Pre-Calculus 20 Final Exam Review provides comprehensive coverage of key mathematical concepts and problem-solving strategies essential for success in the course. Topics include arithmetic and geometric sequences, trigonometric ratios, quadratic functions, and rational expressions. This review is designed for high school students preparing for their Pre-Calculus 20 final exam, featuring multiple-choice questions and detailed explanations. Students will find practice problems that reinforce their understanding of critical concepts and enhance their exam readiness.

Key Points

  • Covers arithmetic sequences, including common differences and term calculations.
  • Explains geometric series and their sums, including infinite geometric series.
  • Includes trigonometric ratios for angles in standard position and reference angles.
  • Discusses quadratic functions in vertex form and their characteristics.
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37 pages
AP® Precalculus
newtopiccyclegrowin
37 pages
AP® Precalculus
84
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Name: ________________________
1
Pre-Calculus 20 Final Exam Review
Multiple Choice
Write the correct answer in the blank provided.
____ 1. The common difference in the arithmetic sequence
–10
,
–2
, 6, 14, . . . is
a.
1
5
c.
–8
b. 8 d. 16
____ 2. What is the 18th term of the sequence
−22,−21.2,−20.4,−19.6,−18.8
. . . ?
a.
0
.
8
c.
−
6
.
8
b.
−
3
5
.
6
d.
−
8
.
4
____ 3. The eighth term in the sequence 52 488, 17 496, 5832, 1944, … is
a. 24 c. 3
b.
1
8
d. 8
____ 4. The sum of the geometric series 7 + 14 + 28 +
ë
+ 896 is
a. 1785 c. 445
b. 896 d. 1792
____ 5. Determine the sum of the infinite geometric series 31 +
31
9
+
31
81
+
31
729
+...
a.
279
10
c. 279
b.
25420
729
d.
279
8
____ 6. What is the reference angle for 265° in standard position?
a. 65
°
c. 25
°
b. 5
°
d. 85
°
____ 7. The point (40,
–9
) is on the terminal arm of ∠A. Which is the set of exact primary trigonometric ratios for
the angle?
a.
sin A = −
9
41
,
cos A =
40
41
,
tan A = −
9
40
b.
sin A =
40
41
,
cos A = −
9
41
,
tan A = −
40
9
c.
sin A = −
40
41
,
cos A =
9
41
,
tan A = −
9
40
d.
sin A = −
41
9
,
cos A =
41
40
,
tan A = −
9
40
____ 8. An angle is in standard position such that
cos θ =
1
9
. What are the possible values of
θ
, to the nearest degree,
if
0° ≤ θ ≤ 360°
?
a. 84
°
and 276
°
c. 84
°
and 264
°
b. 6
°
and 276
°
d. 6
°
and 174
°
2
____ 9. What is the exact value for
tan (240
)
?
a.
− 3
c. 1
b.
1
3
d.
3
____ 10. Solve to the nearest tenth of a unit for the unknown side in the ratio
a
sin70°
=
20
sin55°
.
a. 21.3 c. 11.9
b. 17.4 d. 22.9
____ 11. Determine the measure of x, to the nearest tenth of a degree.
a. 37.4
°
c. 52.6
°
b. 23.9
°
d. 118.8
°
____ 12. What is the quadratic function in vertex form for the parabola shown below?
a.
f x( ) = −(x − 3)
2
+ 1
c.
f x( ) = 1(x + 1)
2
+ 1
b.
f x( ) = −(x − 1)
2
+ 3
d.
f x( ) = 1(x − 1)
2
− 3
3
____ 13. What is the vertex of
y = −8(x − 2)
2
+ 5
?
a. (
–8
,
–5
) c. (2, 5)
b. (
–5
,
–2
) d. (
–2
, 5)
____ 14. What information can be determined from the quadratic function
f x( ) = −
3
4
(x − 3)
2
− 4
?
a. the vertex is at (
–4
, 3) and the graph opens upward
b. the vertex is at (3,
–4
) and the graph opens upward
c. the vertex is at (3,
–4
) and the graph opens downward
d. the vertex is at (
–4
, 3) and the graph opens downward
____ 15. Identify the characteristics of this graph.
a. vertex: (2,
–10
)
axis of symmetry:
x = 2
y-intercept:
–8.4
x-intercepts: 7 and
–3
opens upward
c. vertex: (2,
–10
)
axis of symmetry:
x = −10
y-intercept:
–8.4
x-intercepts:
–7
and 3
opens downward
b. vertex: (
–10
, 2)
axis of symmetry:
x = −10
y-intercept:
–8.4
x-intercepts: 7 and
–3
opens downward
d. vertex: (
–10
, 2)
axis of symmetry:
x = −10
y-intercept:
–8.4
x-intercepts: 7 and
–3
opens upward
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FAQs

What types of sequences are covered in the Pre-Calculus 20 review?
The Pre-Calculus 20 Final Exam Review covers both arithmetic and geometric sequences. It explains how to identify common differences in arithmetic sequences and calculate terms in a sequence. Additionally, it discusses geometric series, including how to find the sum of finite and infinite geometric series, which is crucial for understanding series and sequences in mathematics.

How does the review assist with understanding trigonometric ratios?
The review provides detailed explanations of primary trigonometric ratios for angles in standard position. It includes examples that demonstrate how to calculate sine, cosine, and tangent using coordinates from the terminal arm. Students will learn how to find reference angles and apply these concepts to solve problems involving trigonometric functions.

What quadratic functions are discussed in the review?
The review discusses quadratic functions in vertex form, emphasizing how to identify the vertex, axis of symmetry, and intercepts. It provides examples of how to convert standard form to vertex form and explains the significance of these characteristics in graphing quadratic equations. This understanding is essential for solving quadratic equations and analyzing their graphs.

Are there practice problems included in the review?
Yes, the Pre-Calculus 20 Final Exam Review includes multiple-choice practice problems that cover a wide range of topics. These problems are designed to test students' understanding of key concepts and provide opportunities for hands-on practice. Detailed solutions and explanations accompany the problems, helping students learn from their mistakes and reinforce their knowledge.

What is the significance of the review for exam preparation?
This review is significant for students preparing for their Pre-Calculus 20 final exam as it consolidates essential topics and provides a structured approach to studying. By working through the problems and reviewing the explanations, students can identify areas where they need further practice. This targeted review helps build confidence and improve performance on the final exam.