consolidtion Worksheet N Consolidtion Worksheet Opertions must be worked out in certin order nd not lwys from left to right. 2 + 5 is 6 + 5 but 2 + 5 is NOT 5 5 75 B I D M A S tells you the correct order. B brckets st I indices 2nd D nd M divide nd multiply rd A nd S dd nd subtrct th So 2 + 5 is 2 + 5 27 becuse multiply comes before dd in BIDMAS. Work these out without clcultor using the BIDMAS rules. + 7 2 b (6 5) 2 c 2 7 2 d 2 + 5 6 27 e (7 ) f 2 2 6 g 2 2 2 h 6 2 2 Doing some clcultions involves using INVERSE opertions. Add nd subtrct re inverses so + is the inverse of. Multiply nd divide re inverses so 0 is the inverse of 0. Squre nd squre root re inverses so is the inverse of 2 2. Write the inverse of the following opertions. 0 b + c 7 d 5 Which is the correct method for finding x? x 2 6 x 6 2 x 6 2 x 6 b x 8.5 2 x 8.5 2 x 8.5 x 8.5 2 c (x 28) 7 2 x (28 + 2) 7 x 2 7 + 28 x 2 + Originl mteril Cmbridge University Press 2009
Cmbridge Essentils Mthemtics Core 8 N Consolidtion Worksheet Answers cn be checked nd mistkes cn be spotted in vriety of wys. You cn estimte n nswer. 8 2 Round numbers to n esier number, like to the nerest ten. 0 0 600 You cn check n nswer using BIDMAS. 2 60 This cnnot be correct becuse multipliction must be done before subtrction so the nswer must be smller thn. It is useful to remember tht multiplying by positive number less thn mkes the originl number smller. 0.2 0.8 Dividing by positive number less thn mkes the originl number bigger. 0.2 8 Pick out possible nswer to ech clcultion. 6 79 09 89 700 b 6.5 0.5. 0. c 7 5 2 2 7 9 5 Frctions cn be simplified by dividing the top (numertor) nd the bottom (denomintor) by the sme number. 0 2 5 0 0 5 (simplest form) or 50 5 50 25 5 0 2 5 Frctions nd rtios re two wys of describing proportion of n mount. Rtios cn be simplified in the sme wy s frctions. 2 : 20 : 5 But 0 cm : m is not 0 : becuse the units in rtio must be the sme. So chnge m to 00 cm. This gives 0 cm : 00 cm. Now the units re the sme we cn simplify. 0 0 : 00 : 0 0 Check tht the units re the sme. If they re different then chnge one unit before simplifying. Simplify ech rtio. Show how you simplified it. 20 : 28 b 6 : 60 c 6 : 8 d 2 : 7 e : 50p f 8 cm : mm g kg : 20 g h min : s Originl mteril Cmbridge University Press 2009 2