Plan for Beginning of Year 2: Summer assignment (summative) Cumulative Test Topics 1-4 (IB questions only/no retakes) IA!!

Transcription

1 Summer Assignment 018 The IB Math SL class covers six different mathematical topics (Algebra, Functions, Trigonometry, Vectors, Probability and Statistics, and Calculus). In an effort to best prepare you for the IB Math exam at the end of next year 4 (Algebra, Functions, Trigonometry, Vectors) of these topics will be reviewed this summer. This will leave our class with more time during the school year to focus on Statistics and Calculus and review for your IB exam. Instructions: Complete the following assignments. Please do not WAIT until the end of the summer to begin this. You will be swamped with math problems! You will turn this in the first day I see you in August. I will grade these problems and it will be your first summative grade. If you get stuck, please use your resources. You ve got an IB textbook, youtube, and each other. I do not mind if you get together this summer to work on this together, but please remember that you should turn in your own work. Your work should support your answer. I tried to leave enough room so that you can put all of your work on the paper provided. If you need extra space then please put it neatly on an extra sheet of notebook paper. Please be thinking of your IA this summer. I expect you to come back to me in August with a chosen topic. There are a number of resources in the IA folder on schoology. Plan for Beginning of Year : Summer assignment (summative) Cumulative Test Topics 1-4 (IB questions only/no retakes) IA!! 1

2 Topic 1: Algebra Arithmetic Sequences and Series: 1) Consider the sequence 6, 17, 8, 39, 50,... a) Find formula for general term u n b) Find its 50 th term c) Is 35 a member? d) Is 761 a member? e) Find the sum of first 10 terms ) Consider the sequence 87, 83, 79, 75,... a) Find formula for general term u n. b) Find the 40 th term. c) Is -143 a member? d) Find the sum of the first terms. 3) A sequence is defined by U n = 3n- a) Find u 1 and d. b) Find its 57 th term

3 c) What is the fist term of the sequence to exceed 450? d) Find the sum of the first 57 terms 4) Find the general term u n for an arithmetic sequence given that u 7 = 41 and u 13 = 77 5) Find the general term u n for an arithmetic sequence given that u 5 = - and u 1 = -1.5 Geometric Sequences and Series: 6) Consider the sequence 5, 10, 0, 40,... a) Find formula for general term u n b) Hence, find the 15th term c) Find the sum of the first 1 terms 3

4 d) Find the first term to exceed 10,000 7) Consider the sequence 1, -6, 3, -1.5,... a) Find formula for general term u n b) Hence, find the 13th term c) Find the sum of the first 10 terms d) Find the infinite sum of the sequence 8) Find the general term u n for an geometric sequence given that u 4 = 4 and u 7 = 19 9) In 1998 there were 3000 koalas on Koala Island. Since then, the population of koalas on the island has increased by 5% each year. (hint r is not.05) a) How many koalas were on the island in 001? b) In what year will the population first exceed 5000? 4

5 Sigma Notation: 5

6 6

7 Topic : Functions 7

8 7a) 7b) 7c) 7d) 8a) 8b) 8c) 8d) 8

9 9) Given the point (3,6) on a function f(x). If g(x) = f(x - 3) - 5, find the point (3,6) in g(x). Quadratic Equations: 10) Determine the equation of the axis of symmetry and the vertex of the quadratic relation y=-3x +8x+7 11) For y = -(x+)(x-1): a) state the x-intercepts b) State the equation of the axis of symmetry c) find the vertex d) Find the y-intercept e) sketch the graph 1) For y = ½ (x-) - 4: a) state the x-intercepts b) State the equation of the axis of symmetry c) find the vertex d) Find the y-intercept e) sketch the graph 9

10 13) For y = x +6x-3: a) Use completing the square to convert into the form y= a(x - h) + k b) state the equation of the axis of symmetry c) find the vertex d) find the y-intercept e) sketch the graph 14) Solve the following equations without a calc using any method. (complete the square, quadratic equation, factoring) a) x +10=7x b) x +!"! = 7 c) x -7x+3=0 10

11 15) Solve using a calculator a) 3x -x-5=0 b) (x-)(x+1)=3x-4 16) Find the point of intersection of the graphs with equations y=-x -5x+3 and y=x +3x+11 The Disciminant: 17) Using the discriminant only. Determine the nature of the solutions of: a)x -5x-7=0 b)3x -4x+48=0 11

12 Topic 3: Trigonometry 1

13 The Unit Circle 14) Evaluate without a calculator. a) Sin 60 b) Cos 45 c) Tan 150 d) Sin 300 e) Sin /6 f) Cos g) Tan 5/6 h) Sin 3/ i) Cos 10 j) Cos 5/4 k) Tan 315 l) Tan 11/6 13

14 15) Without a calculator evaluate: 16) Without using a calculator, find: (Hint- draw a triangle in the appropriate quadrant) 17) Solve WITHOUT a calculator: 18) Use technology to solve for 0 < x < 8 ; give answers to 3 significant figures a) sin x = 0.16 b) cos (x 1.3) =

15 Trig Identities 15

16 Graph of Trig Functions

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18 Topic 4: Vectors 18

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20 Vector representation of a line: 10) Find a vector equation of the line passing through ( 1, 4) and (3, 1). Give your answer in the form r = a + t b. 0

21 15) 16) 1

22 17)