Lesson for Reference. 1-8 Complete Square and Vertex Form 1-5 Compositions and Inverse Functions. 1-6 Transformations

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1 1B Math SL Year Name: Date: 1-101B Math SL Year 1 Quarter 1 Cumulative Review Use the table below to identify the lesson in which the topic presented in each question can be found. If you are stuck on any problem, you should refer back to your notes!! Be sure to utilize your formula booklet as you work! Question Number Lesson for Reference 1 1- Sigma Notation 1- Compound Interest 1-4 Functions and Relations Functions and Relations 5a 5b 6b 7b 1-8 Complete Square and Vertex Form 1-5 Compositions and Inverse Functions 1-8 Complete Square and Vertex Form 1-6 Transformations 1-8 Complete Square and Vertex Form 1-6 Transformations Series and Sequences 1- Sigma Notation Transformations Complete Square and Vertex Form Series and Sequences Transformations Series and Sequences Series and Sequences 1- Sigma Notation Factoring a quadratic Applications and Graph Equations Applications and Graph Equations Compositions and Inverse Functions

2 1B Math SL Year complete each question to the best of your ability. This will be used to review all material in Unit 1 and prepare you for your exam tomorrow. Show all work where necessary. Evaluate the expression )Ž=1 k. Jake deposits $000 into an investment account that pays 4.5% nter st er annum, compounded twice a year. How many years would it take Jake's investment to double in value? [ marks] 100k (-Ò 15,c. Find the domain and range for each of the functio elow. [6 marks] x (11] xer (Is-I) x x

3 1B Math SL Year 4. State the domain and range of h(x) = K-Ä=O [ marks) 00, o, 5. The functionfis given byf (x) =x 6x+ 1, forxè. (a) Write f (x) in the form (x + b. the / marks] -.Ë(xò Find the inverse function r 1 q-z-q- 6. The quadratic functionfis de Ined byf (x) = x-1x+11. (a) Write fin the form f (x) = (x h) The graph of f is translated units in the positive x-direction and 5 units in the positive y-direction. Find the function g for the translated graph, giving your answer in the form g (x) = (x p) + q.

4 1B Math SL Year Express y x 1x + in the form y = (x + d. -18 [ marks/ The graph of y = x is transformed into the graph of y = r 1x + by the transformations 6 a vertical stretch with scale factor k followed by a horizontal translation ofp units followed by a vertical translation of q units. Write down the value of [ marks] (ii) p; (iii) q 5 8. Consider the infinite geometric sequence 00Cì00, 1080, 648 (a) Find the common ratio. \ Ýoc 000 Find the 10th term. 5 vtb 000 (c) Find the exact sum of the infinite sequence. OSR s

5 ド を ) W ⅱ ゝ (x ー一 )+ ー (To 巨 4 ma ks) 0)0=- ま旨 0 一品 0=. ま 0 只 =0 一目 00 一 = 0 一ま minimum 0 を一 =0 0 0 も =0 " 0,0 ~\0 ) 毛与 ~ ) X.5 の (0 0) 目 0( 一. 一 一 8 Math StYea こ ( を必 : 一ン一 Math SLYea

6 1B Math SL Year 10. Let Rx) = (a) Show that f(x) = x 4x For the graph of f (i) (ii) mite down the coordinates of the venex: down the equation of the axis of symmetry: (iii) suite down the yṟintercept; (iv) find both x-intercepts. [8 marks] (c) Hence sketch the graph of f. )vse -10 calc / c) Consider the infinite geometric sequence, (0.9),,, (a) Write down the 10' term of the sequence. Do not simpli$ryour answer. [1 mark] Find the sum of the infinite sequence. [4 marks] 09)

7 V 1B Math SL Year 1. Let f(x) = x and g(x) = (x-1). (a) The graph of g can be obtained from the graph of f using two transformations. Give a full geometric description of each of the two transformations. e Q) CcOO 1. In an arithmetic series, the first term is 7 and the sum of the first 0 terms is 60. (a) Find the common difference. - G 0 [ marks] (n-dd) Find the value of the 78th term In a geometric series, 111 = and 114 = (a) Find the value of r. [ marks] Find the smallest value of n for which Sn > 40. [4 marks] 0 H qnao> -t Use the discriminant to determine the nature of the roots of9x + 6x + 1 = O idevvti(xq foots C.CR7h C,íR

8 1B Math SL Year 16. Greg is in a car at the top of a roller-coaster ride. The distance, d, of the car from the ground as the car descends is determined by the equation d t, where t is the number of seconds it takes the car to travel down to each point on the ride. n-tz t 50 How many seconds will it take Greg to reach the ground? 17. Write the equation of the quadratic function shown in the graph. Give your answer in the form y = ax + bx + c. x (, -1) 18. Let f (x) =.r and g (x) =.r -s (a) Find g -l Find [ marks]