MCR 3U Exam Review. 1. Determine which of the following equations represent functions. Explain. Include a graph. 2. y x

Transcription

1 MCR U MCR U Em Review Introduction to Functions. Determine which of the following equtions represent functions. Eplin. Include grph. ) b) c) d) 0. Stte the domin nd rnge for ech reltion in question.. If f ( ) nd g ( ), determine the following: ) f ( ) g( ) b) g( ) f (). Let f ( ). Determine the vlues of for which ) f ( ) 0 b) f ( ) Recll the bse grphs.. Grph. Stte the domin nd rnge. Describe how the grph cn be obtined from the grph of.

2 MCR U Also Tr! ) Grph b). Given f ( ) ( ), ) determine the eqution of the inverse b) grph f() nd its inverse c) Is the inverse function? Eplin. If not, restrict the domin of f() so tht the inverse is function.

3 MCR U Algebric Epressions. Evlute ech of the following. ) 7 8 b) c) 0. Simplif. Epress ech nswer with positive eponents. ) n m n m n m b) 7 r r r c). Simplif nd stte restrictions ) b) c) 8 d) Is? 9 ) ( z z Justif our response.. Is? ) ( ) ( Justif our response.

4 MCR U Qudrtic Functions. Simplif ech of the following. ) 7 08 b) ( ) c) ( )( ). Solve. 9 ) b) 8 c). Solve. Epress solutions in simplest rdicl form. ) 0 b) Find the mimum or minimum vlue of the function nd the vlue of when it occurs. ) b). Write qudrtic eqution, in stndrd form, with the roots ) nd nd tht psses through the point (, ). b) nd nd tht psses through the point (-, ).. The sum of two numbers is 0. Wht is the lest possible sum of their squres? 7. Two numbers hve sum of nd their product is 0. Wht re the numbers,in simplest rdicl form.

5 MCR U Eponentil Functions. Grph nd on the grid below. ) Wht trnsformtion on will give s its imge? b) How re the curves like? How re the different?. Grph nd on the grid below. ) Wht trnsformtion on will give s its imge? b) How re the curves like? How re the different? ( ). Grph. Grph. Solve ech of the following. ) 7 b) 7 9. Hlf-Life A lbortor hs 0 mg of iodine. After ds there re onl mg remining. Wht is the hlf life of iodine?

6 MCR U Trigonometr. Given cos, where ) Find the si trigonometric rtios. Epress ech in simplest rdil form. b) Determine the mesure of, to the nerest degree.. If 0 0, find the possible mesure of ngle. ) sin b) cos c) tn. Find the length of the indicted side. ) b). Solve ech of the following tringles. Include digrm. ) DEF, D, d 9cm, f 8cm b) RST, S, t 7cm, s cm c) PQR, P 0, p cm, q cm. Prove ech identit. ) csc sec (csc )(sec ) cos sin b) 0 sin cos tn c) cos sin tn. Clculte ech of the following vlues ectl nd then simplif. ) sin cos sin 0cos( 0) b) sin cos tn 0tn 0 7. A crnivl Ferris wheel with rdius of. m nd le 7 m bove the ground, mkes one complete revolution ever s. ) Drw grph to show how person s height bove the ground vries with time, strting when the person gets on to the Ferris wheel t its lowest point. b) Find n eqution for the grph. 8. Sketch one ccle of the grph of ech of the following. Stte the domin nd rnge of the ccle. ) sin b) cos 90

7 MCR U Sequences nd Series. A blloon filled with helium hs volume of cm. The blloon loses one fifth of its helium ever h. Wht volume of helium will be in the blloon t the strt of the sith d? the seventh d?. An ccelerting rocket rises 0 m in the first second, 0 m in the second second, nd 70 m in the third second. If the rithmetic sequence continues, how high will the rocket be fter 0 s?. The ir in hot ir blloon cools s the blloon rises. If the ir is not reheted, the blloon rises more slowl ever minute. Suppose tht hot-ir blloon rises 0 m in the first minute. In ech succeeding minute, the blloon rises 70% s fr s it did in the previous minute. How fr does the blloon rise in 7 min, to the nerest metre?. In geometric sequence, =, t = 08 nd the sum of ll terms of the series is 0. How mn terms re in the series?. Determine the first nd lst terms of n rithmetic series with 0 terms, common difference of, nd sum of Determine the vlue of tht mkes ech sequence geometric. ), 8,, +,... b),,, Determine the vlue of tht mkes ech sequence rithmetic. ), +,, 9,... b),,, Epnd nd simplif ) ( ) b) ( ) c) Finnce. Gil s grndfther sved for trip b depositing $00 t the end of ech month for 8 months. The ccount erns.8% per nnum, compounded monthl. How much will be in the ccount when the lst deposit is mde?. Leil is borrowing $ 000 for ers. She is deciding between lon t.9% per nnum, compounded monthl, nd lon t 7% per nnum, compounded nnull. ) Predict which lon is the better del. b) How much interest is pid on the lon tht is the better del?. Mrci wnts to receive $0 000 ever months, for ers for living epenses when she goes bck to school, strting months from now. How much mone must she invest now t.% per nnum, compounded semi-nnull.