Complex numbers Questions and Answers

Find the peaks for f x cos x sin x x

Solve the System Give answer as x y z 3x 4y 5z 6x 4y 2z 12x 4y 1z 4 No solution Infinite number of solutions

1 Evaluate the following integrals 8x 3 a 5 marks 4x2 3x 6 dx b 5 marks e x cos 3xdx c 5 marks sin x cos dx

10 20 points BONUS Solve the equation cos 4x 2 sin 3x3 cos 2x 4 sinx 2 0

The two way frequency table contains data about how students access Computer 28 Mobile device 46 Column totals 74 64 O 55 Traditional Online Row totals O 32 33 Splen 62 64 126 What is the joint relative frequency of students who use a mobile device in an online class 90 110 200

The entire graph of the function g is shown in the figure below Write the domain and range of g as intervals or unions of intervals 5 domain range w 0 0 2 5 34 2 2 3 5 2 0 0 0 0 0 0 0 0 8 OUD

the Ex 6 3 You are given the Quadratic Relation in Standard Form You must fin by factoring Exact answer for each x intercept Find the AOS vertex and y intercept as taught Show all your work in a neat and well organized manner Graph a Quadratic Relation by its x intercepts y intercept vertex and AOS Make a sketch It is not necessary to put a scale on each axis You must indicate the co ordinates of each feature as taught Continue your work on next page Not necessary to reflect any point y x 8x 20 Factor fully Find the x intercepts the AOS and the vertex on this side of the sheet 6 marks

17 Ms Sanders invested in a stock During the first year the value of the stock tripled The next year the value of the stock decreased by 600 Write an expression that can be used to represent the value of her stock at the end of the second year Be sure to indicate what the variable in your expression represents U Font Family Y AA A FE Y E

or each scenario below choose the graph that gives the best representation a Lashonda begins her jogging workout by running faster and faster for about a minute Once she hits a comfortable pace she runs at that pace for several minutes Then she gradually slows down to a stop over the next few minutes Speed 0 Distance from the Nest Time 0 Speed Time 0 Distance from the Nest 0 O y Time Speed Time 0 b A bird of prey leaves the nest to go hunting It flies for several miles away from the nest before stopping to eat After eating it continues flying away from the nest for several more miles looking for more food Distance from the Nest 0 Time y x Time Speed X 0 Distance from the Nest 0 Time y S Time

7 Graph the quadratic functio y x 4x 4

15 Find the absolute value of the complex number

A cookie company uses one cup of sugar for every 25 cookies it makes Let S represent the total number of cups of sugar used and let N represent the number of cookies made Write a equation relating S to N and then graph your equation using the axes below Equation 6 5 w N S 0 0 X 0 0 X 3

6 13 d reflection in the line y x Question 25 1 point 4 Listen All asymptotes to the function f x csc z occur when a sinz 0 b cosz 1 Oc cos z 0 i 1

It is an odd function Question 29 1 point Listen Evaluate the following statement as true or false In f x sin z d if d 0 the function f z sin z moves down and if d 0 f x sin z moves up a True b False

14 If the base of a triangle is 6a 2 and its height is 13a represent the area of the triangle NOTE A bh

Question 38 1 point Listen The function f x a sin x contains the point A 1 The function is a f x sin x b f x sin x Oc f x 2 sin x d f x 2 sin x

Listen One cycle of a sine function begins at x period of the function a Not enough information Ob 2 3 Od 5 d 3 and ends at x What is the

40 Listen A ferris wheel at an amusement park completes one revolution every 40 seconds The cars can reach the maximum of 5 metres above the ground and a minimum of 1 metre above the ground The height h in meters above the ground can be modelled using a sinusodial function What is the radius of the ferris wheel a 4 meters Ob 5 meters Oc 2 5 meters d 2 meters

Are you ready for more On October 16 1843 while walking across the Broom Bridge in Dublin Ireland Sir William Rowan Hamilton came up with an idea for numbers that would work sort of like complex numbers Instead of just the number i and its opposite i squaring to give 1 he imagined three numbers i j and k each with an opposite that squared to give 1 The way these numbers multiplied with each other was very interesting i times j would give k j times k would give i and k times i would give j But the multiplication he imagined did not have a commutative property When those numbers were multiplied in the opposite order they d give the opposite number So j times i would give k k times j would give i and i times k would give j A quaternion is a number that can be written in the form a bi cj dk where a b c and d are real numbers Let w 2 3i jand z 2i 3k Write each given expression in the form a bi cj dk 1 w z 2 Wz

Determine the function that best represents the following graph 2 30 2 A 1 2 pdf A N 1 2 O a f 2 2 cos z 1 Ob f 2 2 sin z 3 Oc f x 2 cos z 3 3221

Use the following information to answer Questions 11 12 The Moondance Riding Academy held its annual horse show for 3 days The total amount collected in entry fees for the 3 days was 1 450 The amount collected in dollars is shown for each of the 3 days in the bar graph below Entry fees collected S 600 500 400 300 200 100 Day 2 11 Approximately what percent of the money collected from entry fees over the 3 days was collected on Day 2 A 29 B 34 C 38 D 66 E 90 Day 1 H 577 J 1 450 K 4 350 Day 3 12 The mean amount collected per day during the 3 day period is what to the nearest dollar F 300 G 483 13 For all n 3n 5 A 6n 15n 10 B 6n 30n 25 C 9n 6n 10 D 9n 15n 25 E 9n 30n 25 1 DO YOUR

Question 14 1 point 4 Listen The maximum height of water near a tidal power station in New Brunswick is 6 4 metres at 4 30 am and the minimum height is 3 6 m 6 2 hours later Which function can be used to model this relation Oa H t 6 4 cos 2x 4 Ob H t 1 4 cos 2 24 5 Oc H t 12 4 cos 2 4 5 Od H t 1 4 cos 5 5 12

Listen For the function f x 2 cos 3x 1 the phase shift is Oa units to the right Ob units to the left Oc units to the right d 3 units to the right

As Drake s OVO private jet approaches its horizontal distance from the airport is 22 miles when his altitude is 2 2 miles To the nearest degree what is the 1 1 Sin 0 15 1 angle of depression of Drake s plane Using the diagram 22 write an equation and solve A bike ramp has an elevation of 15 If the height is 22 feet what is the length of the ramp Create a diagram write an equation and solve Round to the nearest foot 19 22 x0 43 S 8 2 3 LEVEL tan 1 tan 0 2 5 202 8 88 9 22

1 10 10 Simplify your answer as much as possible X 0 1 log Olog No

5 points Let P denote the vector space of all polynomials in the variable of degree less than or equal to 2 Let C 1 1 x 1 3x x be an ordered basis for P2 a Write 4 x x as a linear combination of elements from the basis C 1 b Let g c denote the coordinate representation of q relative to the basis C Find the coordinate vector representation for 4 x x relative to the basis C Your answer should be a vector of the general form 1 2 3 4 x x c 4 x x 1 x 1 3x x

Find the radius of the inside the sphes Gylinder with A 12 Cm B 30cm

Multiply and Simplify 2x 7 4 Points

Multiply and Simplify 4 Points 5x3 4x0

A 253 ft tower is located on the side of a mountain that is inclined 25 to the horizontal A guy wire is to be attached to the top of the tower and anchored at a point 64 ft downhill from the base of the tower Find the shortest length of wire needed NOTE The picture is NOT drawn to scale length of guy wire 25 ft 64 ft 253 ft

The weekly sales of Honolulu Red Oranges is given by q 814 22p Calculate the price elasticity of demand when the price is 32 per orange yes 32 per oranget Interpret your answer The demand is going down by Also calculate the price that gives a maximum weekly revenue Find this maximum revenue per 1 increase in price at that price level

My friend Kathy just bought a home borrow ing 160 000 at a fixed 6 6 interest rate com pounded monthly for 20 years What monthly payment does she make If she decides to sell the house after making exactly 24 monthly pay ments what is the unpaid balance

Let sin A sin 2A 3 with A in QIV and find 5 Preview TIP your answer as a number like 5 3 2 2172 Enter

Suppose sin x cos x 7 5 sin x cos x 1 2 Find cos 2x

Long Term Investments This exercise is based on the following table which lists interest rates on long term investments based on 10 year government bonds in several countries in 2014 Country U S Yield Japan Germany Australia 2 5 0 5 1 0 3 5 Brazil 4 2 If the Interest on a long term U S Investment is compounded continuously how long will it take the value of an investment to double Give the answer correct to two decimal places yr

Simplify each expression and eliminate any negative exponent s a x y 1 b a b 3 4 a4 3 c 3 3y 3

Use the graph of the relation to identify the domain and range y 4x 3 10 8 64 2 2 4 6 8 10 10 X G O A domain 0 0 range 0 B domain 00 3 range 4 OC domain 3 0 range o 0 O D domain 3 range

Let S 2 1 0 1 1 2 2 4 Determine which elements of S satisfy the inequality Enter your answers as a comma separated list 215 4 20 2x

Find all the real zeros of the polynomial Use the quadratic formula if necessary as in Example 3 a Enter your answers as a comma separated list Enter all answers including repetitions P x 4x5 18x4 6x3 91x2 60x 9 X

Solve the system of linear equations If the system is dependent express your answer in terms of t where x x t y y t z z t and w t If the system is inconsistent enter INCONSISTENT x 2y z 3w 3 3x 4y z w 9 y Z W 0 X 2x y 4z 2w 3 x y z w 1

4 5 marks Find the area under the graph given below using the limits 0 and 2 476 Express the answer with 3 decimal places 0 1 2 0 1 0 496 0 2 076 0 652 1 664 0 1 066 1 176 2 476 0 3 901 0 4 3 16 1 525 5

Eric Schneider s bank statement shows a previous balance of 974 95 He made deposits of 246 00 and 98 48 He wrote checks for 721 00 and 35 35 He has a 3 00 service charge and earned 0 75 in interest What is his present balance 560 08 O 560 83 O 506 83

When you work more than 40 hours per week it is called time and a half O False True

Time and a half pay means you receive an overtime pay of twice your regular hourly rate O False O True

A budget is a plan for using your money in a way that meets your wants and needs False True

Hawks do not like the noise that humans make so they tend to move out of an area as more and more people move into the area If p represents the number of thousands of people in an area and h represents the number of hawks in the same area the relationship between the hawk population and the human population can be modeled with the equation h p 1000 2 Since hawks eat mice as the hawk population decreases the mice population in the area will increase If m represents the number of mice in the area this relationship can be modeled with the equation m h 800 If the mice population is found to be 940 in the area how many people would live in the area al 300 000

P x 2x 4 2x 3 2x 2 15x 9 Number of complex zeroes Possible rational zeroes

minor axis from 2 2 to 8 2 major axis from 3 4 to 3 8

Solve the equations using the quadratic formula What is the discriminant and describe the types of solutions e solution two real solutions or two imaginary solutions 1 x 9x 4 0 a Discriminant b Types of solutions c Solution 2 3x 5x 4 a Discriminant b Types of solutions C Solution 3 2x 12x 18 0 a Discriminant b Types of solutions

Question 2 Let p be prime Using Fermat s little theorem prove that n 2P 2 2 x 5P 10P 2 1 is a multiple of p if and only if p 2 5 Hint for p 2 5 consider 10n