Name: 13-1 Final ReviewPeriod:

13-1 Final review-Units #1-3Directions: The following are Topics that we covered in Units #1-3(Calc Permitted). Your task is to:

1. Read the Key Ideas/Tips on your own and highlight important ideas/concepts.(everyone does this)

2. Answer the sample IB Question and look up to check answers. (Everyone does this)3. If you find that you get stuck on a question or if you get ANY PART OF THE QUESTION wrong, go to

Google classroom to and watch a teacher take you through the main ideas of the unit and the answer to that question. Then move on to review questions.

Unit Cram Sheet/Big IdeasSample question/s

Arithmetic sequences How to recognize them, Common difference d Notation: u1, n, un what do they mean? Writing the nth term Writing the general term

( use Formula Booklet)Arithmetic series Sum /addition Notation Sn

Use formula booklet for sum, pick either formula based on what you have!

un is the last term of sequence..Geometric Sequences How to solve for common ratio/ how to check if it is

geometric. r= NextPrevious

Writing the nth term Writing the general term ( use Formula Booklet)

Variable in the exponentuse power rule of logs.Geometric series Sum/addition If solving for n and get a decimal, try a whole

number above and one below! Watch out for order of operations!Applications of geometric series Watch out for tricky worded questions! List out your terms if the question involves years. Percentsgeometric! % increase (r= 1 plus %)

%decrease ( r=1 minus %)Sum of infinite series

Series converges to value u1

1−r if |r|<1 .

look for word “ infinite”Sigma Notation•Know difference between “Expand” , “ Evaluate” , “Show the expression as a sum of the series”•Make connections between Sigma and formulas in formula booklet.

1.Consider the infinite geometric sequence 3000, – 1800, 1080, – 648, …(a) Find the common ratio.

(b) Find the 10th term.

(c) Find the exact sum of the infinite sequence.

2. In an arithmetic sequence, u10=37 and u21=4. Find the common difference and the first term, then find the general term.

Unit 1-Series and sequences

Unit Cram Sheet/Big IdeasSample question/s

Domain all possible x values Range all possible y values Vertical line test to test for functionsDomain and Range from a graph Open circle vs closed circle Arrows infinity Watch out for asymptotes.Composition of functions Work from the inside out.Inverse Functions Reverses the action of that function. Can check using Horizontal line test. Reflects the original graph across y=x line

( swap coordinates)Transformations Translations Reflections DilationsCompositions of Transformation Order of composition matters! ( HDRV) Horizontal shift negative means move right! Vertical stretching changes the y’s ( think!

Which axes moves vertically? The y axis!)Versus

Horizontal stretching changes the x’s (think! Which axes moves horizontally? The x axis!)

1.

2. Write the equation of the following function given the original functions of the transformations performed.f ( x )=x2, horizontal compresses by a factor

of 13 , reflected in both the x –axis and y-axis, translated 11

units to the left and 4 units up.

Unit Cram Sheet/Big IdeasSample question/s

Factoring and solving Factoring methods( GCF, Sum/Product, DOTS,

AC method) Solving Methods (Set equal to zero and Factor

OR use Quad Formula OR Complete the square.)

Discriminant b2−4 ac If ∆=0- roots are real, rational, equal If ∆>0 AND a perfect square- roots are real,

rational, unequal. If ∆>0 AND not a perfect square- roots are

real, irrational, unequal. If ∆<0 roots are imaginary.Solving Quadratic Inequalities.1. Replace the inequality symbol with an equal

sign and solve the resulting equation. The solutions to the equation will allow you to establish intervals that will let you solve the inequality.

2. Plot the solutions on a number line creating the intervals for investigation. Pick a number from each interval and test it in the original inequality. If the result is true, that interval is a solution to the inequality.

DO THIS ONLY WHEN YOU END UP WITH AN INEQUALITY THAT HAS TWO SOLUTIONS (∆<0,

∆>0)Vertex and factorized form. vertex form: y=a ( x−h )2+k vertex(h,k)

a. Don’t forget to change sign of only h coordinate when you put into equation.

b. Complete the square when switching from standard form to Vertex form.

Factorized form: y=a(x−p)(x−q ). p and q are the roots. Don’t forget to change sign of BOTH roots

when they go into equationEquation from a graph. See what is given, choose the appropriate form,

solve for a. turn back to standard form if asked to do so. to find X intercepts set y=0 and solve for x to find y intercepts set x=0 and solve for y

Equations to memorize/Know how to use!

Vertex form: y=a ( x−h )2+k vertex(h,k)Factorized form: y=a(x−p)(x−q ). p and q are the roots.

1. Find the values of m such that the equation has no real roots.

x2+5mx+25=0

2. Let f ( x )=2x2+4 x−6a) Express f (x) in the form f ( x )=2(x−h)2+k

b) Write down the equation of the axis of symmetry of the graph of f .

c) Express f ( x ) in the form f ( x )=2(x− p)( x−q)

Axis of Symmetry: x=−b2 a .

Review of Units #1-3

1. In an arithmetic series, the first term is – 7 and the sum of the first 20 terms is 620.(a)Find the common difference. [3 marks]

(b)Find the value of the 78th term. [2 marks]

2.

3. For each function, write a single equation to represent the given combination of transformations.

a. f ( x )=√x, stretched vertically by a factor of 2, and translated 3 units left and 2 units down.

b. f ( x )=x2, reflected in the x-axis, translated 5 units right and 1 unit down.

4. The graph of the function f (x), for −2 ≤ x ≤ 4 is shown on the right.a.

b. Let g ( x )=12

f ( x−1). The point A(3 ,2) on the graph of f is transformed to the point P on the graph of g. Find the

coordinates of P.

5. Let f ( x )=2 x3+3 and g ( x )=3 x−2.

a. Find g(0).

b. Find ( f ∘ g )(0).

c. Find f−1(x).

6.

7. Let g ( x )=2 x−1 ,h ( x )= 3 xx−2

, x≠ 2.

a. Find an expression for (h∘g )(x). Simplify your answer.

b. Solve the equation (h∘g ) ( x )=0.

8.

9. Express y = 2x2 – 12x + 23 in the form y = 2(x – c)2 + d. [2 marks]

10.

11.

12.

13. Write the equation of the quadratic function shown in the graph. Give your answer in the form y=a x2+bx+c.

14. Let f ( x )=a ( x−p ) (x−q ). Part of the graph of f is shown below. The graph passes through the points (−5 , 0 ) , (1,0 ) and (0 , 10 ).

a. Write down the value of p and q.

b. Find the value of a.