High School Calculus Questions

Fill in the blanks Do not rationalize at b e d tan 57 12 11 1 b 3 3 d

S00 V tve 7 b 4

Find a b and c Note that the fraction is not simplified sin 57 6 X 1 2

5 6 A A 7 C b 8 b 12 b 4 c 8 C c 16 a 6 C a 6 a 10 B B B

ind the domain and range of the relation Use interval notation where appropriate 5 4 3 2 1 57 4 3 2 O 1 0 0 2 3 4 5 2 3 4 5 K

Use a calculator to evaluate the function at the indicated value of x Round your result to the nearest thousandth f x 6 3e x X 100 X 2 344

Let f x x ax 2a x a such that f x has a point of inflection located at x 2 What is the value of A 3

4 y cot 20 2 A B D 3x 2x 3x 7 270 4 2 Period Period Period x Period I

2 y cot A B cot 1 2 D 2x 3x 3x 2x 3r 2x

Choose the correct graph and explain your choice 1 y tan 20 A B D x fr Cr 12 T 3r 2x 27 3x 3

3 y cot A B D 0 3 1 27 2x 3x 4 2x 3x 4x 2x Period 3r Period Period 3x Period 3x

6 y tan 0 A B D 3 2x Z 3x 2 3r 4x

5 y cot 6 A B D 2 45 6 A 3r 8 2 3x 2r

Instructions Use the image to help answer the questions about the trig values of the given angle in the Unit Circle unit circle trig EIN 3r 01 3 2 112 e 0 The given angle theta is shown with a terminal ray at point P which has 19 0 5 points tan 0 1 2 3 3 3 Clear my selection

4 A particle moves along a line so that its position at any time t 0 is given by the function s t t 3t 8t 5 where s is measured in meters and t is measured in seconds a Find the instantaneous velocity at any time t b When is the particle at rest c Find the acceleration of the particle at any time t d What is the displacement of the particle for the first 3 seconds

11 People are entering a museum at a rate modeled by f t people per hour and exiting the buildin at a rate modeled by g t people per hour where t is measured in hours The functions f and g are honnegative and differentiable for all times t Which of the following inequalities indicated that the ate of change of the number of people in the building is decreasing at time t a g t 0 b g t 0 c f t g t 0 d f t g t 0

2 Calculator active The rate of R t of a certain item produced in a factory is given by R t 4000 48 t 3 4 1 3 3 where t is the number of hours since the beginning of the workda 8 00 am At what time is the rate of production increasing most rapidly d 1 00 pm a 8 00 am b 10 00 am c 11 00 am

1 Alvaro is studying the extinction of the bear population of Siberia over time The following function gives the number of bears t years since Alvaro started tracking it B t 2190e 0 3t a What is B 3 b Interpret B 3 in the context of tis problem

If the vector v O a A 4 O b A 1 O c None Od A 1 O e A 5 is an eigenvector of the matrix A then the eigenvalue A that corresponds to vis

If A a O b 1 to then adj A 1 1 20 2 1 O e O c None O d 0 1 1 07 22 2 2 0 L 2 2

4 Find an equation of the line through the first quadrant that cuts off the least area from the first quadrant

Write Name Date Period Show all work including labeled triangles in the unit circle showing direction 1 Graph y tan x 3TT 2 T TT 2 y 3 2 0 1 2 3 TT 2 TT 3TT 2 X

10 Use the unit circle to explain why the graph of y tan is increasing for 0 0 2

A tangent function of the form y tan be has no vertical asymptotes for 2 x 2 Find a possible value of b

T and a 9 Geraldine and Miranda were asked to write an equation of a cotangent function with an x intercept at x vertical asymptote at x Geraldine said there was more than one correct answer Miranda said there was only one correct answer Who is correct Explain your answer 4

2 Find the period of y cot 2

4 Let f 0 tan and g 0 cot 0 Which of the following statements is true A If f 0 0 g 0 0 B If f 0 0 g 0 0 C f 0 g 0 when 0 F D f 0 g 0 0 for all 0

7 Graph y cot x 3TT 2 TT y 34 N TT 2 0 2 TT 2 TT 3TT 2 X

Write the equation of a tangent function with a period of 3r and a vertical shift up 4 units

a I only f x 5 c lim x 2 X 2 d lim f x 7 1 g is continuous at x c II lim g x exists x c III lim X C 7 g x g c x c a lim f x 5 b m f x lim f x 2 x 2 dy 7 20 x 2 exists b Ill only must be true 3 If f is a differentiable function such that f 2 5 and f 2 7 which of the following statements could be false c I and II only Q 11 II and III 2 7 Product Rule 1 Let f be a differentiable function with f 2 7 and f 2 2 Let g be the function defined by g x x f x Which of the following is an equation of the line tangent to the graph of g at x 2 a y 7 2 x 2 b 28 2 20 x 2 c y 7 x 2

Find the average rate of change of f x of f x sin x In x on the interval 1 x a Sin 1 In 1 Sinaing 1 9

2 Let f x x g h x where g 4 2 g 4 3 h 3 4 and h 3 2 Find f 3 a 18 b 16 c 7 d 11 3 2 4 32 1 12 3

1 Let f x 2e x and g x 5x At what value of x do the graphs of f and g have parallel tangents a 0 445 b 0 366 Graph of f c 0 344 d 0 251

3 If f is a differentiable function such that f 2 5 and f 2 7 which of the following statements could be false a lim f x 5 b lim f x lim f x C lim f x 5 X 2 X 2 7 d lim f x 7 h 0

Solve the equation Write the solution set with the exact values given in terms common or natural logarithms e2y7ey 12 0

orodeoxyglucose is a derivative of glucose that contains the radionuclide fluorine 18 A patient is given a sample of this material containing 245 MbQ of fluorine 18 a megabecquerel is a unit of radioactivity The patient then undergoes a PET scan to detect areas of metabolic activity indicative of cancer After 138 minutes one third of the original dose remains in the body Use a function of the form Q t Qoe kt to model the radioactivity level of fluorine at a time t minutes after the initial dose Give the value of k to three decimal places Do not round intermediate calculations Your Answer

16 If g is a differentiable function such that g x 0 for all real numbers x and if f x x 4 g x which of the following is true A f has relative maxima at x 2 and x 2 B f has relative minima at x 2 and x 2 C f has a relative minimum at x 2 and a relative maximum at x 2 D has a relative maximum at x 2 and a relative minimum at x 2

Solve each triangle Round your answers to the nearest tenth 7 m B 27 a 28 ft b 18 ft 8 m C 54 b 24 km c 23 km

x 1 3bx 13bx 6x 1x 1 x ax 3

the number of possible triangles that can be formed using the given measurements 1 mA 110 c 19 cm a 32 cm 2 mA 131 a 25 yd c 8 yd 3 m B 100 a 33 km h 29 km 1 4 m B 61 a 35 mi b 32 mi

1 In the right angle triangle 4ABC where ZC is 90 ZA 42 and side c 45 cm determine the unknown side a Round your answer to the nearest centimetre a sin42 45 A 30 cm B 32 cm C 29 cm D 31 cm 2 Use right angle trigonometry to determine ZA Round your answer to the nearest degree b 12 C A 36 B 45 C 30 D 37 c 15 B unknown ride a Bound your answer to the nearest tenth of a unit

Find the instantaneous rate of change of the function at the given f x f a x a x value using the form lim x a 2 y 3x2 4x 7 at x

Find the average rate of change on the given interval 1 s t t t 4 15

13 A landowner says his property is triangular with one side 500 m long and another side 350 m long The opposite angle to the 350 m side measures 20 Determine two possible lengths of the third side to the nearest metre 4 marks

15 What are all values of x for which the function f defined by f x x 32 9x 7 is increasing A x 3 or x 1 B x 1 or x 3 C 3 x 1 D 1 x 1

4 3 2 1 3 2 Y 2 3 You might need 2 What is the slope of the line 3 Lato

4 3 2 1 y 3 2 2 3 2 What is the slope of the line

A 2010 estimate of the population of Mexico is 102 million people with a projected growth rate of 0 92 per year At this rate the population P t in millions can be approximated by P9t 102 1 0092 t where t is the time in years since 2010 Find the population in the 2 017 Round your answer to the nearest million Your Answer

Consider the function f x 9x Graph the exponential function by hand 2 2 Identify any asymptotes 1 1 150 100 50 y 150 100 50 1 2 2 3 X 4 1 3 2 2 3 1 4 5 1 x X

Use a calculator to evaluate the function at the indicated value of x Round your result to three decimal plac Value 67 f Function f x 1 2x X 7