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Precalculus Midterm Practice
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the equation with the appropriate graph.
- f(x) =
2x
x
A)
x -10 10
y
10
x -10 10
y
10
B)
x -10 10
y
10
x -10 10
y
10
C)
x -10 10
y
10
x -10 10
y
10
D)
x -10 10
y
10
x -10 10
y
10
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the inequality.
x
x
- x + 5 x - 4 ≥ 0 3)
Solve the inequality algebraically. Write the solution in interval notation.
- ∣ 4 x - 5 ∣ ≥ 6 4)
Find the value of the unique real number θ between 0 and 2π that satisfies the given conditions.
- tan θ = -
and cos θ > 0 5)
Solve the equation.
- Solve cot θ = 3 for θ, where 0° ≤ θ ≤ 90° 6)
x
x
x
- log
(2x + 5) - log
(x - 2) = 1 8)
=
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the polynomial function graph to the appropriate zeros and multiplicities.
-10 10
600
-10 10
600
A) 2 (multiplicity 2), - 5 (multiplicity 2) B) 2 (multiplicity 3), - 5 (multiplicity 3)
C) 2 (multiplicity 3),
5 (multiplicity 2) D) 2 (multiplicity 2),
5 (multiplicity 3)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the
polynomial in standard form.
- 3 and 2 - i 11)
Find the exact solution to the equation.
3x)
Find the zeros of the function.
- f(x) = x
Find the zeros of the polynomial function and state the multiplicity of each.
- f(x) = - 4x
(x - 9)(x + 4)
Use the arc length formula and the given information to find the indicated quantity.
- s =
12 cm, θ
36 °; find r 25)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Choose the graph which matches the function.
- f(x) = e
3 - x
x -5 -4 -3 -2 -1 1 2 3 4 5
y 5 4 3 2 1
x -5 -4 -3 -2 -1 1 2 3 4 5
y 5 4 3 2 1
A)
x -5 -4 -3 -2 -1 1 2 3 4 5
y 5 4 3 2 1
x -5 -4 -3 -2 -1 1 2 3 4 5
y 5 4 3 2 1
B)
x -5 -4 -3 -2 -1 1 2 3 4 5
y 5 4 3 2 1
x -5 -4 -3 -2 -1 1 2 3 4 5
y 5 4 3 2 1
C)
x -5 -4 -3 -2 -1 1 2 3 4 5
y 5 4 3 2 1
x -5 -4 -3 -2 -1 1 2 3 4 5
y 5 4 3 2 1
D)
x -5 -4 -3 -2 -1 1 2 3 4 5
y 5 4 3 2 1
x -5 -4 -3 -2 -1 1 2 3 4 5
y 5 4 3 2 1
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Assume that θ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric
function.
- csc θ =
; cos θ 27)
Write the product in standard form.
- ( 7 - 3 i)( 7 + 6 i) 28)
Solve the equation algebraically.
- x(x
Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational.
- f(x) = x
Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f(x) =
1/x.
- f(x) =
4 x
x - 5
Find the exponential function that satisfies the given conditions.
- Initial mass =
476 g, halving once every 24 hours 32)
Give the equation of the function g whose graph is described.
- The graph of f(x) =
x is shifted 7.3 units to the left. This graph is then vertically stretched
by a factor of 3.0. Finally, the graph is reflected across the x-axis.
Find a cubic function with the given zeros.
Find the domain of the given function.
- f(x) =
x + 3
(x
8)(x
Find all rational zeros.
- f(x) = x
State the domain of the rational function.
- f(x) =
(x
3 )(x
x
Write a linear factorization of the function.
- f(x) = 5x
Answer Key
Testname: PRECALCULUS PRACTICE MIDTERM
1) D
] ∪ [
11 π
- x = -
10) D
- f x = x
x = 3
2 , 4 , and 6
- 4 , multiplicity 3; 0, multiplicity 2; 9 , multiplicity 1
- y = (x + 2)
19) [
2 , 6 ]
x = 4 , x = - 4
y = 1
x
-10 -5 5
y
10
5
x
-10 -5 5
y
10
5
π
cm
26) C
- 67 + 21i
Answer Key
Testname: PRECALCULUS PRACTICE MIDTERM
- 4 (rational), 3 (irrational), and - 3 (irrational)
Shift the graph of the reciprocal function right 5 units, stretch vertically by a factor of 19 , and then shift 4 units up.
m(t) = 476 ·
t/ 24
- g(x) = -
x
- f(x) = x
35) [
- f(x) = 5 x(x + i)(x - i)
i
- Reflect across the y-axis and then translate 6 units to the right.
