CFE ational 5 - Pack 1

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1 CFE tionl - Pck Unit : Epressions & Formule (EF) A T I O A L WORKSHEETS Pegsys 0 Worksheets covering ll the unit topics Answers

2 INDEX (EF) EXPRESSIONS nd FORMULAE. Working with surds Simplifiction Rtionlising denomintors. Simplifying epressions Multipliction nd division using positive nd negtive indices including frctions Clcultions using Scientific Nottion. Rounding to given number of significnt figures. Working with lgebric epressions with brckets (b c) d(e f) ( b)(c d) (b c) ( b)(c² d e), b, c, d nd e re integers. Fctorising n lgebric epression Common fctor Difference of two squres ² y² ; p² y² Common fctor with difference of two squres Trinomils with unitry ² coefficient Trinomils with non-unitry ² coefficient Pegsys 0

3 . Completing the squre in qudrtic epression with unitry ² coefficient. Reducing n lgebric epression to its simplest form /b where nd b re of the form ( p)n or ( p)( q). Applying the four opertions to lgebric frctions /b c/d where, b, c nd d re simple constnts or vribles * cn be dd, subtrct, multiply or divide. Determining the grdient of stright line given two points m = y y /. Working with the length of rc nd re of sector of circle. Working with the volume of solid sphere, cone, pyrmid Pegsys 0

4 . WORKING with SURDS. Epress ech of the following in its simplest form: () 8 (c) (h) 7 00 (j) 7 (k) 9 (l) 8 (n) 98 (o) 90 (p) 8 (q) 8 (r) 80 (s) (t) 0 (u) 0 (v) (w) () 7. Simplify: () 8 (c) (h) (j) (k) (l) 0. Epress ech of the following in its simplest form: () 7 7 (c) 8 (h) (j) (k) (l) 7. Epress ech of the following in its simplest form: () 7 8 (c) (h) (j) (k) 7 08 (l) (n) 8 (o) 7 0 (p) 98 (q) 80 0 (r) (s) 8 (t) 7 (u) 8 8 Pegsys 0

5 . Simplify: () (c) c c k k (h) 8 (j) (k) (l) y 8 (n) (o) 0 (p) (q) b (r) 0 (s) p q (t) k (u) 0 (v) (w) 0 () (y) 0 (z) 8. () (c) 7 8 (h) 7. Simplify: () 8 7 (c) (h) (j) (k) 88 8 (l) (n) (o) 98 7 (p) 0 0 Pegsys 0

6 8. Epnd nd simplify: () ( ) ( ) (c) ( ) ( ) ( ) ( 8 ) ( 8) (h) ( ) ( 8) (j) 8( ) (k) ( ) (l) ( 00 0) ( ) (n) ( 8 ) (o) ( ) (p) ( ) 9. Epnd nd simplify where possible: () ( )( ) ( )( ) (c) ( )( ) ( )( ) ( )( ) ( )( ) ( )( - ) (h) ( 8 )( 8 ) ( )( ) (j) ( ) (k) ( ) (l) ( ) ( 7 ) (n) ( ) (o) ( )( ) (p) ( 7 ) (q) ( ) (r) ( )( ) 0. Epress ech of the following with rtionl denomintor nd simplify where possible: () (c) 0 (h) 0 (j) (k) (l) 0 (n) 7 Pegsys 0

7 . Epress ech of the following with rtionl denomintor nd simplify where possible: () (c) (h) 0. Epress ech of the following in its simplest form with rtionl denomintor. () (c) (h) 8 (j) (k) 7 (l) 8 (n) (o) (p) (q) 8 (r) 0 0 (s) (l). Epress ech of the following with rtionl denomintor nd simplify where possible: () (c) (h) 0 (j) (k) (l) Pegsys 0

8 . Rtionlise the denomintor, in ech frction, using the pproprite conjugte surd. () (c) (h) (j) (k) 7 (l) (n) 0 (o) (p) 9 Pegsys 0

9 SURDS PROBLEMS. A right ngled tringle hs sides, b nd c s shown. For ech cse below clculte the length of the third side, epressing c your nswer s surd in its simplest form. b () Find if b = nd c =. Find c if = nd b =. (c) Find c if = 8 nd b = Find b if = 8 nd c =.. Given tht = nd y =, simplify: () y y (c) y ( y)( y). Given tht p = nd q =, simplify: () p q pq (c) p q. A rectngle hs sides mesuring ( ) cm nd ( ) cm. Clculte the ect vlue of () its re the length of digonl.. A curve hs s its eqution y =. () If the point P(, k) lies on this curve find the ect vlue of k. Find the ect length of OP where O is the origin. Pegsys 0

10 . In ABC, AB = AC = cm nd BC = 8cm. Epress the length of the ltitude from A to BC s surd in its simplest form. [The line AM in the digrm] A cm cm 7. An equilterl tringle hs ech of its sides mesuring metres. () Find the ect length of n ltitude of the tringle in terms of. Hence find the ect re of the tringle in terms of. [Drw digrm to help you with this question] B M 8cm C 8. The ect re of rectngle is ( ) squre centimetres. Given tht the bredth of the rectngle is cm, show tht the length is equl to ( ) cm. 9. ( chllenge) Given tht tn 7 o = o, show tht tn 7 =. Pegsys 0

11 . INDICES. Write ech of the following in its simplest inde form. () (c) (h) 8 (j) c c 9 (k) (l) y y b 0 b 0 (n) p p 9 (o) d d (p) q q 9 (q) t t 7 (r) f f (s) k k (t) z 0 z 0 (u) 0 0 (v) y 9 y (w) () b b 0. Write ech of the following in its simplest inde form. () 8 (c) (h) 7 (j) 9 (k) y 0 y 0 (l) b b p p (n) c 7 c 7 (o) q 8 q (p) d d 9 (q) 8 (r) (s) m 7 s (t) 7 m s 0 d (u) d 00 y (v) 0 y (w) t 00 0 w () 0 t w. Write ech of the following in its simplest inde form. () ( ) (8 ) (c) (0 ) ( ) ( ) ( 7 ) ( ) (h) ( ) ( ) (j) (y 8 ) (k) ( ) 7 (l) (m ) (b ) (n) (p ) (o) (k ) 0 (p) (z ) 0 Pegsys 0

12 . Write the following without brckets. () (7) (c) () (y) (b) (y) 7 (wz) (h) (st) (pq ) (j) ( y) (k) ( b ) (l) ( ) (0 ) (n) (c ) (o) (b ) (p) (m k). Simplify these epressions. () (c) p 7 p 0b 0b y (y ) (q ) q (c ) 8c (h) 7z (z ) k (k k ) (j) m (m m ) (k) ( ) (l) ( ) ( m (n) m ) c c (o) c 7 (q ) q (p) 7 q (q) (y ) 9 y ( b ) (r) (b) ( p ) (s) p 8 p (b ) (t) b b. Write down the vlue of () 0 0 (c) 00 0 () 0 0 ½ 0 0 (h) k 0 (mn) 0 (j) (b ) 0 (k) (0 ) 0 (l) (y z ) 0 7. Rewrite the following with positive indices. () (c) (h) p 7 (j) y 0 (k) b (l) 0 q (n) w (o) 0 (p) 8 c (q) t (r) y Pegsys 0

13 8. Rewrite the following with negtive indices. () 9 (c) 7 0 (h) p (j) 0 y (k) q (l) 8 c 9. Simplify the following epressions. () m m 7 (c) p 8 p (y ) (c ) (q ) (h) (w ) b b (j) 9 (k) k k (l) 8d d ( ) (n) p (p p 8 ) (o) ( ) (p) ½ m (m 0m v v ) (q) v 7 h h (r) h c 9c (s) c (t) 8 0. Find the vlue of () 8 (c) (h) 8 (j) (k) (l) (n) (o) 9 (p) 7 (q) (r) 000 (s) (t) 8 (u) 8 (v) ( 8) (w) () 00 (y) ( ) (z) ( ) 8 Pegsys 0

14 . Simplify the following epressions, giving your nswers with positive indices. () ( ) ( p ) (c) ( ( ) 8 ( y ) 9 q ) 0 ( k ) (g ) (h) ( m ) (c 9 ) (j) ( h ) (k) ( z ) (l) ( b ) (n) y y (o) d d (p) s s (q) (r) (u) (v) (s) (t) (w) 8 () 9 7. Write the following in surd form. () y (c) y b c (h) c (j) z (k) m (l) k 7 p (n) (o) w (p) d. Write the following in inde form. () (c) y z c p (h) m (j) z (k) (l) b (n) m (o) y (p) c Pegsys 0

15 . Simplify ech of the following by... chnging root signs to frctionl powers; (ii) moving 's onto the numertors; (iii) epnding brckets where necessry. () ( ) ( ) (c) ( ) ( ) ( ) ( ) (h) (j) (k) (l) ( ) INDICES EXAM QUESTIONS. () Simplify 7 b b If = nd b =, find the vlue of the epression in prt ().. Given tht y =, find y when = 8.. Simplify ( ) m. () Simplify m Evlute p 8 p. Epress p in its simplest form.. Simplify, writing your nswer with positive inde: 7. Simplify the frction, giving your nswer in positive inde form: 9 8. Simplify. 9. () Remove the brckets nd simplify: p ( p ). Hence, or otherwise, find the vlue of p ( p ) when p =. Pegsys 0

16 . CALCULATIONS USING SCIENTIFIC NOTATION. Rewrite these sentences with the numbers written out in full () (c) The speed of light is 0 8 metres per second. The dimeter of the erth is 8 0 kilometres. A Building Society hs. 0 9 in its funds. The rdius of the orbit of n electron is 0 8 mm. A spce probe reched speed of 9 0 m.p.h. The erth weighs 0 tonnes. A film of oil is mm thick.. Use your clcultor to nswer the following, giving your nswers in Stndrd Form. () ( 0 ) ( 0 ) ( 0 7 ) ( 0 8 ) (c) ( 8 0 ) ( 0 ) (9 0 ) ( 0 ) ( 0 ) ( 9 0 ) ( 0 ) ( 0 7 ) ( 0 ) ( 8 0 ) (h) ( ) ( 0 9 ) (8 7 0 ) (7 0 0 ) (j) ( 0 0 ) ( ) (k) ( 0 ) ( 0 8 ) (l) ( 0 ) ( 0 ) ( 8 0 ) ( 0 7 ) (n) ( 0 0 ) ( 0 8 ) (o) ( 0 8 ) ( ) (p) (8 0 ) ( 0 7 ) (q) ( 0 ) ( 0 ) (r) (8 8 0 ) ( 0 ) (s) (9 7 0 ) ( 0 0 ) (t) ( 8 0 ) ( 0 ) 8 0 (u) (v) (w) 0 0 Pegsys 0

17 . Answer ech of the following questions leving your nswers in stndrd form. () Light trvels t 8 0 miles per second. How fr will it trvel in n hour? The rdius of the erth is 0 metres. Wht is its circumference (in km)? (c) If hert bets 70 times minute, how mny times will it bet in lifetime of 80 yers?[tke ll yers to hve dys] 00 grms of wter contins 000 drops. How mny drops would there be in tnk contining tonne of wter? In grm of crbon there re there in kg of pure crbon? 0 toms. How mny crbon toms re. Answer ech of the following questions leving your nswers in stndrd form () (c) The weight of droplet of wter is grms. Clculte the weight of droplets. A spce probe cn trvel t speed of 0 miles per dy. Wht distnce will it trvel in week? A biscuit fctory produces 7 0 teckes every dy. How mny teckes were produced in the month of Februry 008? The speed of light is pproimtely 99 million metres per second. How fr cn light trvel in minute? Lst yer 8 0 copies of DVD were sold on its first dy of relese. If the cost of one DVD ws, how much money ws collected on tht first dy? In relity TV show there were clls mde to vote for the contestnts. If ech cll cost p clculte how much the clls cost in totl. Give your nswer in pounds. There re of April? 8 0 seconds in one dy. How mny seconds re there in the month (h) Orgnisers of the London Mrthon provide enough wter to give ech runner 7 litres during the rce. If runners tke prt, how mny litres of wter re provided? The echnge rte in Turkey is = Turkish Lir. Stephen is going on n Adritic cruise nd chnges 700 into Turkish Lir. How much will he get in Lir? Pegsys 0

18 SCIENTIFIC NOTATION EXAM QUESTIONS. The distnce between the erth nd mrs is on verge pproimtely 0 8 miles. A spceship hs been designed to trvel between the erth nd mrs t n verge speed of miles per hour. How mny dys will the spceship tke to rech mrs? Give your nswer correct to the nerest dy.. Urnium is rdioctive isotope which hs hlf-life of 9 0 yers. This mens tht only hlf of the originl mss will be rdioctive fter 9 0 yers. How long will it tke for the rdioctivity of piece of Urnium to reduce to one eighth of its originl level? Give your nswer in scientific nottion.. The popultion of Scotlnd in June 00 ws.0 0 people. The popultion of Chin in June 00ws pproimtely 0 times lrger thn tht of Scotlnd. Clculte, correct to three significnt figures, the popultion of Chin in 00, epressing your nswer in stndrd form.. The Blckbird is two-seter high speed jet. In December 9 it broke world speed record by trvelling t 0 0 metres per second. Clculte, correct to three significnt figures, the distnce trvelled if the jet were to mintin this speed for one hour. Epress your nswer in scientific nottion. Pegsys 0

19 . SIGNIFICANT FIGURES. Round to significnt figure : (). (c) (h) 8. 7 (j) 98 (k) 800 (l) (n) (o) 98 (p) (q) 0 (r) 9 (s) 0 8 (t) 0. Round to significnt figures : () (c) (h) 8 7 (j) 8 7 (k) 97 (l) (n) 0 00 (o) (p) 8 (q) (r) 9 (s) 9 0 (t) 0 7. Round to significnt figures : () 9 (c) (h) (j) 8 (k) (l) 7 8 (n) (o) 7 (p) 0 0 (q) 79 (r) 08 (s) 007 (t) Round 88 correct to () sig. figs sig. figs (c) sig. figs sig. fig. Round correct to () sig. figs sig. figs (c) sig. figs sig. fig Pegsys 0

20 . Clculte nd give your nswer correct to significnt figures () (c) (h) (0 08 ) (j) (0 08 ) (k) ( 0) (l) 7 7. Clculte nd give your nswer correct to significnt figures () (c) ( 0 ) (h) ( 9) (j) ( 9 8) (k) 0 9 (l) 0 8. The speed of light is pproimtely 8 0 times fster thn the speed of sound in ir. If the speed of sound in ir is 7 metres per second, clculte the speed of light. Give your nswer in scientific nottion correct to significnt figures. Pegsys 0

21 . ALGEBRAIC EXPRESSIONS with BRACKETS. Multiply out the brckets: () ( ) (y 7) (c) 8 ( ) ( t) ( 9) y ( y) b (b ) (h) p ( p) (b c) (j) ( y) (k) p (q r) (l) ( ). Epnd the brckets: () ( ) 7 (y ) (c) ( ) 9 (c 7) ( ) ( 8) 0y ( y) (h) t (t ) ( 9) (j) y (7 y) (k) b (b 8) (l) ( ). Epnd nd simplify: () ( ) ( ) (c) 8(b ) 9 (h ) 7 ( ) (c ) 8 (t ) 0t (h) p(p q) pq 7( c) 0 (j) ( ) (k) 7 ( ) (l) ( 7) (y ) (n) 9b (b ) (o) 8 ( 7) (p) ( ) (q) c ( c) (r) 7 ( ). Multiply out the brckets: () ( )( ) (y )(y ) (c) ( )( ) (b )(b ) ( 9)( ) (s )(s 8) (y 7)(y ) (h) (b )(b ) (c )(c 7) (j) ( 8)( ) (k) (y )(y ) (l) ( 9)( 8) (p )(p 7) (n) (c )(c ) (o) (t 7)(t 9) (p) ( )( 9) (q) (y )(y ) (r) ( )( 9) Pegsys 0

22 . Multiply out the brckets: () ( )( ) (c )(c ) (c) (y )(y 7) (b )(b 8) ( )( ) (s 8)(s ) (y )(y 9) (h) ( )( ) (t )(t ) (j) ( )( ) (k) (b )(b ) (l) (c 0)(c ) ( )( 9) (n) (y 8)(y 7) (o) ( )( ) (p) (s )(s 7) (q) (d )(d ) (r) (b 0)(b ). Multiply out the brckets: () ( )( ) ( )( 7) (c) (t )(t ) (y 8)(y ) (c )(c 7) ( )( ) (b )(b 9) (h) (p 0)(p ) (y 8)(y 7) (j) (z )(z ) (k) ( )( ) (l) ( )( ) (c )(c ) (n) (p 7)(p ) (o) (b 0)(b ) 7. Multiply out the brckets: () ( ) (w ) (c) ( ) (c 8) (y ) ( ) (b ) (h) (s 7) (b 9) (j) ( 0) (k) (c ) (l) (y ) ( ) (n) (y ) (o) ( ) (p) (b ) 8. Multiply out the brckets: () ( b)(c d) ( )( y) (c) ( )(b ) (p q)(r s) ( )(7 b) (c )(d 8) 9. Multiply out the brckets: () ( ) ( ) (c) ( 8) ( ) ( 8 ) ( 7) Pegsys 0

23 0. Multiply out the brckets nd simplify: () ( )( ) ( )( ) (c) ( )( ) ( )( ) ( 8)( ) ( )( 7 ) ( )( 7) (h) ( 0)( 9) ( 9)( 7) (j) ( 7)( 9 ) (k) ( )( ) (l) ( )( ) ( )( 8 ) (n) ( )( 7) (o) ( 0)( ) (p) ( 9)( ) (q) ( )( ) (r) ( 7)( 8 ). Multiply out the brckets nd simplify: () ( )( ) ( 7)( ) (c) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) (h) ( )( 7) ( 9)( ) (j) ( )( 8 ) (k) ( 8)( 7) (l) ( )( 9 ) ( )( ) (n) ( 0)( 8) (o) ( )( 7 ) (p) ( )( 7 ). Multiply out the brckets nd simplify: () ( )( 9) ( )( ) (c) ( )( 7) ( 7)( 9 ) ( )( 8) ( )(7 ) ( )( ) (h) ( )( ) ( )( 7) (j) ( )( ) Pegsys 0

24 . Epnd nd simplify ech of the following epressions: () ( ) ( ) ( )( ) ( ) (c) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( )( ) (h) ( ) () ( ) ( ) ( )( ) (j) ( ) ( ) (k) ( ) ( ) (l) ( ) ( ) Pegsys 0

25 . FACTORISING n ALGEBRAIC EXPRESSION. Fctorise by first finding common fctor: () y c d (c) s t y 9 9b 8b 8c p q (h) 7g 7h m n (j) 9e 9f (k) j k (l) v w. Fctorise by finding the common fctor: () d 9 (c) s 9 b 8 y 0 (h) 0 c (j) 8m (k) 0 y. Fctorise by finding the common fctor: () y 8 (c) 8 0c 9s b 0 (h) m 0 (j) 8 y (k) b 0 (l) 8d 0. Fctorise by finding the common fctor: () b 0 y (c) 8m n 0c d 9 8s t y (h) 7b c 0d (j) 9b y (k) 8 y 8b. Fctorise by finding the common fctor () y y (c) pqr pst y bc pq p y y b (h) b bc n n (j) y y (k) bc bd (l) fgh efg Pegsys 0

26 . Fctorise by finding the highest common fctor: () y 9y (c) b pq pq y 9z b b 7h (h) bc 0bd s 9s (j) yz (k) 0b c bcd (l) πr πrh 7. Fctorise by finding the highest common fctor: () p q r b c (c) e f g p pq p b bc 9bd ½ h ½ bh ½ ch 8y (h) c d 0 p 0pq 0ps 8. Fctorise the following epressions, which contin difference of squres: () b y (c) p q s t p 9 (h) c b (j) y (k) m (l) 9 d (n) q (o) 9 w (p) 9. Fctorise the following epressions, which contin difference of squres: () b y (c) p q c d 8 g w y (h) g 8h 9 y (j) 9c d (k) p 9q (l) b 00c (n) d (o) 9k (p) Fctorise the following epressions which contin common fctor nd difference of two squres: () b p (c) d y 0 b 00 q 7 (h) 8 b b (j) y (k) bc b (l) 8p 0q 88 (n) k (o) 0s (p) ½ y 0 Pegsys 0

27 . Fctorise the following qudrtic epressions: () (c) y y b 8b 9 (h) w 0w 9 d 7d 0 (j) 0 (k) p 9p 0 (l) c 0c s s (n) 8 (o) y 0y. Fctorise the following qudrtic epressions: () (c) c 9c 8 y y b b c 0c (h) 7 y n (j) p p (k) (l) b b (n) q q 0 (o) 7y. Fctorise the following qudrtic epressions: () b b 0 7 (c) y y 0 q q d d (h) c 9c p p (j) y 7y 8 (k) (l) b b (n) s s (o) d d. Fctorise the following qudrtic epressions: () 7 (c) c 8c p p 9 y y d d q 9q (h) b 8b (j) (k) 0 7 (l) 9c c y y (n) b b (o) 8 Pegsys 0

28 . Fctorise the following qudrtic epressions: () 7 (c) p 7p b 7b 7 y y 7c 9c (h) m 9m 0 (j) 8y y (k) p 7p (l) (n) c c (o) b b. Fctorise the following qudrtic epressions: () (c) p p c 7c y y w 0w 8 m m (h) q q b 7b 0 (j) t t (k) z z (l) d d 7s 7s (n) (o) v v (p) v 0v 7 (q) l l (r) m m 7 (s) n 9v 8 (t) b 0b (u) 9c 8c 8 (v) q q (w) () 8b b (y) m 8m (z) n n 8 7. Fully fctorise these epressions: () p p 0 (c) 9 0 y y c 7c (h) b 8b 9q q 8 (j) 0s s (k) 8m 0m (l) 8 t t (n) 90d 0d 80 (o) 00 Pegsys 0

29 . COMPLETING THE SQUARE. Write the following in the form nd write down the minimum vlue of ech one. () (c) (h). Write the following in the form nd write down the minimum vlue of ech one. () (c) (h) (j) (k) (l). Write the following in the form nd write down the mimum vlue of ech one. () (c) Pegsys 0

30 . REDUCING n ALGEBRAIC FRACTION to SIMPLEST FORM. Epress these frctions in their simplest form: () 8 (c) b 8 (h) y c c (j) 8 p (k) p (l) b bc (n) 0 v t (o) y 9vt (p) 0b b 0 p q (q) pq 8 y (r) y (s) mn mn (t) 8def 0e f (u) b c c k m (v) 8km efg (w) 0e fg y (). Simplify by first finding the common fctor: () b y (c) b y y y y y b b 9b b b 0b (h) p 0q s b c (j) 9 9y (k) st rs st (l) c 0c bc p 8 p 8 p (n) 8c c d d (o) 8n n n (p) y 0 y Pegsys 0

31 Pegsys 0. Simplify the following by first fctorising the numertor nd/or denomintor: () b b 9 8 (c) y y 9 c c p p (h) 9 9 q q b b (j) y y (k) 8 m m (l) 8 8 d d (n) p p p (o) (p) (q) 9 9 b p b (r) c c c (s) (t) 8 y y y y (u) p p p p (v) c c c c (w) 8 9 () (y) b b b b

32 . APPLYING the FOUR OPERATIONS to ALGEBRAIC FRACTIONS. Epress ech sum s frction in its simplest form: () (c) 0 8 (h) 9 (j) (k) (l) 8 7 (n) (o) (p) Epress ech difference s frction in its simplest form: () (c) (h) 7 7 (j) (k) (l) (n) (o) (p) Epress ech product s frction in its simplest form: () (c) (h) 7 8 (j) (k) (l) (n) (o) (p) Pegsys 0

33 . Epress s single frction: () (c) (h) (j) (k) (l) (n) (o) (p) Epress ech sum s frction in its simplest form: () (q) b b p p (c) 0 8 y y (h) 9 m m 8 (j) (k) (l) y y p p b y (n) (o) (p) m n p q c d y 9 7 (r) (s) (t) b b m n p q (u) (v) (w) b b () 8 m m. Epress ech difference s frction in its simplest form: () b b p p (c) 0 8 8y y 7 (h) 9 m m 8 (j) (k) (l) 8 y y p p b y Pegsys 0

34 . (continued) (q) (n) (o) (p) m n p q c d y 7 (r) (s) (t) b b m n p q (u) (v) 7 (w) b b () 7 p p 7. Epress ech product s frction in its simplest form () y y b p q (c) 7 8 c c 0 (h) y p p m (j) (k) (l) m m b c m 7 y (n) 9 y 7 (o) p p (p) t s s t pq 7b c m (q) (r) (s) pq c mn n yz z b cd (t) (u) (v) 9 y c bc 7 cd 0y y st (w) () y 8s t (y) pq p 8. Epress s single frction: () y b (c) p p c c 0 t t Pegsys 0

35 8. (continued) 9 (h) k m y y bc c (j) (k) y 0y q 9q (l) z z p 0 p 8b 9b (n) c c 0m 8mn 0 (o) n 9 y y 9. Simplify the following: () (c) d d b b u v u v (h) 7 (j) (k) (l) ALGEBRAIC FRACTIONS EXAM QUESTIONS. Write s single frction in its simplest form :, 0.. Simplify this frction 9. Simplify fully the frction e e e. Simplify. Write s single frction in its simplest form:. Epress s single frction in its simplest form:. Pegsys 0

36 . DETERMINING the GRADIENT of STRAIGHT LINE given TWO POINTS. () Clculte the grdient of ech line in the digrm opposite. (ii) (iii) (iv) (v) Copy nd complete ech sttement below: The grdient of ny horizontl line is. The grdient of ny verticl line is. A line sloping upwrds from left to right hs grdient. A line sloping upwrds from right to left hs grdient.. Find the grdients of the lines shown in ech of the digrms below: b c g h i j e k d f l Pegsys 0

37 . Find the grdients of the lines below: y b c d y O O e f. Clculte the grdient of the line joining ech pir of points below: () (, ) nd (, ) (, ) nd (, ) (c) (, 0) nd (, ) (, ) nd (8, ) (, 9) nd (, ) (7, ) nd (, ) (, ) nd (, ) (h) (, ) nd (, ) (, ) nd (, ) (j) (, ) nd (, ) (k) (, ) nd (, ) (l) (, ) nd (0, ). Clculte the grdient of the line joining ech pir of points below: () A(, ) nd B(8, 8) C(, ) nd D(, ) (c) E(, 9) nd F(8, ) G(0, ) nd H(, ) I(, ) nd J(7, 9) K(, 0) nd L(, ) M(, ) nd N(, ) (h) P(, ) nd Q(, 0) R(, ) nd S(8, ) (j) T(, ) nd U(7, ) (k) V(, ) nd W(, ) (l) X(, 7) nd Y(, ) J(, 8) nd K(, ) (n) S(, ) nd T(, 8) (o) D(, ) nd E(0, ) (p) F(, 9) nd G(, ) Pegsys 0

38 . Prove tht the following sets of points re colliner: () A(,), B(, ) nd C(, ) P(, ), Q(, ) nd R(7, 0) (c) E(, ), F(, ) nd G(7, ) K(, ), L(, ) nd M(9½, 0) 7. Given tht ech set of points re colliner, find the vlue of k in ech cse: () P(, ), Q(, ) nd R(8, k) A(, ), B(, k) nd C(, ) (c) E(, ), F(k, ) nd G(8, 7) S(k, ), T(9, ) nd U(, ) 8. The points E nd F hve coordintes (, ) nd (, ) respectively. Given tht the grdient of the line EF is, find the vlue of. 9. If the points (, ), (, 0) nd (, k) re colliner, find k. 0. Given tht the points (, ), (, ) nd (, ) re colliner, find the vlue of.. The line which psses through (, ) nd (, ) is prllel to the line through (, 7) nd (k, ). Find the vlue of k.. The line which psses through (, ) nd (, 9) is prllel to the line through (, k) nd (, ). Find the vlue of k. Pegsys 0

39 . WORKING with the LENGTH of n ARC of CIRCLE. Clculte the length of the rc in ech digrm below, giving your nswer correct to d.p. A () D (c) E O 90 o mm 0 o o F 8cm B C O O m. Clculte the perimeter of ech sector in Question. Giving your nswers correct to d.p.. Find the length of the minor rc AB in ech of the following circles, giving your nswers correct to d.p. () A (c) O 90 o O O cm 9 cm 90 o cm 0 o B A B A B O 7 cm 0 o A 7cm B (h) h. A A 0 o O cm B O 80 o cm A 8 cm O O 0 o B 7 o 0 cm B A B. Clculte the length of the mjor rc in the circles shown in Question, giving your nswers correct to d.p. Pegsys 0

40 . WORKING with the AREA of SECTOR of CIRCLE. Clculte the re of the sector in ech digrm below, giving your nswer correct to significnt figures. A E () (c) D O 90 o mm 0 o o F 8cm B C O O m. Clculte the re of minor sector OAB in the circles shown below, giving your nswers correct to significnt figures. () (c) A O 90 o O O cm 9 cm 90 o cm 0 o B A B A B (h) A O 7 cm 0 o A 7cm B A 0 o O cm B O 80 o cm A 8 cm O O 0 o B 7 o 0 cm B A B. Clculte the re of the mjor sector for the circles in Question, giving your nswers correct to significnt figures.. The length of minor rc CD is 7 cm. Clculte the re of the circle. O 0 o C D Pegsys 0

41 . WORKING with the ARCS nd SECTORS of CIRCLE EXAM QUESTIONS Give your nswers correct to significnt figures unless otherwise stted.. Clculte the re of the sector shown in the digrm, given tht it hs rdius 8cm. O o o. A tble is in the shpe of sector of circle with rdius m. m The ngle t the centre is 0 o s shown in the digrm. 0 O o Clculte the perimeter of the tble. o. The door into resturnt kitchen swings bckwrds nd forwrds through 0 o. 0 o 90cm The width of the door is 90cm. Clculte the re swept out by the door s it swings bck nd forth. Pegsys 0

42 . The YUMMY ICE CREAM Co uses this logo. It is mde up from n isosceles tringle nd sector of circle s shown in the digrm. The equl sides of the tringle re cm The rdius of the sector is cm. 00 o Clculte the perimeter of the logo. cm. A sensor on security system covers horizontl re in the shpe of sector of circle of rdius m. 0º The sensor detects movement in n re with n ngle of 0º. Clculte the re covered by the sensor.. A biscuit is in the shpe of sector of circle with tringulr prt removed s shown in the digrm. The rdius of the circle, PQ, is 7 cm nd PS = cm. R Q Angle QPR = 80 o. Clculte the re of the biscuit. P S Pegsys 0

43 7. Two congruent circles overlp to form the symmetricl shpe shown below. Ech circle hs dimeter of cm nd hve centres t B nd D. A D B C Clculte the re of the shpe. O 8. A sector of circle with rdius cm is shown opposite. o Angle AOB o = If the ect re of the sector is π squre centimetres, clculte the size of the ngle mrked. A cm B 9. A hnd fn is mde of wooden slts with mteril on the outer edge. 9cm cm 0 () Clculte the re of mteril needed for the hnd fn. Clculte the perimeter of the shded re in the digrm bove. Pegsys 0

44 0. O 7 o The re of the shded sector is ˑ0 cm. Clculte the re of the circle. P Q. The re sector OPQ is 78. cm. Clculte the size of ngle o. of the circle. O 0 cm o P Q. A school bsebll field is in the shpe of sector of circle s shown. Given tht O is the centre of the circle, clculte: () the perimeter of the plying field; O 80 o the re of the plying field. 80m. In the digrm opposite, O is the centre of two concentric circles with rdii cm nd 0cm s shown. Angle o AOB = 0. A Clculte: () The perimeter of the shded shpe. 0cm 0 o B The shded re. O cm Pegsys 0

45 . A Jpnese pper fn is fully opened when ngle o PQR= 0 s shown. () Using the dimensions shown in digrm, clculte digrm 9cm cm the pproimte re of pper mteril in the fn. P 0 o Q R digrm Decortive silk bnds re plced long the edges s shown in digrm, clculte the pproimte totl length of this silk edging strip.. A grndfther clock hs pendulum which trvels long n rc of circle, centre O. The rm length of the pendulum is 0cm. O The pendulum swings from position OA to OB. The length of the rc AB is cm. Clculte the size of ngle AOB to the nerest degree. A B. The shpe opposite is the sector of circle, centre P, rdius 0m. The re of the sector is squre metres. Q Find the length of the rc QR. 0m P 0m R Pegsys 0

46 7. A metl strip hs been moulded into n rc of circle of rdius centimetres which subtends n ngle of 8 o t the centre of the circle s shown in the digrm below. cm 0cm 8 o o Metl strip The sme strip of metl hs now been remoulded to form n rc of circle of rdius 0 centimetres s shown. Clculte the size of, the ngle now subtended by the metl strip. 8. Drw digrm to help you nswer these questions. () A circle, centre O, hs n rc PQ of length 0cm. If the dimeter of the circle is 80cm, clculte the size of ngle POQ correct to d.p. A circle, centre O, hs sector EOF with n re of 0cm. If the rdius of the circle is 8cm, clculte the size of ngle EOF correct to d.p. (c) An rc AB on circle, centre O, hs length of mm. If ngle AOB = 7 o, clculte the rdius of this circle. A sector of circle hs n re of cm. If the ngle t the centre is 0 o, clculte the dimeter of the circle correct to -deciml plces. Pegsys 0

47 WORKING with VOLUME of CYLINDER This topic is not mentioned in Ntionl rrngements but worth covering t this stge. Circulr bsed prism (cylinder) Find the volume of circulr-bsed prism for the vlues of r nd h given. r () r = cm h = cm r = 8 cm h = cm h (c) r = cm h = cm r = 0 cm h = 8 cm r = 0 cm h = 0 cm r = 7 cm h = 0 cm r = cm h = 0 cm (h) r = cm h = cm r = cm h = cm (j) r = 8.8 cm h = 0 cm. A milk dispenser is cylindricl in shpe with dimeter 0cm. () If litres of milk re poured into it, clculte the depth of the milk in the cylinder. 0cm cm The height of the cylinder is cm. How mny more litres of milk re needed to completely fill it? Pegsys 0

48 . 8cm Clculte the volume of cylinder with dimeter cm nd height 8cm. cm. This pint tin hs dimeter 0 cm nd height 0 cm s shown in the digrm. 0litres 0cm 0cm It is climed tht it cn hold 0 litres of pint. Is this clim correct? You must show ll working nd give reson for your nswer. Pegsys 0

49 . WORKING with the VOLUME of SOLID SPHERE, CONE, PYRAMID. Clculte the volume of ech sphere described below, rounding your nswer to deciml plce. r () (c) r = cm r = m r = 9mm r = cm. Find the volume of sphere for the following vlues of r nd d. (give your nswers correct to significnt figures) () r = 0cm d = 8cm r r = cm r = 80mm (c) d = m (h) d = cm r = 00mm r = m d = cm (j) d = 8cm. A sphere hs dimeter of 8cm. Clculte its volume giving your nswer correct to significnt figures.. Find the volume of cone for the following vlues of r nd h. (give your nswers correct to significnt figures) () r = cm h = cm r = 7cm h = cm (c) r = cm h = cm r = cm h = 7cm h r Pegsys 0

50 . Find the volume of cone for the following vlues of d nd h. (give your nswers correct to significnt figures) () d = cm h = 0cm d = cm h = 7cm (c) d = cm h = cm d = 8ˑ8cm h = 0cm. Clculte the volume of ech cone described below, rounding your nswers to deciml plce. h r () (c) r = cm nd h = cm r = 8mm nd h = mm r = cm nd h = cm r = m nd h = m 7. A cone hs bse dimeter of 8cm nd height of cm. Clculte the volume of this cone. 8. A cone hs bse dimeter of 0cm nd slnt height of cm. Clculte the volume of the cone. cm cm 9. A cone hs bse rdius of 9cm nd slnt height of cm. Clculte the volume of the cone. 0. A pyrmid hs squre bse of side cm nd verticl height of 7cm. Clculte the volume of the pyrmid correct to significnt figures.. A pyrmid hs rectngulr bse mesuring mm by mm nd verticl height of 0mm. Clculte the volume of the pyrmid. Pegsys 0

51 WORKING with the VOLUME of SOLID SPHERE, CONE, PYRAMID & CYLINDER EXAM QUESTIONS. The Stockholm Globe Aren is the lrgest hemisphericl building in the world. The rdius of the building is 0 m. Clculte the volume of the building in cubic metres, giving your nswer in scientific nottion correct to significnt figures.. A metl bottle stopper is mde up from cone topped with sphere. The sphere hs dimeter cm. The cone hs rdius 0 9cm. Rdius = 0 9cm The overll length of the stopper is cm. Clculte the volume of metl required to mke the stopper. Give your nswer correct to significnt figures. cm. The volume of this sphere is cm. Clculte the dimeter, d cm. dcm. on Clcultor! Clculte the volume of this sphere which hs rdius m. [Tke π = ] m Pegsys 0

52 . Sherbet in sweet shop is stored in cylindricl continer like the one shown in digrm. 0cm cm Digrm The volume of the cylinder, correct to the nerest 000cm, is cm. The sherbet is sold in conicl continers with dimeter cm s shown in digrm. cm 0 of these cones cn be filled from the contents of the cylinder. d cm Clculte the depth, d cm, of sherbet cone. Digrm. on Clcultor! The digrm shows cone with rdius 0 centimetres nd height 0 centimetres. 0 cm Tking π =, clculte the volume of the cone. 0 cm 7. A children s wobbly toy is mde from cone, cm high, on top of hemisphericl bse of dimeter 0 cm. cm The toy hs to be filled with liquid fom. Clculte the volume of fom which will be required. 0 cm Pegsys 0

53 8. The lmp cover in street lmp is in the shpe of cone with the bottom cut off. The height of the cone is 0cm nd its rdius is cm. The height of the lmp is 0cm nd the bse of the lmp hs rdius of 8cm Clculte the volume of the lmp cover. [Answer to significnt figures.] 9. A glss cndle holder is in the shpe of cuboid with cone removed. The cuboid mesures cm by cm by cm. The cone hs dimeter of cm nd height of cm. cm Clculte the volume of glss in the cndle holder. cm cm 0. For the Christms mrket confectioner hs creted chocolte Snt. It consists of solid hemisphere topped by solid cone. Both hve dimeter cm nd the height of the cone is cm s shown in the digrm. cm cm Clculte the volume of chocolte required to mke one chocolte Snt, giving your nswer correct to significnt figures. Pegsys 0

54 . The dimeter of n ordinry snooker bll is cm. Clculte the volume of snooker bll giving your nswer correct to significnt figures.. A dessert is in the shpe of truncted cone [ cone with slice tken from the top]. The rdius of the bse is cm nd is cm t the top. The other dimensions re shown in the digrm. 7cm cm Clculte the volume of the dessert.. A young child ws given slb of moulding cly. It ws cuboid nd mesured cm by 8cm by cm. () Clculte the volume of the cuboid rounding your nswer to significnt figures. The cly ws mde into identicl spheres. Using your nswer from prt (), clculte the rdius of one of the spheres. Pegsys 0

55 cm. An ice crem is shped like the one in the digrm. The overll height of is 7 cm. cm The height of the cylinder is cm. The dimeter of the cone nd cylinder is cm. 7cm Clculte the volume of ice crem.. A compny tht produces bins uses the design of cylindricl bse with hemisphericl lid. If the totl height of the bin is 0cm nd the rdius of the bin is cm, clculte the 0cm totl volume of the bin in litres correct to significnt figures. (Volume of cylinder = πr h; Volume of sphere = / πr ) cm. A Christms buble is mde from sphere of perspe with coloured cylinder in the middle. The volume round the cylinder is filled with thick liquid. The sphere hs dimeter of 8 cm. The cylinder hs rdius of cm with height of cm. Clculte the volume of liquid needed to fill the sphere, giving your nswer correct to significnt figures. Pegsys 0

56 Ntionl Epressions nd Formule ANSWERS. WORKING WITH SURDS. () (c) (h) 0 (j) (k) (l) (n) 7 (o) 0 (p) (q) 7 (r) (s) (t) 0 (u) (v) (w) 7 () 7. () 0 (c) (h) 0 (j) 9 (k) 7 (l) 8. () 8 7 (c) 9 (h) 7 0 (j) (k) (l). () (c) 8 (h) 7 0 (j) (k) 0 (l) 7 8 (n) (o) (p) 8 (q) (r) (s) 7 (t) 8 (u). () (c) c k (h) (j) (k) (l) y (n) (o) 0 (p) 8 (q) b (r) 0 (s) pq (t) k (u) (v) (w) () (y) (z). () 0 (c) 0 8 (h) 7. () (h) (c) (j) (k) (l) 0 (n) (o) (p) Pegsys 0

57 8. () (c) (h) 8 (j) 8 (k) (l) 0 (n) (o) (p) 9. () (c) 0 (h) (j) (k) (l) 0 (n) 7 0 (o) (p) 8 7 (q) 8 (r) 0. () (c) (h) 0 (j) (k) (n) 7 (l). () 0 0 (h) (c) 7. () 0 (c) (h) 0 (j) (k) (l) (n) (o) (p) (q) (r) (s) (l) 0. () 0 (c) 0 (h) 0 Pegsys 0

58 (j) (k) (l). () ( ) ( ) (c) ( ) ( ) ( ) (h) ( ) ( 7 ) (j) ( ) (k) 7 (l) ( ) (n) ( 0 ) (o) ( ) (p) (9 79 ) SURDS PROBLEMS. () (c). () 0 (c). () 8 (c). () cm cm. () () 8. Proof 9. Proof. INDICES. () (c) (h) 8 (j) c (k) (l) y 0 b 0 (n) p 0 (o) d (p) q 0 (q) t 0 (r) f 7 (s) k (t) z 00 (u) 80 (v) y 0 (w) 90 () b. () (c) (h) (j) (k) y 0 (l) b p (n) (o) q (p) d (q) (r) (s) m (t) (u) 8 d (v) 90 y (w) 99 t () 0 w Pegsys 0

59 . () 8 8 (c) (h) 8 (j) y 0 (k) (l) m b 8 (n) p (o) k 00 (p). () b (c) 8 y b 7 y 7 w z (h) s t p q (j) 8 y (k) 0 b (l) (n) c 0 (o) 7 b (p) m k. () (c) p b y 7 80q 0 8c 7 (h) 8z k k 7 (j) m 7 m 8 (k) 7 (l) (n) m (o) 0c (p) q (q) y (r) 0 8 (s) b p (t) 8 b. () (c) (h) (j) (k) (l) 7. () (c) (h) 7 p (j) 0 y (k) b (l) 0 q (n) w (o) (p) 8 0c (q) t (r) y 8. () 9 (c) 7 0 (h) p (j) 0 y (k) q (l) 8 c 9. () m (c) p 8 y c q (h) w 8 0b (j) 7 (k) k (l) d - (n) p p (o) 9 (p) m m (q) 0 v (r) h (s) c (t) 0 Pegsys 0

60 0. () (c) 9 0 (h) 7 (j) 8 (k) (l) (n) (o) (p) 9 (q) (r) 00 (s) (t) (u) (v) (w) () 000 (y) (z). () y p (c) q k m g (h) 8 c (j) h (k) z (l) b (n) y (o) d (p) s (q) (r) (s) 0 (t) (u) (v) (w) (). () (c) y b c (h) c (j) z (k) m (l) k p (n) (o) w (p) d 7. () (c) y z c p (h) m (j) z (k) (l) b (n) m (o) y (p) c 9. () (c) (h) (j) Pegsys 0 (k) (l)

61 INDICES EXAM QUESTIONS. () 7 b... () m 8. p () p p 0. CALCULATIONS USING SCIENTIFIC NOTATION. () The speed of light is metres per second. (c) The dimeter of the erth is 80 kilometres. A Building Society hs in its funds. The rdius of the orbit of n electron is mm. A spce probe reched speed of m.p.h. The erth weighs tonnes. A film of oil is mm thick.. () (c) (h) 0 0 (j) (k) 0 (l) (n) 9 0 (o) 0 7 (p) 0 (q) (r) 0 (s) (t) (u) 0 (v) 9 0 (w) 9 0. () (c) () grms. 0 7 (c) (h) SCIENTIFIC NOTATION EXAM QUESTIONS. dys. 0 0 yers Pegsys 0

62 . SIGNIFICANT FIGURES. () 0 (c) (h) (j) 000 (k) 8000 (l) 000 (n) 00 (o) (p) 0000 (q) (r) 90 (s) 0 9 (t) 00. () (c) (h) (j) 9 (k) 00 (l) (n) 0 00 (o) (p) 000 (q) (r) 000 (s) 9 (t) 0 7. () 9 (c) (h) (j) 00 (k) (l) 8 (n) 0 (o) 70 (p) 0 0 (q) 8 (r) 090 (s) 0 (t) () (c) () (c) () 0 0 (c) (h) (j) 7 (k) 00 (l) 7. () 78 (c) (h) 0 9 (j) (k) 07 (l) Pegsys 0

63 . ALGEBRAIC EXPRESSIONS with BRACKETS. () y (c) t ² 9 y y² b² b (h) p p² b c (j) ² y (k) pq pr (l) ². () 8 0 y 8 (c) c ² ² 0 0y 0y² (h) t² 8t ² 7 (j) y 0y² (k) b² b (l) ² 0. () 7 (c) 8b 7 8h 9 c t (h) p² pq c (j) (k) 9 (l) 9 y (n) b (o) (p) 0 (q) 7c (r) 0. () y 7 y 0 (c) 0 b 7b s s y y 8 (h) b b 9 c c (j) (k) y y 8 (l) 7 7 p 9 p 8 (n) c c 0 (o) t t (p) (q) y 7y 0 (r) 0 9. () c c 8 (c) y 0y b b s s 0 y y 8 (h) 8 t 9t 8 (j) 0 (k) b 8b (l) c c 0 7 (n) y y (o) (p) s s 8 (q) d d (r) b b 0. () (c) t t 0 y y c c Pegsys 0

64 b 7b8 (h) p 8p 0 y y (j) z z (k) (l) 0 c 9 (n) p p 7 (o) b b 0 7. () ² 9 w w (c) 0 c² c y 8y ² b² b (h) s² s 9 b 8b 8 (j) 0 00 (k) c c (l) y y 9 (n) y² 0y (o) 9² (p) b² 0b 8. () c bc d bd y y (c) b b 0 pr qr ps qs 7 7 b b cd d 8c 8 9. () 9 (c) () (c) (h) 9 90 (j) 7 (k) (l) 7 7 (n) (o) 0 (p) 9 (q) 9 (r). () (c) 8 (h) (j) 0 (k) 7 (l) (n) 80 (o) 0 (p) 8 Pegsys 0

65 . () 9 8 (c) (h) (j) 9. () 7 8 (c) (h) 8 (j) 0 (k) 9 (l). FACTORISING n ALGEBRAIC EXPRESSION. () ( y) (c d) (c) (s t) ( y) 9( b) 8(b c) (p q) (h) 7(g h) (m n) (j) 9(e f) (k) (j k) (l) (v w). () ( ) (d ) (c) (s ) ( ) ( ) (b ) (y ) (h) ( c) ( ) (j) (m ) (k) ( ) 7(y ). () ( ) (y ) (c) 8( ) (c ) (s ) (b 7) ( ) (h) (m ) ( ) (j) ( y) (k) (b ) (l) (d ). () ( b) ( y) (c) (m n) (c d) ( ) (s t) ( y) (h) 7( b) (c d) (j) (b y) (k) ( y) ( b). () ( y) (y ) (c) p(qr st) (y bc) p(q ) y(y ) ( b) (h) b( c) n(n ) (j) y ( y) (k) b(c d) (l) fg(h e). () ( ) y( y) (c) 8( b) pq(q ) (y z) b(b ) ( 9h) (h) b(c d) s (s ) (j) (7 yz) (k) bc(b d) (l) πr(r h) Pegsys 0

66 7. () (p q r) ( b c) (c) (e f g) p(p q ) b( c d) ½ h( b c) ( 8y ) (h) (c d ) p(p q s) 8. () ( b)( b) ( y)( y) (c) (p q)(p q) (s t)(s t) ( )( ) ( )( ) (p 9)(p 9) (h) (c )(c ) (b )(b ) (j) (y )(y ) (k) (m )(m ) (l) ( )( ) ( d)( d) (n) ( q)( q) (o) (7 w)(7 w) (p) ( 8)( 8) 9. () ( b)( b) ( y)( y) (c) (p 8q)(p 8q) (c d)(c d) (9 g)(9 g) (w y)(w y) ( )( ) (h) (g 9h)(g 9h) (7 y)(7 y) (j) (c d)(c d) (k) (p q)(p q) (l) (b 0c)(b 0c) ( )( ) (n) (d )(d ) (o) ( 7k)( 7k) (p) ( 0 )( 0 ) 0. () ( b)( b) (p )(p ) (c) ( )( ) (d )(d ) (y )(y ) (b )(b ) (q )(q ) (h) 8( b)( b) (b 8)(b 8) (j) (y )(y ) (k) b(c )(c ) (l) (p q)(p q) ( )( ) (n) (k )(k ) (o) (s (s ) (p) ½( y 0)(y 0). () ( )( ) ( )( ) (c) (y )(y ) ( 7)( ) ( )( ) (b )(b ) ( 7)( ) (h) (w )( 9) (d )(d ) (j) ( 7)( ) (k) (p )(p ) (l) (c )(c ) (s )(s ) (n) ( 7)( ) (o) (y )(y ). () ( )( ) ( )( 8) (c) ( )( ) (y )(y ) (b )(b ) ( )( ) (c )(c 8) (h) ( )( ) (y )(y 8) (j) (p 8)(p ) (k) ( 9)( ) (l) ( )( ) (b )(b ) (n) (q 0)(q ) (o) ( )( ) Pegsys 0

67 . () (b )(b ) ( 7)( ) (c) (y )(y ) ( )( ) (q )(q ) ( )( 0) (d 7)(d ) (h) (c )(c ) (p )(p 8) (j) (y )(y 8) (k) ( )( ) (l) ( )( 9) (b )(b ) (n) (s )(s ) (o) (d 8)(d ). () ( )( ) ( )( ) (c) (c )(c ) (p 9)(p ) (y )(y ) (d )(d ) (q )(q ) (h) (b )(b ) ( )( ) (j) ( )( ) (k) ( )( ) (l) (c )(c ) (y )(y ) (n) (b )(b ) (o) ( )( ). () ( )( ) ( )( ) (c) (p )(p ) (b )(b ) ( )( ) (y )(y ) (7c )(c ) (h) (m )(m ) (8 )( ) (j) (y )(y ) (k) (p )(p ) (l) ( )( ) ( )( ) (n) (c )(c ) (o) (b )(b 9). () ( )( ) ( )( ) (c) (p )(p ) (c )(c ) (y )(y ) (w )(w ) (m )(m ) (h) (q )(q ) (b )(b ) (j) (t )(t ) (k) (z )(z ) (l) (d )(d ) (7s )(s ) (n) ( )( ) (o) (v )(9v ) (p) ( v 7)( v ) (q) ( l )( l ) (r) ( m 7) (s) ( n 7)( n ) (t) ( b )(b ) (u) ( c )(c ) (v) ( q )( q ) (w) ( )( ) () ( b )(b ) (y) ( m )(m ) (z) ( n 7)( n ) 7. () ( )( ) ( p )( p ) (c) 9 ( )( ) ( )( ) ( )( ) ( y )( y ) (c )( c ) (h) (b )(b ) (q )( q ) (j) (s )( s ) (k) (m )( m) (l) ( )( ) (t 7)( t ) (n) 0(d )(d ) (o) (0 )(0 ) Pegsys 0

68 . COMPLETING THE SQUARE. () ( ) [] ( ) [] (c) ( ) [ ] ( ) 0 [0 ] ( ) 9 [9] ( ) [] ( ) [ ] (h) ( ) 0 [0 ]. () ( ) [] ( ) 7 [7] (c) ( ) 7 [7] ( ) [] ( ) [] ( 8) 7 [7] ( ) [] (h) ( ) [] ( ) 8 [8] (j) ( 7) [] (k) ( ) [] (l) ( 0) 0 [0]. () ( ) [] ( ) [] (c) ( ) [] ( ) [] ( ) [ ] 7 ( ) [7 ]. REDUCING n ALGEBRAIC FRACTION to SIMPLEST FORM. () (h) y (c) 8 c (j) (k) p (l) b c (n) y (o) v t (p) b (q) p q (r) 7 (s) n (t) df e (u) b (v) k 7m (w) eg 7 y (). () b ( y) (c) b y y y b b b b (h) 7 p q s b c (j) ( y) (k) t r t (l) b 7 p (n) (o) n (p) Pegsys 0

69 Pegsys 0. () b 9 (c) y c7 8 p (h) q b (j) y (k) m (l) d (n) p (o) (p) (q) b b (r) c c (s) (t) y y (u) p p (v) 7 c c (w) () (y) b b. APPLYING the FOUR OPERATIONS to ALGEBRAIC FRACTIONS. () (c) (h) (j) 0 9 (k) (l) (n) 0 (o) (p) 9. () (c) 7 (h) 0 0 (j) (k) 7 (l) 0 9 (n) 0 7 (o) (p). () 7 0 (c) (h) 8 (j) 9 (k) 0 (l) (n) (o) 7 0 (p). () 7 (c) 9 (h) (j) (k) 8 (l) 8 7 (n) 8 (o) 9 (p)

70 . () b (c) 7 8 p 7y 9 m (h) n 7m mn 9 (n) y q p pq (j) (o) (k) p 9 d 7c cd b b (l) (p) 9 y y y y (q) 8 b b (r) b 9 b (s) n m mn (t) 7 q p pq (u) (v) b (w) b m () m. () b 0 (c) 8 p y 9 m (h) 9 y (j) 7 p (k) b b (l) y y 7n m mn (n) q p pq (o) 9d 7c cd (p) 9y y (q) 0b 9 b (r) b b (s) n m mn (t) 7q p pq (u) 7 (v) b 9 (w) b 8p () p 7. () 8 0 y y 8 (h) p (c) b 8 pq m (j) bc (k) c 0 (l) 0 8 y (n) 7 0 (o) p (p) s t (q) 8q (r) 7b c 9 8m (s) n z (t) y b (u) p (v) d (w) 8 y () s t 8q (y) p 8. () y (c) b p c m k (h) y b (j) 8 (k) 8 (l) 8pq 7 (n) 8n (o) y 9 Pegsys 0

71 9. () 7 b (j) ( )( ) 7 0 u 7v 8 ( )( ) (c) (k) d ( )( ( )( ) ) (h) (l) ( )( ) 7 ( )( ) ALGEBRAIC FRACTIONS EXAM QUESTIONS. 9 8 ( ). ( ). e e. ( )( ).. ( ). DETERMINING the GRADIENT of STRAIGHT LINE given TWO POINTS. () (ii) (iii) (iv) (v) 0; undefined; positive; negtive. () (c) (h) (j) (k) (l) 8. () (c). () (c) (h) (j) (k) (l). () (c) (h) 7 (j) (k) 7 (l) 9 (n) 7 (o) (p). () both grdients both grdients (c) both grdients both grdients 7. () k = k = (c) k = k = 8. = 9 9. k = 0. = 0. k =. k = 9 Pegsys 0

72 . WORKING with the AREA of SECTOR of CIRCLE. () 0 cm² 9mm² (c) m². () 9 cm² 7 07cm² (c) 8 8cm² 8cm² 88cm² 00cm² 8 7cm² (h) 8cm². () 8 9cm² cm² (c) 70cm² cm² 7 8cm² cm² 7cm² (h) cm². 8cm². WORKING with the ARCS nd SECTORS of CIRCLE EXAM QUESTIONS. cm². 8m. 7770cm². 7cm. m². cm² 7. 0 cm² 8. 0 o 9. () 7cm² cm 0. cm². 90 o. () 7m 70m². () 8 cm cm². () 0cm² 77cm. 0 o. cm 7. 0 o 8. () 7 o 89 o (c) mm 9 8cm WORKING with VOLUME of CYLINDER. () 9 cm 8 cm (c) 0 cm cm 798 cm cm 87 cm (h) 0 cm 70 cm (j) 798 cm. () 9 8cm 7 litres. 90cm³. No; volume is 9 7 litres Pegsys 0

73 . WORKING with the VOLUME of SOLID SPHERE, CONE, PYRAMID. () 90 cm³ m³ (c) 0 mm³ 0cm³. () 90cm³ 00cm³ (c) 9m³ 00000mm³ 97cm³ 00cm³ 0000mm³ (h) 8700cm³ 80m³ (j) 7900cm³. 8cm³. () cm³ 80cm³ (c) 07cm³ 00cm³. () 9cm³ 70cm³ (c) 800cm³ 08cm³. () cm³ 80 8mm³ (c) 7 cm³ cm³ cm³ 8. cm³ 9. 00cm³ 0. 7cm³. 0mm³ WORKING with the VOLUME of SOLID SPHERE, CONE, PYRAMID nd CYLINDER EXAM QUESTIONS m³. 0cm³. 0cm. 0m³. cm. 0cm³ 7. 9cm³ cm³ 9. 8 cm³ cm³. 7 7cm³. 9 cm³. () 0cm³ cm. 0cm³. litres. 0 cm Pegsys 0