Precalculus
1. Does the table describe a function?
A) no
B) yes
2. Does the table describe a function?
A) yes
B) no
3. Which set of ordered pairs represents a function from P to Q?
P = {3, 6, 9, 12} Q = {–4, –2, 0}
A) {(3, –4), (6, –2), (6, 0), (9, –2), (12, –4)}
B) {(9, –4), (9, –2), (9, 0)}
C) {(9, –2), (6, –4), (3, –2), (6, 0), (9, –4)}
D) {(6, –2), (9, 0), (12, –2)}
E) {(3, 0), (9, –2), (3, –4), (9, 0)}
4. Evaluate the function at the specified value of the independent variable and simplify.
g (y) = 6y + 2
g (–0.9)
A) –5.4y + 12
B) –7.4
C) –3.4
D) –0.9y + 2
E) –0.9y – 2
5. Evaluate the function at the specified value of the independent variable and simplify.
f (x – 1)
A) B) C) D) E)
6. Find all real values of x such that f (x) = 0.
A) B) C) D) E)
7. Find the value(s) of x for which f (x) = g (x).
f (x) = x2 + 5x – 18 g (x) = 4x – 6
A) –18, –23, B) –18, 5, C) 3, –4
D) –3, 4
E) 13,
8. Find the domain of the function.
A) all real numbers B) all real numbers , C) all real numbers
D) s = –6, s = 0
E) s = –6
9. Find the difference quotient and simplify your answer.
f (x) = 4×2 + 3x, , h 0A) 5 + h
B) C) D) 3 + 4h
E) 11 + 4h
10. A rectangle is bounded by the x-axis and the semicircle (see figure). Write the area A of the rectangle as a function of x and determine the domain of the function.
–9 9
A) , –9x9B) , x0C) , –9x9D) , all real numbersE) , x0
11. Use the Vertical Line Test to determine in which of the graphs y is not a function of x.
A) x
B) x
C) x
D) x
E) All of the choices (A, B, C, and D) represent functions.
12. Find the zeroes of the functions algebraically.
A) x = 3, x = –7, B) x = 3, x = –7
C) D) x = –3, x = 7
E) x = –3, x = 7,
13. Determine the intervals over which the function is increasing, decreasing, or constant.
A)
B)
C)
D)
E)
14. Graph the function and determine the interval(s) for which f (x) 0.
f (x) = –x2 – 2x
A) B) C) D) E) {–2}
15. Determine whether the function is even, odd, or neither.
A)
B)
C)
16. Evaluate the function for the indicated values.
(i) f (1) (ii) f (–5.5) (iii) f A) (i) 24 (ii) –5 (iii) 19
B) (i) 24 (ii) –5 (iii) 23
C) (i) 23 (ii) –1 (iii) 23
D) (i) 23 (ii) –1 (iii) 19
E) (i) 23 (ii) –5 (iii) 19
17. Which function does the graph represent?
A)
B)
C)
D)
E)
18. Which graph represents the function?
A)
B)
C)
D)
E)
1. Graph the given function.
A)
B)
C)
D)
E)
2. Compare the graph of with .A) shifts right units, shifts downward units, and shrinks by a factor of .B) shifts right units, shifts upward units, and stretches by a factor of .C) shifts left units, shifts downward units, and stretches by a factor of .D) shifts right units, shifts upward units, and shrinks by a factor of .E) shifts left units, shifts upward units, and stretches by a factor of .
3. Determine the vertex of the graph of the quadratic function .A) B) C) D) E)
4. From the graph of the quadratic function , determine the equation of the axis of symmetry.
A) B) C) D) E)
5. Determine the x-intercept(s) of the quadratic function .A) B) C) D) E) no x-intercept(s)
6. Determine the x-intercept(s) of the quadratic function .A) B) C) D) E) no x-intercept(s)
7. Write the quadratic function, , in standard form.A) B) C) D) E)
8. Write the quadratic function, , in standard form.A) B) C) D) E)
9. Find the standard form of the quadratic function shown below:
A)
D)
B)
E)
C)
10. Write the standard form of the equation of the parabola that has a vertex at and passes through the point .A) B) C) D) E)
11. Match the equation with its graph.
A)
D)
B)
E)
C)
12. Find all real zeros of the polynomial and determine the mutiplicity of each.
A) , multiplicity 2; , multiplicity 1B) , multiplicity 1; , multiplicity 1; , multiplicity 1C) , multiplicity 2; , multiplicity 1D) , multiplicity 1; , multiplicity 1; , multiplicity 1E) , multiplicity 3
13. Find all real zeros of the polynomial and determine the mutiplicity of each.
A) , multiplicity 2; , multiplicity 2B) , multiplicity 2; , multiplicity 2C) , multiplicity 2; , multiplicity 1D) , multiplicity 2; , multiplicity 2E) , multiplicity 1; , multiplicity 1; , multiplicity 1; , multiplicity 1
14. Use long division to divide.
A) B) C) D) E)
15. Use synthetic division to divide.
A) B) C) D) E)
16. Use synthetic division to divide.
A) B) C) D) E)
17. Write in the form when .A) B) C) D) E)
18. If , use synthetic division to evaluate .A) B) C) D) E)
19. If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) ; B) ; C) ; D) ; E) ;
20. Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.A) B) C) D) E)
21. Simplify the rational expression, , by using long division or synthetic division.
A) B) C) D) E)
22. Simplify the rational expression, , by using long division or synthetic division.
A) B) C) D) E)
23. Write the complex number in standard form.A) B) C) D) E)
24. Simplify and write the answer in standard form.A) B) C) D) E)
25. Write the complex conjugate of the complex number .A) B) C) D) E)
26. Combine and write the answer in standard form.A) B) C) D) E)
27. Use the quadratic formula to solve .A) B) C) D) E)
28. Simplify and write the answer in standard form.A) B) C) D) E) The expression cannot be simplified.
29. Find all the rational zeros of the function .A) B) C) D) E)
30. Find all real solutions of the polynomial equation .A) B) C) D) E)
1. Evaluate the trigonometric function using its period as an aid.
A) B) C) D) E)
2. Use trigonometric identities to transform the left side of the equation into the right side. Assume all angles are positive acute angles, and show all of your work.
3. Use trigonometric identities to transform the left side of the equation into the right side. Assume all angles are positive acute angles, and show all of your work.
4. Solve for y.
19
A) B) C) D) E)
5. Solve for x.
23
A) B) C) D) E)
6. Solve for r.
9
A) B) C) D) E)
7. Using the figure below, determine the exact value of the given trigonometric function.
A)
B)
C)
D)
E)
8. The point is on the terminal side of an angle in standard position. Determine the exact value of .A) B) C) D) E)
9. The point is on the terminal side of an angle in standard position. Determine the exact value of .A) B) C) D) E)
10. The point is on the terminal side of an angle in standard position. Determine the exact value of .A) B) C) D) E)
11. State the quadrant in which lies.
> 0 and > 0A) Quadrant III
B) Quadrant IV
C) Quadrant I
D) Quadrant II
E) Quadrant II or Quadrant IV
12. State the quadrant in which lies.
< 0 and > 0A) Quadrant III
B) Quadrant I
C) Quadrant IV
D) Quadrant II
E) Quadrant I or Quadrant III
13. Use the function value and constraint below to evaluate the given trigonometric function.
Function Value Constraint Evaluate:
A)
B)
C)
D)
E)
14. Use the function value and constraint below to evaluate the given trigonometric function.
Function Value Constraint Evaluate:
A) B) C) D) E) undefined
15. The terminal side of lies on the given line in the specified quadrant. Find the value of the given trigonometric function of by finding a point on the line.
Line Quadrant Evaluate:
IV A) B) C) D) E)
16. Find the reference angle for the given angle .
A) B) C) D) E)
17. Evaluate the sine of the angle without using a calculator.
A) B) C) D) E) 0
18. Evaluate the cosine of the angle without using a calculator.
A) B) C) D) E) 0
19. Evaluate the tangent of the angle without using a calculator.
A) B) C) D) E) 0
20. Find the indicated trigonometric value in the specified quadrant.
A) B) C) D) E) undefined
21. Sketch the graph of the function below, being sure to include at least two full periods.
A)
B)
C)
D)
E)
22. Sketch the graph of the function below, being sure to include at least two full periods.
A)
B)
C)
D)
E)
23. Find a andd for the function such that the graph of matches the graph below.
A)
B)
C)
D)
E)
24. Find a, b, and c for the function such that the graph of matches the graph below.
A)
B)
C)
D)
E)
25. Evaluate the trigonometric function using its period as an aid.
A) B) C) D) E)
1. Determine the quadrant in which the angle lies. (The angle measure is given in radians.)
A) II
B) III
C) IV
D) I
E) The angle lies on a coordinate axis.
2. Determine two coterminal angles (one positive and one negative) for the given angle. Give your answer in radians.
3. Find (if possible) the complement and supplement of the given angle.
A)
B)
C)
D)
E)
4. Rewrite the given angle in radian measure as a multiple of . (Do not use a calculator.)
A) B) C) D) E)
5. Rewrite the given angle in radian measure as a multiple of . (Do not use a calculator.)
A) B) C) D) E)
6. Rewrite the given angle in degree measure. (Do not use a calculator.)
A) 630°
B) 345°
C) 285°
D) 330°
E)
7. Rewrite the given angle in degree measure. (Do not use a calculator.)
A) –216°
B) –78°
C) –138°
D) –93°
E)
8. Find the angle in radians.
A)
B)
C)
D)
E)
9. Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
radius: r = 7 centimeters arc length: s = 25 centimeters
A) B) C) D) E) 10. Find the length of the arc on a circle of radius r intercepted by a central angle .
radius: r = 11 inches central arc: A) B) C) D) E)
11. Find the area of the sector of the circle with radius r and central angle .
radius: r = 3 kilometers central arc: A) B) C) D) E)
12. Determine the exact value of .
A) B) C) D) E)
13. Determine the exact value of .
A) B) C) D) E) 1
14. Find the point (x, y) on the unit circle that corresponds to the real number t.
A)
B)
C)
D)
E)
15. Evaluate, if possible, the given trigonometric function at the indicated value.
A)
B)
C)
D)
E)
16. Find the exact value of the given trigonometric function of the angle shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
a = 8
A) B) C) D) 1
E)
17. Find the exact value of the given trigonometric function of the angle shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
a = 8
A) B) C) D) 1
E)
18. Find the exact value of the given trigonometric function of the angle shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
a = 4
A) B) –1
C) D) 1
E) 4
19. Find the exact value of the given trigonometric function of the angle shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
b = 16, c = 34
A) B) C) D) E)
20. Find the exact value of the given trigonometric function of the angle shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
b = 8, c = 17
A) B) C) D) E)
21. Given that , find .
[Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle , then use the Pythagorean Theorem to determine the third side.]A) B) C) D) E)
22. Given that , find .
[Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle , then use the Pythagorean Theorem to determine the third side.]A) B) C) D) E)
23. Given that , find .
[Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle , then use the Pythagorean Theorem to determine the third side.]A) B) C) D) E)
24. Given that , find .
[Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle , then use the Pythagorean Theorem to determine the third side.]A) B) C) D) E)
25. Use the given function values and the trigonometric identities (including the cofunction identities), to find the indicated trigonometric function.
; find A) B) C) D) E) 1
26. Use the given function values and the trigonometric identities (including the cofunction identities), to find the indicated trigonometric function.
; find A) B) C) D) E)
27. Use the given function values and the trigonometric identities (including the cofunction identities), to find the indicated trigonometric function.
; find A) B) C) D) E)
28. Use the given function values and the trigonometric identities (including the cofunction identities), to find the indicated trigonometric function.
; find A) B) C) D) E) 1. If , evaluate the following function.
A)
B)
C)
D)
E)
2. If , evaluate the function below.
A)
B)
C)
D)
E)
3. Which of the following is equivalent to the expression below?
A)
B)
C)
D)
E)
4. Which of the following is equivalent to the expression below?
A)
B)
C)
D)
E)
5. Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent.
A)
B)
C)
D)
E)
6. Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent.
A)
B)
C)
D)
E)
7. Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.
A)
B)
C)
D)
E)
8. Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.
A)
B)
C)
D)
E)
9. Add or subtract as indicated; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.
A)
B)
C)
D)
E)
10. Which of the following is equivalent to the given expression?
A)
B)
C)
D)
E)
11. If , use trigonometric substitution to write as a trigonometric function of , where .A) B) C) D) E)
12. Verify the identity shown below.
13. Verify the identity shown below.
14. Verify the identity shown below.
15. Verify the identity shown below.
16. Find the exact value of given that and . (Both u and v are in Quadrant II.)
A) B) C) D) E)
17. Find the exact value of given that and . (Both u and v are in Quadrant II.)
A) B) C) D) E)
18. Verify the given identity.
HW Chapter 5 End
Name: __________________________ Date: _____________
1. Solve the following equation.
A)
B)
C)
D)
E)
2. Find all solutions of the following equation in the interval .
A)
B)
C)
D)
E)
3. Find the exact value of the given expression.
A) B) C) D)
4. Find the exact value of the given expression using a sum or difference formula.
A) 1
B) –1
C) D) E) undefined
5. Write the given expression as the sine of an angle.
A) B) C) D) E)
6. Write the given expression as the cosine of an angle.
A) B) C) D) E)
7. Find the exact value of given that and . (Both u and v are in Quadrant II.)
A) B) C) D) E)
8. Find the exact value of given that and . (Both u and v are in Quadrant II.)
A) B) C) D) E)
9. Use a double angle formula to rewrite the given expression.
A) B) C) D) E)
10. Use a double-angle formula to find the exact value of when .A) B) C) D) E)
11. Use the power-reducing formulas to rewrite the given expression in terms of the first power of the cosine.
A)
B)
C)
D)
E)
12. Use the half-angle formula to simplify the given expression.
A) B) C) D) E)
13. Use the product-to-sum formula to write the given product as a sum or difference.
A) B) C) D) E)
14. Use the sum-to-product formulas to write the given expression as a product.
A) B) C) D) E)
15. Verify the given identity.
Test Chapter 2 – Pre Calculus Fall 2015
Name: __________________________ Date: _____________
1. Graph the given function.
A)
D)
B)
E)
C)
2. Compare the graph of with .A) shifts right units, shifts downward units, and shrinks by a factor of .B) shifts right units, shifts upward units, and stretches by a factor of .C) shifts left units, shifts downward units, and stretches by a factor of .D) shifts right units, shifts upward units, and shrinks by a factor of .E) shifts left units, shifts upward units, and stretches by a factor of .
3. Compare the graph of with .A) shifts right units, shifts downward units, and shrinks by a factor of .B) shifts right units, shifts upward units, and shrinks by a factor of .C) shifts left units, shifts downward units, and shrinks by a factor of .D) shifts right units, shifts upward units, and shrinks by a factor of .E) shifts left units, shifts upward units, and shrinks by a factor of .
4. Determine the vertex of the graph of the quadratic function .A) B) C) D) E)
5. From the graph of the quadratic function , determine the equation of the axis of symmetry.
A) B) C) D) E)
6. Determine the x-intercept(s) of the quadratic function .A) B) C) D) E) no x-intercept(s)
7. Write the quadratic function, , in standard form.A) B) C) D) E)
8. Find the standard form of the quadratic function shown below:
A)
B)
C)
D)
E)
9. Write the standard form of the equation of the parabola that has a vertex at and passes through the point .A) B) C) D) E)
10. Use long division to divide.
A) B) C) D) E)
11. Use long division to divide.
A) B) C) D) E)
12. Use synthetic division to divide.
A) B) C) D) E)
13. Use synthetic division to divide.
A) B) C) D) E)
14. If , use synthetic division to evaluate .A) B) C) D) E)
15. If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) ; B) ; C) ; D) ; E) ;
16. If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) ; B) ; C) ; D) ; E) ;
17. If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) ; B) ; C) ; D) ; E) ;
18. Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.A) B) C) D) E)
19. Simplify and write the answer in standard form.A) B) C) D) E)
20. Write the complex conjugate of the complex number .A) B) C) D) E)
21. Combine and write the answer in standard form.A) B) C) D) E)
22. Use the quadratic formula to solve .A) B) C) D) E)
23. Find the zeros (if any) of the rational function .A) B) C) and D) E) There are no zeros.
24. Find the zeros (if any) of the rational function .A) and B) C) D) E) There are no zeros.
25. Find all x-intercepts for the function . A) and B) and C) D) E)