Write in the boxes the prt of the unit which hs been shded. i) i iv) v) b) i) i Answer with frctions in your exercise book. Wht prt of metre is: 0 cm, 0 cm, 7 cm, 0 cm? b) Wht prt of n hour is: min, 6 min, 0 min, 60 min, 0 min? c) Wht prt of dy is: 6 hours, 8 hours, hours, hours, 0 hours? How mny cm re these prts of 6 cm line segment? i) 6 i 6 iv) b) How long re these prts of m length of ribbon? i) 8 i c) How mny pples re in these prts of box of 8 pples? i) 6 i iv) iv) v) v) v) 9 8 7 8 vi) vi) 8 Drw squre in your exercise book. olour of its re in yellow, then colour Wht prt of the whole re is the red prt? of the yellow prt in red. b) Drw 6 rectngle in your exercise book. olour of its re in green, then shde of the green prt in blue. Wht prt of the whole re is the blue prt? onvert these frctions to ths nd write them in incresing order in your exercise book.,,,,,, 7, 6 8, 6, b) onvert ech frction to n equivlent frction with numertor. Write them in incresing order in your exercise book.,, 6,, 6 7, 0, 9 6,,, Pge
Step long the number line by from. Lbel the numbers tht you lnd on. 0 b) Step long the number line by from. Lbel the numbers tht you lnd on. 0 Multiply the numertor of by,,, nd 6 nd write the frctions in your 8 exercise book. Write sentence bout how the vlue of the frction chnges. b) Multiply the numertor of by,,, nd 6 nd write the frctions in your exercise book. Write sentence bout how the vlue of the frction chnges. e) 8 7 = b) 8 = c) = d) 8 = = f) 6 7 = g) 7 0 = h) 0 = i) = j) = k) 7 = Divide the numertor of 6 by, nd 6 in your exercise book. 8 Write sentence bout how the vlue of the frction chnges. b) Divide the numertor of by,, 6 nd in your exercise book. Write sentence bout how the vlue of the frction chnges. d) 6 7 = b) 9 0 = c) 8 9 = 8 7 = e) 8 = f) 8 7 9 = 6 66 66 66 Multiply the denomintor of by,,, nd 6 in your exercise book. Write sentence bout how the vlue of the frction chnges. b) = = = = 6 = c) = = 7 = = 6 = Pge
i) 6 = 6 = i 6 = iv) 6 = b) i) + = i = c) i) 6 8 = 6 8 = i 7 = iv) = d) i) = = i 9 = iv) = Divide the denomintor of by nd by in your exercise book. 6 Drw digrm to show ech division. Write sentence bout how the vlue of the frction chnged s its denomintor decresed. b) Divide the denomintor of: i) by 9 by i 0 by Drw digrms to show ech division. = 6 = = 9 0 = 7 6 = b) i) = 8 = i = c) Write sentence bout how the vlue of frction chnges if its denomintor is: i) multiplied,,,... divided by,,,... Multiply the numertor nd the denomintor of by, nd. How did the vlue of the frction chnge? Drw digrms to show it. b) Divide the numertor nd the denomintor of by, nd 6. 0 How did the vlue of the frction chnge? Drw digrms to show it. Fill in the missing digits. = 8 = = = = 8 = 0 = = 70 =0. 8 00 b) 7 = 8 = 70 = 6 0 = = = 6 9 = 0 c) 0 = 0. = 00 = 00 = 0 000 = 0. = 0. d) = 0 =. = = 0 = 8 Pge
ircle the numbers which re less thn. Tick the numbers which equl. 7 9 9 7 7 9 6 0 6 6 9 8 b) onvert the numbers greter thn to mixed numbers in your exercise book. Fill in the missing digits. = 0 = 0 = 6 = 0 = = 8 = 00 = = 7 000 b) 0 = 7 =. = 0 = = = = 00 0 70 0 = c).0 =. =. = 00 = 00 = 00 d) 60 = = = = = 7 = 6 8 9 6 lculte the sums nd differences in your exercise book. i) 8 + 8 b) i) + + 8 c) i) + 0 + 7 0 + 0 7 6 + i i 6 7 7 i 9 + 9 9 + iv) + 7 9 iv) 8 8 iv) 0 + onvert the frctions to common denomintor, then do the clcultion. i) b) i) + + 6 7 0 i + 7 8 i 6 + 8 iv) 7 8 iv) 0 v) 7 9 Write pln, do the clcultion nd write the nswer in your exercise book. Yesterdy I bought qurters of kg of pottoes nd tody I bought hlf kg of pottoes. How mny kg of pottoes did I buy ltogether? b) A fmily took qurters of kg of grpes on picnic. How mny kg of grpes did they bring home if they te fifths of kg during the picnic? c) Two friends decide to wlk to the bech, which is nd qurter kilometres from their cmp site. They wlk nd sixths kilometres, then hve rest. How fr do they still hve to go? Pge
List t lest numbers which could be written insted of the squre. < < :........................................ b) < < c) < < :........................................ :........................................ Prctise multipliction nd division. Simplify the frctions where necessry. e) 9 9 = b) 6 = c) = d) 7 7 = = f) 7 8 = g) = h) 7 0 0 = i) = j) 6 6 = k) 8 9 = l) 0 = m) q) 8 = n) = o) 0 = p) 6 = 0 7 = r) 0 = s) 7 = t) 8 7 = Write ech of these decimls in hundredths nd in thousndths. i) 9..7 i 0. iv) 0.0 v).0 b) Write ech of these numbers s deciml. i) 6 0 00 i 0 00 iv) 8 000 v) 7 000 Fill in the missing digits. = 0 = = 0 = = 60 = 88 = = 80 = 60 000 b) 7 = = 0 = 9 = = 0 = = 8 00 000 = c) 8.6 = 8. = 8. = = 00 00 = 86 I hd lots of hristms crds to write. I wrote third on Mondy, eighths on Tuesdy, sixth on Wednesdy nd wrote the remining 7 crds on Thursdy. How mny hristms crds did I send? Pge
Simplify these frctions nd mrk them on the number line. 60 0 = b) 0 60 = c) 7 = d) 7 = 6 0 Write pln, do the clcultion, check the result nd write the nswer in sentence. A frmer hd beehives. He collected kg of honey from one of the beehives nd. kg of honey from nother. If he collected 9 kg of honey ltogether, how much honey did he collect from the rd beehive? b) Two cyclists strted t the sme time from either end of n 80. km journey nd cycled towrds ech other. They both hd rest brek t the sme time. By then, one cyclist hd covered 0 km nd the other hd covered. km. How fr prt were they when they stopped to rest? c) Mum bought 00 g of grpes. Andy te fifth of them, Betty te qurter of them nd hrlie te third of them. Dd te the rest. Wht mount of grpes did ech of them et? d) Kte gthered.6 kg of strwberries in hours. Julie worked for 0 hours but collected 8 kg less thn Kte. Wht mount of strwberries did Julie gther? Prctise ddition nd subtrction in your exercise book. + b) 8 c) 0 0 6 d).6 (. + 0.) e).0 (. 0.8) f).8 (0.6.) g) + h) 8 i) 9 Write pln, do the clcultion nd write the nswer in your exercise book. One side of rectngle is m long nd the other side is m long. Wht length is its perimeter? b) The side of squre is cm long. Wht length is its perimeter? Pge 6
Show the solution to ech inequlity on the number line. x < b) x 0 0 Show the solution to ech inequlity on the number line. Numbers which re less thn + but re not less thn (.). 0 b). x <, nd x is whole number c) x <. 0 0 Prctise ddition nd subtrction in your exercise book. i) b) i) + + 7 i 8 + 7 9 + 9 0 9 i 8 7 c) i). (0..6). 0. +.6 iv) 6 + 6 6 iv) 9 d) i).6 (+.) + (.) (.7).6.. +.7 Write pln, clculte, check nd write the nswer s sentence in your exercise book. Tommy Tortoise took hour to move 6 metres. This ws 6 6 metres more thn the distnce covered by Timmy Tortoise in the sme time. Wht distnce did Timmy Tortoise move in n hour? b) Jenny cut pieces from 0.8 m length of ribbon. The lengths of the pieces were m, 7. m nd m. ould Jenny cut nother piece 6. m long from the ribbon tht is left? c) The sum of two frctions is. One frction is greter thn the other frction. 8 Wht re the two frctions? Pge 7
onvert the decimls to frctions. Simplify where possible. i) 0.7 = 0.6 = i 0. = iv) 0. = b) i) 0. = 0.0 = i 0.7 = iv) 7. = c) i) 0. = 0.7 = i 0.6 = iv) 0.87 = onvert the frctions to decimls. = = = = 6 = b) c) d) = = = = 8 = 8 = 8 = 6 8 = 7 8 = = = = = 9 = = e) f) g) = = = = = 6 = 6 = 6 = 6 = 6 = 9 = 9 = 9 = 9 = 7 9 = Do the clcultions in your exercise book. 6 8 + 7 7 90 b) + 0 6 + 0 8 Solve the problems nd equtions in your exercise book. If I dd to number, the sum is 7. Wht is the number? 8 b) If I subtrct from number, the result is. Wht is the number? 8 c) x 7 + = 8, d) d 70 = 0, x =? d =? Pge 8
In your exercise book, clculte ech product in two wys: i) b) i) 8 7 0 i 8 7 iv) 6 ( ) v) 8 8 8 i iv) 7 9 9 v) vi) 8 7 ( 7) ( ) ( ) lculte 7 of the re of unit by unit rectngle. b) lculte: i) of times lculte in your exercise book: i) of 60 60 b) i) of 6 6 8 8 c) i) 7 of 8 8 7 d) i) 7 of 7 Solve these problems in your exercise book. Henry Hedgehog te of his 9 pples. How mny pples did he hve left? b) Pul hd 0. He spent of 0, then of 0. i) How much did Pul spend? How much money did he hve left? c) Liz hd 0. Then she ws given some money by her grndprents so she now hs of her originl mount. If she spends of her money, how much will she hve left? d) How much money do I hve if of of it is 80? e) One side of rectngle is cm long nd its djcent side is of its length. i) How long is the other side? How long is its perimeter? i Wht is the re of the rectngle? Pge 9
A rtionl number is ny number which cn be written s frction, where the numertor nd denomintor re whole numbers but the denomintor is not zero. Lbel in frction form the rtionl numbers mrked on the number line. 0 b) Mrk the opposite vlue of ech number in red. c) Write ech of the mrked numbers s deciml. d) Wht is their sum? Prctise ddition nd subtrction in your exercise book. i) b) i) 9 + 9 + 9 6 i 00 + 0 + 0 0 i 9 6 iv) 8 7 0 + iv) 8 7 c) i) 9 (0.7.8). 8.0 + 9. d) i). (+.) + (.) (.) 00. 7.98 + 0.6 Write n inequlity to mtch the solution shown on ech number line. b) c) 0. 0. 0 0. 0. 0. 0. 0 0. 0. 0. 0. 0 0. 0. Solve the problems in your exercise book. Emm sved 0 per month for qurter of yer but ech month she spent tenth of wht she hd sved. How much hd she sved by the end of the qurter? b) How mny kg do I weigh if 8 of of my weight is 000 g? c) A litre jug ws full of lemonde. Brry drnk 7 tenths of the lemonde nd Steve drnk wht ws left. How mny cl did Steve drink? d) Kngroo took jumps to get from one bush to the next in serch of better shde from the sun. His first jump ws.7 m, his second jump ws ninth longer thn the first, his rd jump ws one sixth shorter thn the nd nd his th jump ws fifths of his rd jump. How fr prt were the two bushes? Pge 0
Which description fits which solids? Write the numbers of the mtching solids. 6 7 8 9 0 It hs only plne fces.................................... b) It hs t lest one plne fce.................................... c) It hs t lest plne fces.................................... d) It hs perpendiculr fces.................................... e) It hs t lest one tringulr fce.................................... f) It hs only rectngulr fces.................................... g) It hs t lest prllel edges.................................... h) It hs perpendiculr edges.................................... ount the fces, edges Solid nd vertices of the bove Number of fces solids which hve only plne fces. Number of edges Number of vertices omplete the tble. omplete the sentences. When we divide up surfce, the surfce pieces re bounded by. b) A line cn be curved or. c) When we divide up line, the segments strt nd end with. d) A point on stright line divides the line into hlf lines or rys. e) The prt of stright line between two different points is clled. f) A stright line in plne divides tht plne into hlf plnes. g) Two different prllel lines divide their plne into prts. h) Two intersecting lines divide their plne into prts. olour red point on the plne P. b) olour green point which is not on the plne P. c) olour yellow n edge which is in the plne P. d) olour blue n edge which is not in the plne P. P E A H D F B G Pge
omplete the sentences bout circles. The line segment joining the centre of circle () nd point (D) on its circumference is clled the. A D r d E B F b) A section between two points on the circumference is clled n. c) A chord which lies on the centre of the circle is clled the. d) Two points on the circumference divide it into rcs. e) Two rdii of circle divide the circle into sectors. A r B r f) A chord divides the circle into segments. g) Line f is n nd line t is of the circle. r f T t Fill in the missing items bout ngles. The two hlf lines (e nd f) form two. α f e b) is the nd e nd f re the of the ngle α. c) null ngle ngle ngle ngle π π = 80 (pi) ngle α 0 < α < 90 (lph reflex ngle γ 80 < γ < (gmm β 90 90 < β < 80 (bet whole ngle Which description fits which polygons? Write the numbers of the mtching polygons. 6 7 8 9 It hs only cute ngles.................................... b) It hs no ngle greter thn 90.................................... c) It hs more thn digonls.................................... d) It cn be divided into more thn prts by one stright cut.................................... Pge
In your exercise book, drw: i) tringle qudrilterl i pentgon. omplete the sentences. A polygon is enclosed only by. b) A polygon hs the sme number of s it hs. c) Ech vertex of polygon is shred by only sides. d) The broken line enclosing polygon is closed nd does not itself. In your exercise book, drw three seprte cute ngles. ut the rms of ech ngle with stright line so tht these tringles re formed: cute-ngled tringle b) obtuse-ngled tringle c) right-ngled tringle. Write the letters of these tringles in the correct prt of the set digrm. Equilterl Acute Tringles Isosceles Right Obtuse b c A b D b E b B c b b F c b c b G Write the numbers of these qudrilterls in the correct prt of the set digrm. Qudrilterls Trpeziums x Prllelogrms Rectngles Rhombi 6 7 x 8 9 0 Write the nmes of the solids below ech digrm. b) c) d) e) f) g) Pge
Mesure these ngles. β B α A α β A N M K L B M A B K L N Drw these ngles in your exercise book. 0 b) 6 c) 70 How mny degrees re these ngles? Wht is the sum of the ngles in this tringle? The shding might help you. + + = Is the sum the sme for ny other tringle in the grid? b) D Fill in the missing items. i) The sum of the ngles in AB is A B The sum of the ngles in AD is i The sum of the ngles in ABD is Remember tht = 60' (ngle minutes) nd ' = 60'' (ngle seconds). lculte the rd ngle of tringle which hs ngles of 8 0' nd 6 '. b) Wht kind of tringle is it?..................... Pge rd ngle:
Study these plne shpes. Wht do some of them hve in common? 8 6 7 9 0 Wht do the shpes listed below hve in common? Write sentence bout ech set.,, 7.................................................... b),, 9....................................................... c),,, 6, 8, 9..................................................... d),, 6, 7, 0...................................................... e),, 7, 0....................................................... f),, 6, 8, 9, 0.................................................... g),,, 6, 9...................................................... h) Mke up set which is different from those given. Write sentence bout it................................................ Drw circle with rdius. cm. Drw its dimeter. Drw ny chord AB. i) Wht length is the dimeter of the circle? Wht length is AB? b) Drw squre with side length 8 mm. Drw digonl BD. i) Wht length is BD? Wht is the perimeter nd re of the squre? c) Drw.6 cm by.9 cm rectngle. Drw digonl A. i) Wht length is A? Wht is the perimeter nd re of the rectngle? d) Drw tringle AB, with AB =. cm, A = 0 nd B =. i) Wht length is its perimeter? Wht size is? i Wht is its perpendiculr height from AB to?. Mesure ech ngle. Write its size in the box nd its type on the dotted line. A α b e δ D h β B f g α = β = δ = b) On plin pper, drw ngles of: i) 78 i iv) 90. Pge
Fill in the missing items. Length mm < cm < < km 0 00 b) mm < < m < hectre < km 00 0 000 0 000 c) Mss mg < g < kg < 000 000 d) ml < < litre 0 e) Volume mm < < m < 000 million billion f) " < ' < 60 60 g) Time sec < min < hour < < week < 7 Write the missing numbers..6 m = cm = mm = km b) 0.6 tonnes = kg = g c) 67 g = kg = tonnes d) 68 ml = cl = litres e). hours = min = sec f). m = cm = mm Wht is: of kg b) 0.7 of 0 m c) of 0 litres d) of km? lculte the times nd ngles. h min sec b) ' 6" c) 0' d) h 9 min + h 9 min sec 7 ' 7" Pge 6
Precise mesurements re importnt in design, technology, engineering, chemistry, medicine, etc. In everydy life, it is enough to use rough estimtes nd conversions. omplete the missing items. Write s frctions nd s decimls. If inch. cm, then cm in inches b) If foot 0. m, then m ft feet c) If metre. yrds, then yrd m metres d) If mile.6 km, then km miles miles e) If ounce 8 g, then g oz ounce f) If kg. lb, then lb kg kilogrms g) If pint 0.7 litres, then litre pt pints h) If gllon. litres, then litre gl gllons On mp of the Bleric Islnds, Plm on the islnd of Mjorc is situted t ltitude 7. Est nd longitude 9. North. Find Plm on your mp. b) The re of Mjorc is 60.6 km. onvert its re to squre miles. [ squre mile.6 km ] c) The length of Mjorc's cost is.7 km. onvert it to miles. [ km 8 mile] d) The nnul verge temperture in Mjorc is. 8. onvert it to degrees Fhrenheit using this formul: x x = 9 + F e) The shortest shipping route between Mjorc nd Menorc is Miles long nd is bout 6 km. Is this nuticl Mile the sme s the usul rod mile? f) On the plne to Mjorc, the cptin informed us tht our plne ws flying t height of 0 000 feet. Wht is the height in metres nd kilometres? g) The cptin told us tht our plne ws flying t speed of 900 km per hour. lculte the speed in miles per hour (mph). Solve the problems in your exercise book. The rod sign shows tht it is miles to Stnsted Airport. If our coch is trvelling t speed of 96 km per hour, how long will it be before we get there? b) Wht is thirds of 60 lb in kg? c) A cpcity of litre is prcticlly equivlent to 000 cm, nd kg of wter is close to litre. How mny kg is 600 cm of wter? Pge 7
Which quntity is more? c) of 00 kg or 8 of tonne b) 0. of 0 or of 700 m or times 900 cm of 0 The vlue of one currency ginst nother is lwys chnging. For exmple, on.0.000: GBP.6 USD [GBP mens Gret Britin's Pound ( ) GBP.69 EUR USD mens United Sttes Dollr ($) so EUR 0.87 USD EUR mens Euro ( ) ] on.08.00: GBP.60 USD GBP. EUR so EUR. USD Wht chnges do you notice in the vlue of: i) the ginst the $ the ginst the i the ginst the $? b) How mny Dollrs nd how mny Euros were the equivlent of 00 on ech of these two dtes? The chnge in vlue of the Hungrin Forint (HUF) very interesting. during the sme time is On.0.000: GBP HUF On.08.00: GBP 67 HUF USD 0 HUF USD 8 HUF EUR 6 HUF EUR 9 HUF c) To which of the currencies ws the Hungrin Forint most closely linked? d) How mny Hungrin Forints were equivlent to 00, $00 nd 00 on ech of these two dtes? The qulity of gold nd jewels is mesured in crts. The crt for gold is different from the crt for dimonds. The purity of gold is mesured in ths. For exmple, -crt gold ring mens tht one th of its mss is pure gold. How much pure gold is in n 8-crt gold ring which weighs g? b) How much pure gold is in -crt gold necklce which weighs. g? Wht is your mss: i) in grms in tonnes? (Answer to the nerest kg.) b) The weight of ny object on the moon would be sixth lighter thn it is here on Erth. Wht would the mss of kg lof of bred be on the Moon? c) A plne took off t 8. m in Budpest nd lnded t. pm in New York. If New York time is 6 hours erlier thn Budpest time, how long ws the flight? Pge 8
This is the pln of house nd its grden. Scle: : 00 Grge Trees Pth House Vegetble Plot Mesure on the pln, then clculte the rel lengths nd widths of: i) the house the grge i the vegetble plot iv) the whole grden. b) lculte: i) the perimeter of the vegetble plot the re of the grden. These re digrms of living cell nd longitudinl section of bcterium. Living cell b) Longitudinl section of bcterium Scle: 00 : Scle: : Mesure the lengths nd widths on the digrms, then clculte their sizes in rel life. Wht do you think the digrm in could be? Mesure the sides of ech shpe, then clculte its perimeter nd re. b) Pge 9
Join up the equl mounts.. hours 0. h min. litres 9 tonnes 00 0 ml 0 p 0 g 7 00 litre.0 kg dy 0. cm. cl ml cl 0 kg lculte the times. 6 h min 0 sec + 8 h 9 min sec b) h min sec h min 7 sec c) 6 h 7 min 9 sec h min 6 sec Fill in the missing numbers. The Erth tkes hours to turn by 60 round its xis. So the Erth turns ech hour nd tkes minutes to turn. b) Becuse the Erth is turning, the light from the sun hits different prts of it t different times, so ll the countries on Erth re in different time zones. The tble shows the time difference (in hours) for vrious cities round the world compred with the time in the UK, which is Greenwich Meridien Time (GMT). Sn Frncisco 8 h New York h Rio de Jneiro h GMT London 0 h Budpest + h i) When it is 8.00 m GMT, wht time is it in: Moscow + h Beijing + 8 h New York Sydney Beijing Budpest Moscow London? Sydney + 0 h When it is :0 in Budpest, wht time is it in: London Beijing Sn Frncisco Rio de Jneiro? A plne left London t.00 m on Sturdy for n hour flight to Sn Frncisco. Wht ws the time in Sn Frncisco when it lnded? b) A plne left London for Moscow t 0.00 pm on Sundy. It ws.00 m on Mondy in Moscow when it lnded. How long ws the flight? c) A plne lnded t noon in London fter 9 nd hlf hour flight from Beijing. Wht time ws it in Beijing when the plne took off? Pge 0