Precalculus Honors 1st Sem Review (F09) Ch.1 - 4 (Demana 5th ed ...

Precalculus Honors 1st Sem Review (F09) Part I: Graphing Calculator (1-14)

Ch.1 - 4 (Demana 5th ed)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify intervals on which the function is increasing, decreasing, or constant. 1) f(x) = x 3 - x2 + 1 A) Increasing: (0, 0.67); decreasing: (- , 0) and (0.67, ) B) Increasing: (- , 0) and (0.67, ); constant: (0, 0.67) C) Increasing: (- , 0) and (0.67, ); decreasing: (0, 0.67) D) Increasing: (- , -1) and (1, ); decreasing: (-1, 1) Use regression to solve the problem. Round numbers to the nearest hundredth. 2) The first column shows the independent variable (x). The second column shows the dependent variable (y). (10, 35), (12, 40), (15, 49), (15, 58), (20, 63), (22, 70), (25, 76), (28, 88), (30, 91) Find the linear regression equation. A) y = 3.84x + 7.94

B) y = 3.34x + 6.44

C) y = 2.34x + 6.44

D) y = 2.84x + 6.94

Use a graphing calculator to approximate the real zeros of the function defined by f(x). Express decimal approximations to the nearest hundredth. 3) f(x) = - 7x3 +

5x +

A) No real zeros

7 B) 1.46

C) 1.28

D) 1.49, -1.49

C) 2

D) 5

Find the extraneous solution of the equation. 4) log (x + 3) = 1 - log x A) -5

B) -2

Find the amount accumulated after investing a principal P for t years at an interest rate r. 5) P = $3080, t = 9, r = 1% compounded continuously A) $6520.36

B) $3441.96

C) $24,957,498.46

D) $3370.06

Solve the problem. 6) Estimate graphically the local maximum and local minimum of f(x) = 0.02x5 - 0.04x4 - 0.06x3 + 1.46x2 + 1. A) Local maximum: 9.20; local minimum: 1.06

B) Local maximum: 7.86; local minimum: 1

C) Local maximum: 8.65; local minimum 0.91

D) Local maximum: -2.79; local minimum: 0

7) A rectangular piece of cardboard measuring 23 inches by 48 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square. For what value of x will the volume be a maximum? If necessary, round to 2 decimal places. A) 18.76

B) 37.53

C) 4.9

1

D) 22.29

8) Find the amount left after 38 years of 994 mg of an isotope with a half-life of 27.75 years. A) 309

B) 318

C) 159

D) 965

9) Find the annual percentage yield if the interest rate is 5.5% and interest is compounded quarterly. A) 5.61%

B) 5.86%

C) 5.36%

D) 6.11%

10) Find how long it will take for $6900 invested at 5.925% per year compounded daily to triple in value. Find the answer to the nearest year. A) 24,903 years

B) 19 years

C) 0 years

D) 2,470,456 years

11) The radius of a car wheel is 15 inches. How many revolutions per minute is the wheel making when the car is travelling at 45 mph. Round your answer to the nearest revolution. A) 6 rpm

B) 504 rpm

C) 1401 rpm

D) 4976 rpm

Solve the right triangle for all missing sides and angles to the nearest tenth. 12)

c = 20 B = 26° A) A = 64°, a = 8.8, b = 18

B) A = 64°, a = 18, b = 9.8

C) A = 64°, a = 9.8, b = 8.8

D) A = 64°, a = 18, b = 8.8

Solve the problem. 13) From a distance of 46 feet from the base of a building, the angle of elevation to the top of the building is 68°. Estimate the height of the building to the nearest foot. A) 17 feet

B) 43 feet

C) 114 feet

D) 19 feet

14) A tower is supported by a guy wire 390 ft long. If the wire makes an angle of 63° with respect to the ground and the distance from the point where the wire is attached to the ground and the tower is 289 ft, how tall is the tower? Round your answer to the nearest tenth. A) 429.5 ft

B) 535.5 ft

C) 365.1 ft

D) 581.3 ft

No Calculators on the Remaining Questions! 2

Part II: No Calculators on the Remaining Questions! Match the numerical model to the corresponding model. 15) x 3 5 7 9 11 13 y 14 26 38 50 62 74 A) y = 5x-1

B) y = 6x-4

C) y = 3x+5

D) y = 7x-7

B) 1; 1

C) 1; -3

D) -3; -3

B) - 25 ; 1

C) - 5

D) 5

B) 9 - 4 5

C) -9 ± 4 5

D) 9 ± 4 5

Solve the equation algebraically. 16) (x - 2)2 = 1 A) 1; 3 17) x -

10x - 25 = 0

A) 25 ; -1 18) 4 x + x = 1 A) 29 ± 24 5 Find the domain of the given function. x+8 19) f(x) = (x + 5)(x - 7) A) All real numbers C) (- , -8)

(-8 -5)

B) [-8, -5) (-5, 7)

(7, )

(-5, 7)

(7, )

D) (0, )

Identify which of the twelve basic functions listed below fit the description given. 1 1 y = x, y = x2 , y = x 3 , y = x , y = , y = e x , y = x, y = ln x, y = sin x, y = cos x, y = int (x), y = x 1 + e-x 20) The three functions that are even A) y = x2, y = cos x, y = x

B) y = cos x, y = sin x, y = x

C) y = x, y = x2 , y = x 3

D) y = x, y =

1 , y = x3 x

Perform the requested operation or operations. Find the domain of each. 21) f(x) = 4x + 7, g(x) = 4x2 Find (fg)(x). A) 4x2 + 4x + 7; domain: (- , )

B) 16x3+ 28x2 ; domain: (- , )

C) 16x2 + 28x; domain: (- , )

D) 16x + 28; domain: (- , )

Find the (x,y) pair for the value of the parameter. 1 for t = 4 22) x = t + 5 and y = t2 A) -9,

1 16

B)

1 ,- 9 16

C) 1,

3

1 16

D) 9,

1 16

Fill in the blanks to complete the statement. 3 1 3 x + 10 can be obtained from the graph of y = x by shifting horizontally ? units to the 23) The graph of y = 7

? , vertically shrinking by a factor of ? , and then reflecting across the ? -axis. A) 10; left; 1/7; x

B) 10; right; -1/7; y

24) Find functions f and g so that h(x) = f(g(x)). y = A) f(x) =

C) 1/7; right; 10; y

8 10x + 3

10x + 3, g(x) = 8

C) f(x) = 8, g(x) =

D) 10; right; 1/7; x

B) f(x) = 8/x, g(x) = 10x + 3

10 + 3

D) f(x) = 8/ x, g(x) = 10x + 3

25) Perform the requested operation or operations. f(x) = 4x2 + 2x + 7; g(x) = 2x - 8, find g(f(x)). A) g(f(x)) = 8x2 + 4x + 6

B) g(f(x)) = 4x2 + 4x + 6

C) g(f(x)) = 4x2 + 2x - 1

D) g(f(x)) = 8x2 + 4x + 22

Find a direct relationship between x and y. 26) x = t - 6 and y = t2 + t A) y = x2 - 11x + 30

B) y = x2 + 13x + 42

C) y = x2 + x + 42

D) y = x2 + x + 30

Find the inverse of the function. 27) f(x) = x3 - 3 B) f-1 (x) =

A) Not a one-to-one function 3 C) f-1 (x) = x + 3

D) f-1 (x) =

3 3

x+3 x-3

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. 28) f(x) = 15 - 9x + 14x2 - 6x3 - 16x4 A) Degree: 15; leading coefficient: -16

B) Degree: 4; leading coefficient: -16

C) Degree: 4; leading coefficient: 15

D) Not a polynomial function.

Write an equation for the linear function f satisfying the given conditions. 29) f(-3) = 8 and f(1) = 4 A) f(x) = 3x + 1

B) f(x) = -3x - 1

C) f(x) = -8x/3

D) f(x) = -x + 5

Describe the end behavior of the polynomial function by finding lim f x and lim f x . x x 30) f x = -x3 + 7x2 + 3x + 6 A)

,

B)

,

C) ,

D) ,

31) Write the quadratic function in vertex form. y = x2 + 16x + 60 A) y = (x + 8)2 + 4

B) y = (x - 8)2 + 4

C) y = (x + 8)2 - 4 4

D) y = (x - 8)2 - 4

Solve the problem. 32) How many liters of a 10% alcohol solution must be mixed with 70 liters of a 90% solution to get a 80% solution? A) 8 L

B) 80 L

C) 10 L

D) 1 L

33) The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 3 foot-candles, find the intensity on a screen 15 ft from the light. A) 1 1/3 foot-candles

B) 1/4 foot-candle

C) 1/3 foot-candle

D) 2 foot-candles

B) 2 and -2

C) 0, 2, and -2

D) 0 and 2

Find the zeros of the function. 34) f x = x3 - 4x A) 1, 2, and -2

Divide using synthetic division, and write a summary statement in fraction form. 2x5 - x4 + 3x2 - x + 5 35) x-1 A) 2x4 - 3x3 + x +

6 x+1

C) 2x4 + x 3 + 4x 2 + 3x +

8 x+1

B) 2x4 + x 3 - x2 + 2x + 1 +

6 x+1

D) 2x4 + x 3 + x2 + 4x + 3 +

8 x+1

Find the remainder when f(x) is divided by (x - k) 36) f(x) = 4x3 - 3x2 - 2x + 17; k= -2 A) -23

B) 21

C) -50

D) -41

B) -4, -6, 8

C) -3, -6, 4

D) 4, 6, -8

Find all rational zeros. 37) f(x) = x 3 + 5x 2 - 18x - 72 A) 3, 6, -4

Write a linear factorization of the function. 38) f(x) = x 4 - 6x 3 + 33x2 - 150x + 200 A) f(x) = (x + 5)(x - 2)(x - 4i)(x + 4i)

B) f(x) = (x - 4)(x - 2)(x2 + 25)

C) f(x) = (x - 4)(x - 2)(x + 5i)(x - 5i)

D) f(x) = (x - 4)(x + 5)(x - 2i)(x + 2i)

Solve the equation. 5 11 9 + = 39) x-9 x-4 2 x - 13y + 36 A) x =

103 11

B) x = 8

22 5

C) No solution

D) x =

C) (-2, 8)

D) (- , 8)

Solve the polynomial inequality. 40) (x + 2)(x - 8)(x - 10) < 0 A) (10, )

B) (- , -2)

(8, 10) 5

(10, )

For the given function, find all asymptotes of the type indicated (if there are any) x2 + 9x - 2 , slant 41) f(x) = x-5 A) y = x + 4 42) f(x) =

B) x = y + 14

C) None

D) y = x + 14

B) y = 0

C) None

D) y = 5/9

B) 3/2

C) -2/3

D) -3/2

C) x = -20

D) x =

7x2 - 5x - 6 , horizontal 4x2 - 9x + 5

A) y = 7/4 Evaluate the logarithm. 3 43) log8 1/64 A) 2/3

Solve the equation by changing it to exponential form. 44) log x = - 2 A) x =

1

B) x = 20

102

1 210

Rewrite the expression as a sum or difference or multiple of logarithms. 8 r 45) log7 s A) log7 s - log7 8 C) log7 8 ·

1 log7 r 2

B) log7 (8 r) - log7 s

1 log7 r ÷ log7 s 2

D) log7 8 +

1 log7 r - log7 s 2

Write the expression using only the indicated logarithms. 46) log2 10 using common logarithms A) - log 2

B) -

1 log 2

1 log 2

C) log 2

D)

C) x = 25

D) x = 32

C) -30 °

D) -( /6)°

Find the exact solution to the equation. 47) 27x = 32 A) x = 5/7

B) x = 7/5

Convert the radian measure to degree measure. 48) - /6 A) -0.52°

B) -30°

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 49) 124° A) 484°; -56°

B) 484°; -236°

C) 304°; -56° 6

D) 394°; -146°

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. 50)

30

34

16

Find sec A and csc A. 8 15 ; csc A = A) sec A = 17 17 C) sec A =

15 8 ; csc A = 8 15

The given point is on the terminal side of 51) (-6, -4); find tan . 3 A) 2

B)

B) sec A =

17 17 ; csc A = 8 15

D) sec A =

17 17 ; csc A = 15 8

(standard position). Give the exact value of the indicated trig function for . 2 3

C) -

4 7

D) -

6 7

Evaluate without using a calculator by using ratios in a reference triangle. 5 52) cos 3 A)

1 2

B)

Evaluate without using a calculator. 2 and tan 53) sin , if cos = 3 A) -

5

3 2

C) -

3 2

D) -

2 2

3 2

C) -

5 3

D) -

5 2