Sequences & Series Questions and Answers

1 Using math symbols write twelve more than two times a number n is equal to one fifth the same number decreased by ten

14 Let x 2 y 9 and z 2 Evaluate y Round your answer to the nearest hundredth if necessary

9 Rewrite the following word phrase as a variable expression Eight times the number a Ox 8 O x 8 O 8x 00

The graph of f x is shown it goes through the point 4 1 10 5 4 3 2 1 10 7 67 8 9 10 Provide two different graph transformations that produce the curve y f x from the curve y log x as follows 1 The graph can be obtained from the curve y log x by a horizontal translation followed by a vertical translation Give such a pair horizontal translation by then vertical translation by 2 The graph can be obtained from the curve y log x by a horizontal stretch followed by a horizontal translation Give such a pair horizontal stretch by factor then horizontal translation by

Express the series in terms of elementary functions and find the where the series converges n 1 3 nr The series converges for 0 x 0 x 0 0x 0 0 x 1 O x 1

6 Which of the following sets is a finite set of rational numbers O 1 1 3 5 7 9 Otttttt O 1 2 0 1 1 1 4 O 3 T 2 3 14

3 To which number set s does the following number belong 2 Multiple answers may be correct Mark all correct answers Orational numbers counting or natural numbers integers Oreal numbers whole numbers irrational numbers

Graph the quadratic function f x x 3 Give the a vertex b axis c domain and d range a The vertex is 3 0 Type an ordered pair Use the graphing tool to graph the function b The axis is Type an equation 10 4 2 10 8 z 6 4 2 2 4 6 8

Graph the function on the interval 5 1 g x x 5 in 3 ex X

15 If It cot 7 P 9 r s where p q r seN such that p q r s then p s q r equals A 1 B 0 C 1 D 2

Write the compound statement in symbolic form Let letters assigned to the simple statements represent English sentences that are not negated If commas do not appear in compound English statements use the dominance of connectives to show grouping symbols parentheses in symbolic statements We have power if and only if it s not true that both the lines go down and the transformer blows Let p represent the simple sentence The lines go down q represent the simple sentence The transformer blows and r represent the simple sentence We have power The compound statement written in symbolic form is

3 Write a ratio of 36 black candies out of 45 altogether State your answer as a fraction

Find the radius of convergence for n 1 3 5 2n 1 5x W n 1

Determine whether the equation is linear or not Then graph the equation by f y 3x 1 Is the equation y 3x 1 linear or not Onot linear linear Use the graphing tool to graph the equation Click to enlarge graph TEE 10 10 8 6 4 2 2 4 Z 6

Hal has sold 91 39 93 and 79 copiers in the last four months respectively How many copiers will he neec to sell this month s to maintain an average of at least 76 sales per month O 107 O 78 O 63 O 77

13 Simplify completely 6 13 8 5 O 48 65 O different radicands cannot be combined here O 48 18 14 Solve for y Do not use a calculator Keep radical i 5y 45 y x 15 Solve for z Do not use a calculator Keep radical i 2 84

2 Determine which system of inequalities corresponds to the following graph y O 1x 3y 3 and 3x 1y 1 2x 6y2 1 and 5x 2y 3 d fo 2115 1

9 Suppose you own a toy company Toy dogs sell for 6 60 and toy trucks sell for 10 20 Identify the inequality expressing how many of each should be sold to make at least 1000 worth of toys Hint let x the number of dogs and y the number of trucks O 10 2y 1000 6 6x O 6 6x 10 2y 1000 O 6 6x 10 2y 1000 O 10 2y 1000 6 6x

1 Suppose you own a toy company Toy cars sell for 8 10 and toy trucks sell for 4 50 Perhaps you are going to package up the cars and trucks and ship them to a store in your own car You know you can fit no more than 88 toys in your car With these constraints can you take enough toys to the store to sell at least 600 worth O yes O no

Oy 10 x 8 O y 10 x O y 10 r 8 O y 10 X O y 10 T 00 0 8 X O y 10 r 8 10 Solve the systems of linear equations using a graphing method Write none in both blanks if there is no single solution 5x y 31 x 2y 17 5

Find the angular speed w in radians second associated with rotatin a central angle 277 in time t 6 sec

Plot the ordered pair Plot the ordered pair on the graph to the right In which quadrant or on which axis does the point lie ON Oon the x axis 111 State in which quadrant or on which axis the point lies on the y axis CETTE

5 Write an expression for the total number of sticks in the stick design below 6 The stick design above is 6 sticks wide How would you modify your expression in part 5 if the design we

A function from X domain to Y range is a relation which matches each element x of X to exactly one element y of Y Select one O True O False 2 3 5

1 8 Find the characteristic equation and the eigenvalues for the matrix 0 1 1 LO 1 21

4 Use h x log3 x 2 1 to determine the following 1 1 4 marks a Domain b Range c h x

Question 3 Khadijia wants to have 10 000 to use during her retirement in 12 years If the money is compounded annually at 8 how much should she deposit at the end of each year O 526 95 O 600 76 O 940 15 6 pts 913 03

Three students were applying to the same graduate school They systems Number Student GPA School Average GPA School Standard Deviation Thuy 3 2 2 6 0 8 Vichet Vichet is Number 85 77 Kamala 8 2 8 5 Table 2 74 How many standard deviations is each student away from hiir school average If the student GPA is higher tha his school average enter this as a positive number If the student GPA is lower than his school average ente this as a negative number Thuy is Kamala is Number 20 0 3 standard deviations from Thuy s school average standard deviations from Vichet s school average standard deviations from Kamala s school average Which student had the best GPA when compared to other students at his school

What is the exact value of tan 300 O 3 O O 3 3

What is the exact value of cos 60 3 2 O 10 11 1 O O O 171 3 2

Which function is undefined when 2 radians O cos e Ocot e O csc e O tan e

Casandra worked the 22 weekdays of last month in the pediatrics clinic and checked in the following number of patients 14 15 24 26 11 16 25 10 12 27 18 13 20 18 22 24 17 19 19 7 15 30 a Construct grouped frequency and relative frequency distributions Use 5 uniform classes of width 5 where the first class has a lower limit of 6 and loaf display for this data

Which results from multiplying the six trigonometric functions O 1 O 3

The height of an equilateral triangle is 43 What is the perimeter of the equilateral triangle O 12 units O 12 3 units O 24 units O24 3 units

The initial tableau of a linear programming problem is given Use the simplex method to solve it The maximum is when x x x 6 and s 0 Re sure to simplify to lowest terms if necessary CODE X X X3 2 10 1 2 3 30 4 1 1 S

If tan 60 what is the value of cot e O 1 60 11 60 61 11

Which expression is equivalent to sin 6 O sin O sin 5x 6 5x O sin 3 11 O sin R

Which of the following is true for f x 5cos x 1 O The period of the function is 10 O The function has an amplitude of 2 5 O A zero of the function is X O The range of the function is the set of real numbers 4 y 6

1 Which of the following is true of the location of the terminal side of an angle 8 whose sine value is O e has a reference angle of 30 and is in Quadrant I or II O O has a reference angle of 30 and is in Quadrant I or IV has a reference angle of 60 and is in Quadrant I or II O e has a reference angle of 60 and is in Quadrant I or IV

3x The point P x y lies on the terminal side of an angle 4 in standard position What are the signs of the values of x and y O Both x and y are positive O Both x and y are negative O x is positive and y is negative O x is negative and y is positive

7 r Which equation can be used to determine the reference angle r if 12 O r a O O r ex r 2x e

Anik Isabella Kayla Morris Which student is correct O Anik O Isabella O Kayla O Morris The cosecant secant and cotangent of an acute angle may be greater than 1 or less than 1 The cosecant secant and cotangent of an acute angle are always greater than 1 The cosecant and secant of an acute angle are always greater than 1 but the cotangent can be greater than 1 less than 1 or equal to 1 The cosecant and secant of an acute angle may be greater than or equal to 1 but the cotangent of an acute angle is always less than 1

A baby s t shirt requires 3 5 yards of fabric How many t shirts can be made from 54 yards

In the triangle below which is equivalent to sinA A B sinC sinB O COSA cosC C

The terminal side of an angle measuring radians intersects the unit circle at what point 01 FK 213

If sin es 0 7660 which of the following represents an approximate value of tan 8 for 180 8 270 O 0 7660 O 0 8392 O 1 1916 O 1 4198

future Solve each equation inequality algebraically Graph the solutions to the inequalities on a number line and give those answers in interval notation for parts b and c a 13x 2 5 b 13x 21 5

Which equation can be used to find B in the triangle below B 6 A cos B 00 8 O tanB 10 O tanB cos B 8 10 10 6 10 8 C

a Find f 1 b Graph f and f1 in the same rectangular coordinate system c Use interval notation to give the domain and the range of f and f 1 a The inverse function is f x X 7 6 Use integers or fractions for any numbers in the expression b Choose the correct graph which shows f x and f1 x graphed in the same coordinate system The graph of f x is shown as a solid line and the graph of f is shown as a dotted line c State the domain and range of f x using interval notation The domain of f x is 00 and the range of f x is 0 00 State the domain and range of f1 x using interval notation ge of f 16 in Th OB emain off 1 OC G 5

The side length of an equilateral triangle is 6 cm What is the height of the triangle 3 6 cm cm O 3 3 cm O 6 3 cm