Download PRECALCULUS FINAL EXAMss and more Exams Nursing in PDF only on Docsity!
PRECALCULUS FINAL EXAMss
1. Simplify: 𝟑𝒙
𝟐
𝟐
A. 8 𝑥
B. 8 𝑥
2
C. 15 𝑥
4
D. 2 𝑥
2
Answer: B
Rationale: Like terms have the same variable and exponent. Since both terms contain 𝑥
2
, add the
coefficients: 3 + 5 = 8_. Therefore, the simplified expression is_ 8 𝑥
2
2. Solve: 𝟐𝒙 + 𝟓 = 𝟏𝟕
A. 4
B. 5
C. 6
D. 7
Answer: C
Rationale: Subtract 5 from both sides to obtain 2 𝑥 = 12_. Divide by 2 to get_ 𝑥 = 6_._
3. Factor: 𝒙
𝟐
A.
B. (𝑥 − 3 )
2
C. (𝑥 − 3 )(𝑥 + 3 )
D. Prime
Answer: C
Rationale: This is a difference of squares. Use the formula 𝑎
2
2
4. Evaluate: 𝒇(𝒙) = 𝟐𝒙 + 𝟑 , find 𝒇(𝟒)
A. 8
B. 10
C. 11
D. 13
Answer: C
Rationale: Substitute 𝑥 = 4 : 2 ( 4 ) + 3 = 8 + 3 = 11_._
5. Find the slope between (𝟏
𝟐) and (𝟒
A. 2
B. 3
C. 4
D. 6
Answer: A
Rationale: Use the slope formula:
2
1
2
1
Substituting gives
8 − 2
4 − 1
6
3
6. Solve: 𝒙
𝟐
A. 7
B. - 7
C. ± 7
D. 14
Answer: C
Rationale: Both 7 and - 7 square to 49, so the solutions are ± 7_._
7. Evaluate 𝟑
𝟒
A. 12
B. 27
C. 64
D. 81
Answer: D
Rationale: 3
4
= 3 × 3 × 3 × 3 = 81.
12. Solve: 𝟓𝒙 = 𝟒𝟓
A. 7
B. 8
C. 9
D. 10
Answer: C
Rationale: Divide both sides by 5 to obtain 𝑥 = 9_._
13. Evaluate (−𝟐)
𝟑
A. - 8
B. 8
C. - 6
D. 6
Answer: A
Rationale: Multiplying (− 2 )(− 2 )(− 2 ) gives - 8.
14. Simplify 𝒙
𝟑
𝟒
A. 𝑥
7
B. 𝑥
12
C. 𝑥
D. 𝑥
6
Answer: A
Rationale: When multiplying powers with the same base, add exponents.
15. Solve 𝒙
𝟐
A. 2, 3
B. - 2, - 3
C. 1, 6
D. 0, 6
Answer: A
Rationale: Factor as (𝑥 − 2 )(𝑥 − 3 ) = 0 , giving solutions 2 and 3.
16. Find the vertex of 𝒚 = (𝒙 − 𝟐)
𝟐
A. (2,1)
B. (-2,1)
C. (1,2)
D. (2,-1)
Answer: A
Rationale: Vertex form is 𝑦 = (𝑥 − ℎ)
2
17. Convert 45° to radians
A. 𝜋
B.
𝜋
2
C.
𝜋
4
D.
𝜋
6
Answer: C
Rationale: Multiply by
𝜋
180
∘
𝜋
4
∘
A. 0
B.
1
2
C.
√ 2
2
D. 1
Answer: B
Rationale: This is a special-angle value from the unit circle.
∘
A.
1
2
B.
√ 3
2
A. 2
B. 3
C. 4
D. 5
Answer: C
Rationale: Since 16 = 2
4
, the exponent must be 4.
24. Simplify (𝒙
𝟐
𝟑
A. 𝑥
5
B. 𝑥
6
C. 𝑥
8
D. 𝑥
9
Answer: B
Rationale: Multiply exponents when raising a power to a power.
25. Find the midpoint of (𝟐
𝟒) and (𝟔
A. (4,6)
B. (3,5)
C. (5,6)
D. (4,5)
Answer: A
Rationale: Average the x-values and y-values separately.
26. Distance between (𝟎
𝟎) and (𝟑
A. 4
B. 5
C. 6
D. 7
Answer: B
Rationale: Apply the distance formula or recognize the 3- 4 - 5 right triangle.
𝟐
𝟐
A. 0
B. 1
C. 2
D. tan 𝜃
Answer: B
Rationale: This is the fundamental Pythagorean identity.
28. Solve 𝒙
𝟐
A. - 2
B. 2
C. ±
D. 4
Answer: A
Rationale: Factor as
2
= 0 , giving a repeated root of - 2.
29. Evaluate 𝟒
−𝟏
A. - 4
B. 1
C.
1
4
D. 4
Answer: C
Rationale: A negative exponent means take the reciprocal.
30. The graph of 𝒚 =∣ 𝒙 ∣ is:
A. Circle
B. V-shape
C. Parabola
D. Line
Answer: B
Rationale: Absolute value functions form a V-shaped graph.
Degree of 5 𝑥
4
A. 1
B. 2
C. 3
D. 4
Answer: D
Rationale: The highest exponent is 4.
2 / 3
A. 2
B. 4
C. 8
D. 16
Answer: B
Rationale: The cube root of 8 is 2, and 2
2
Domain of √
A. 𝑥 ≤ 0
B. 𝑥 ≥ 0
C. All real numbers
D. 𝑥 > 0
Answer: B
Rationale: The radicand must be nonnegative.
log
2
A. 2
B. 3
C. 4
D. 8
Answer: B
Rationale: 2
3
2
, find 𝑓(− 3 )
A. - 9
B. 9
C. 6
D. - 6
Answer: B
Rationale: Squaring - 3 gives 9.
Period of 𝑦 = sin 𝑥
A. 𝜋
B. 2 𝜋
C. 4
D. 1
Answer: B
Rationale: The sine function repeats every 2 𝜋 radians.
𝟎
A. 0
B. 1
C. 9
D. 81
Answer: B
Rationale: Any Nonzero Number Raised To The Zero Power Equals 1.
42. What Is The Slope Of A Vertical Line?
A. Undefined
B. 0
C. 1
D. Infinite
Answer: A
Rationale: The Slope Formula Requires Division By Zero For A Vertical Line, Which Is Undefined.
43. Factor 𝒙
𝟐
A.
2
B. (𝑥 − 3 )
2
C.
D. Prime
A. 24
B. 60
C. 120
D. 240
Answer: C
Rationale: Factorial Means Multiplying Consecutive Positive Integers: 5 × 4 × 3 × 2 × 1 = 120_._
49. Solve 𝟐𝒙 − 𝟖 = 𝟏𝟐
A. 8
B. 9
C. 11
D. 10
Answer: D
Rationale: Add 8 To Both Sides To Get 2 𝑥 = 20 , Then Divide By 2.
50. Vertical Asymptote Of 𝒚 =
𝟏
𝒙
A. 𝑥 = 0
B. 𝑦 = 0
C. 𝑥 = 1
D. None
Answer: A
Rationale: The Function Is Undefined At 𝑥 = 0 , Creating A Vertical Asymptote.
A. 0
B. 1
C. 10
D. Undefined
Answer: A
Rationale: Since 10
0
= 1 , The Common Logarithm Of 1 Is 0.
∘
A. 1
B.
1
2
C.
√
2
2
D.
Answer: D
Rationale: This Is A Standard Special-Angle Trigonometric Value.
53. Reflect (𝟐
𝟑) Over The X-Axis
A. (-2,3)
B. (2,-3)
C. (-2,-3)
D. (3,2)
Answer: B
Rationale: Reflection Across The X-Axis Changes The Sign Of The Y-Coordinate.
54. Number Of Real Solutions To 𝒙
𝟐
A. 0
B. 1
C. 2
D. Infinite
Answer: A
Rationale: No Real Number Squared Can Produce - 1.
A. 10
B. 11
C. 12
D. 14
Answer: C
Rationale: 12 Squared Equals 144.
𝟓
A. 16
B. 24
C. 25
D. 32
61. Range Of 𝒚 = −𝒙
𝟐
A. 𝑦 ≤ 0
B. 𝑦 ≥ 0
C. All Real Numbers
D. 𝑦 > 0
Answer: A
Rationale: The Parabola Opens Downward, So Its Maximum Value Is 0.
∘
A. 0
B. 1
C. - 1
D. Undefined
Answer: A
Rationale: The Y-Coordinate Of The Unit Circle At 0° Is 0.
𝟑
A. 2
B. 3
C. 9
D. 27
Answer: B
Rationale: 3
3
= 27 , So The Logarithm Is 3.
A. 12
B. 20
C. 30
D. 36
Answer: C
Rationale: Permutations Are Calculated As 6 × 5 = 30_._
A. 6
B. 10
C. 12
D. 15
Answer: D
Rationale:
6!
2! 4!
66. Solve 𝒙
𝟐
A. ± 8
B. ± 4
C. 8
D. - 8
Answer: A
Rationale: Both 8 And - 8 Produce 64 When Squared.
67. Simplify √𝟒𝟗𝒙
𝟐
A. 49 𝑥
B. 7 ∣ 𝑥 ∣
C. 7 𝑥
D. ∣ 49 𝑥 ∣
Answer: B
Rationale: Square Roots Represent Nonnegative Values, So √𝑥
2
−𝟐
A. 9
B. - 9
C.
1
9
D.
1
3
Answer: C
Rationale: A Negative Exponent Means Take The Reciprocal Of The Positive Power.
69. Amplitude Of 𝒚 = 𝟒𝐬𝐢𝐧 𝒙
A. 1
B. 2
C. 3
D. 4
Answer: D
A.
1
2
B.
√ 2
2
C. √ 3
D. 1
Answer: B
Rationale: This Is A Standard Unit-Circle Value.
∘
A.
1
2
B.
√ 2
2
C. √ 3
D. 1
Answer: B
Rationale: At 45°, Sine And Cosine Have Equal Values.
76. Solve 𝟐𝒙
𝟐
A. ± 9
B. ± 6
C. ± 3
D. ± 2
Answer: C
Rationale: Divide By 2 To Obtain 𝑥
2
= 9 , Then Take Square Roots.
77. Solve 𝟕𝒙 = 𝟓𝟔
A. 6
B. 7
C. 9
D. 8
Answer: D
Rationale: Divide Both Sides By 7 To Get 𝑥 = 8_._
𝟑
A. 4
B. 8
C. 16
D. 32
Answer: A
Rationale: 4
3
𝟐
𝟐
A. 10
B. 12
C. 16
D. 20
Answer: C
Rationale: 25 − 9 = 16_._
80. Sum Of The Interior Angles Of A Triangle
A. 90°
B. 180°
C. 270°
D. 360°
Answer: B
Rationale: The Interior Angles Of Every Triangle Add Up To 180°.
