Get strted 2 Equtions, epressions nd formule This unit will help you to work with equtions, epressions nd formule. AO1 Fluency check 1 Work out 2 b 2 c 7 2 d 7 2 2 Simplify by collecting like terms. b 2 c 2 + 2 + 2 Epnd (w + 2) b ( ) c (2 + 1) Complete the function mchines. 1 b 8 2 1 8 2 Number sense 1 b c d ( ) Key points Solve n eqution mens work out the vlue of the letter. Substitute into formul mens replce the letters with the number vlues you re given. These skills boosts will help you to solve equtions, write epressions nd use formule. Solving equtions with the letter on one side Solving equtions with the letter on both sides Writing epressions 1 2 Substituting into formule How confident re you? You might hve lredy done some work on equtions, epressions nd formule. Before strting the first skills boost, rte your confidence with these questions. 1 2 Solve 2 1 Solve 2 + 8 Unit 2 Equtions, epressions nd formule Write n epression for the cost of n pples t 0p ech. R IV Find R when I nd V
1 Solving equtions with the letter on one side In n eqution, the epressions on both sides of the equls sign re equl. To keep both sides equl you need to do the sme to both sides. Guided prctice Solve + 7 b 2 + 10 Worked em question Drw function mchines to show wht hs hppened to nd how to undo it. + 7 7 Use the inverse opertion. + 7 Why? 7 b 2 + 10 2 10 Why? 2 + 10 2 2 6 6 10 1 Solve + 8 11 + 11 11 b y + + y y + 2 Solve m + 7 1 b t c + m t Unit 2 Equtions, epressions nd formule 9
Solve 20 20 20 b 8 c c c c m d Solve t 12 b 2 6 c 2 h d n 16 e 6 1 f 2p 7 Solve 2 + + 2 b y + 7 2 y 2 y y + + 7 7 6 Solve + 11 b 6 2 22 c 2 + 8 d 1 e n + 7 1 f y + 6 Write your nswer s frction. 7 + 6 b 1 c y 6 2 t d 7 + 2 e n +. f 2 6 + 2 0 Em-style question 8 Solve 1 + 2 y b + 6 Reflect In Q, Q6, Q7 nd Q8, how do function mchines help you to use the inverse opertions in the correct order? 10 Unit 2 Equtions, epressions nd formule
12 Solving equtions with the letter on both sides When n eqution hs letter term on both sides of the equls sign, subtrct or dd to remove the smllest letter term from both sides. Guided prctice Solve + 6 + 2 Worked em question Find the smllest letter term: or 6? Subtrct the smllest letter term from both sides. + 6 + 2 + 2 2 2 1 + 1 Solve + 2 1 1 b 2 + 2 2 2 Solve 2 + 2 b y y 10 Solve + 2 6 + + + 2 6 b y 8 y y Solve w w 2 w (w 2) w w b 2 2 Em-style question Solve 6 2 ( mrks) Reflect In Q, why do you need to put brckets round w 2? Unit 2 Equtions, epressions nd formule 11
Writing epressions To write n epression, use letters to stnd for vlues you don t know. The letters re clled vribles becuse their vlues cn chnge or vry. Guided prctice There re tennis blls in bo. Write n epression for the number of tennis blls in boes b 2 boes plus etr blls. How do you get from 1 bo to boes? 1 bo blls boes blls b Go from 1 bo to 2 boes. 1 bo blls 2 2 2 boes blls Add etr. 2 + Why? Why? 1 Write epressions for more thn n b more thn y c lots of m n d lots of e less thn z f hlf of t 2 There re n biscuits in pck. Write n epression for the number of biscuits in 2 pcks c pcks with biscuits tken out Mnesh erns.20 per hour. b pcks plus 6 biscuits Write n epression for the mount he erns in n hours. 1 hour.20 n n hours m m m m m Em-style question Ali buys some festivl tickets nd two cr prk tickets. Write n epression for the totl cost. Festivl tickets 8 Cr prk tickets 20 b Ali pys 76 in totl. How mny festivl tickets does she buy? (1 mrk) (1 mrk) Reflect How cn drwing digrms help you write epressions? 12 Unit 2 Equtions, epressions nd formule
Substituting into formule To use formul, substitute (swp) the letters for the vlues you re given. Guided prctice d st, where d is distnce, s is speed nd t is time. Find d when s nd t 8 b Find s when d 0 nd t 2 Worked em question Swp s nd t for the vlues given. d st d b Swp d nd t for the vlues given. d st 0 s 0 s Solve the eqution. s st mens s t s nd t 8 d 0 nd t 2 1 Find the vlue of ech epression when n n n 2 b n + c 2n d 2 n e 2n + 1 f 1 n g 2 + h n 2 F m, where F is force, m is mss nd is ccelertion. Find F when m nd b Find F when m 10 nd 0. F P A Find P when F 18 nd A 2 b Find P when F 1 nd A y 2 Find y when nd 2 b Find y when 1 2 nd Em-style question d s t Find d when s 0 nd t b v u + t Find u when v 22, nd t Reflect When hve you used your eqution-solving skills in these questions? Unit 2 Equtions, epressions nd formule 1
Get bck on trck Prctise the methods Answer this question to check where to strt. Check up V m 2 Find V when m nd. Tick the correct nswer. A B C D V 16 8 V 8 2 V 1 V 16 If you ticked A go to Q2. If you ticked B, C or D go to Q1 for more prctice. 1 Work out m when m b kn when k 2 nd n 6 c 2 when d rt 2 when r 7 nd t 2 2 A lrge lorry hs n wheels. Write epressions for the number of wheels on 2 of these lorries b lorries plus spre wheels y 2 Find the vlue of y when b Find the vlue of when y 1 y Em-style questions Lucy erns 80 per dy, plus for ech dress she sells. Write n epression for the mount she erns on dy when she sells dresses. b One dy she erned 11. How mny dresses did she sell? (1 mrk) Solve 9 + 1 (1 mrk) b 8 (1 mrk) 6 Solve 2m + 6 m 9 m b 2 + 1 2 Em-style question 1 7 s ut + 2 t2 Find s when u, t 6 nd 2 ( mrks) 1 Unit 2 Equtions, epressions nd formule
Get bck on trck Problem-solve! Em-style questions 1 Write formul for the cost C of cinem tickets t 6.0 ech. 2 In the formul v 2 u 2 2s v is finl velocity, u is initil velocity, is ccelertion nd s is distnce trvelled. Find when v 12, u nd s 10 ( mrks) Solve 2 + 17 b 8 y 2 c + 7 y d 2 e 6 f 10 + 7 Em-style questions The rectngle hs perimeter cm. Find. The rectngle hs re 0 cm 2. Find the length of the longer side. 6 Find. + 2 + 1 7 An electricin uses this formul to clculte his chrges: C 0 + 20h Wht does C stnd for? b Wht does h stnd for? c How much would he chrge for job tht tkes hours? Now tht you hve completed this unit, how confident do you feel? 1 2 Solving equtions with the letter on one side Solving equtions with the letter on both sides Writing epressions Substituting into formule Unit 2 Equtions, epressions nd formule 1