University:
East Georgia State College
Course:
MATH 1001 | Quantitative Skills & Reasoning
Academic year:

2021
Views:

121

Pages:

17
Author:

StellarStrategist

Semester 2 Final Exam REVIEW Name:_______________________________________ Pre-Calculus Chapter 7 – Analytic Trigonometry Simplify the expression. 1. 2. 4. 5. 3. ( ) Verify the identity. 7. 8. 9. 10. 6. Use an addition or subtraction formula to find the EXACT value of the expression. 11. 12. 13. Find 14. and ; from the given information. 15. x in quadrant II Use a half-angle formula to find the EXACT value of the expression. 16. 17. 18. Find the EXACT value of each expression, if it is defined. 19. 22. 20. ( √ ) 23. ( ( √ ) ) 21. 24. ( ) Find all solutions of the equation. Work and answers must be in radians. 25. √ 26. 27. 28. Find all solutions of the equation in the interval 29. ). 30. Chapter 8 – Polar Coordinates & Vectors Graph each point and label them accordingly. Then find the rectangular coordinates of each point. 1. ( 2. ( ) ) 0 3. ( ) 4. ( ) A point P(r, θ) is given in polar coordinates. Give two other polar representations of the point, one with r < 0 and one with r > 0. 5. ( 6. ( ) ) Convert the rectangular coordinates to polar coordinates with r > 0 and 7. ( √ ) 8. ( √ √ ) . Match the equation with its graph. Name each shape. 9. 10. 11. 12. 13. 14. A. B. C. D. E. F. A complex number is given. Find the modulus and then write the complex number in polar form. 15. 16. Find the product 18. ( and the quotient ) ( 17. √ . Express your answer in polar form. ) Find the indicated power using DeMoivre’s Theorem. Write your answer in complex number form. 19. ( √ 20. ( √ ) ) Express the vector with initial point P and terminal point Q in component form. 21. ( ) ( 22. ) Find u + v, -3u + 5v, | |, and | 23. 〈 〉 〈 ) ( |. 24. 〉 25. Find the vector with | | ( and . 26. Find the magnitude and direction of the vector . ) Find (a) 27. (dot product) and (b) the angle between u and v to the nearest degree. 〈 〉 〈 28. 〉 29. Determine whether and 30. Given 31. Find the work done by the force √ √ are orthogonal. , find ( ). in moving an object from P(0, 10) to Q(5, 25). 〈 〉 moves an object along a straight line from point (2, 5) to the point (11, 32. A constant force 13). Find the work done if the distance is measured in feet and the force is measured in pounds. Chapter 10 - Conics Graph the ellipse and identify the center, vertices, and foci. 1. 2. Center:___________ Center:___________ Vert:__________ Vert:__________ Foci:________ Foci:________ 3. ( ) ( ) 4. ( ) ( Center:___________ Center:___________ Vert:__________ Vert:__________ Foci:________ Foci:________ ) Find the standard form of the equation of each ellipse. 5. Foci (0, 3), vertices (0, 4) 6. Major axis vertical with length 20; length of minor axis 10; center: (2, -3) 7. Foci ( 5, 0), length of major axis 12 8. Endpoints of major axis: (7, 9) & (7, 3) Endpoints of minor axis: (5, 6) & (9, 6) 9. 10. Convert the equation to standard form by completing the square. 11. Graph the hyperbola and identify the center, vertices, asymptotes, and foci. 12. 13. Center: ___________ Center: ___________ Vertices:___________ Vertices:___________ Foci:__________ Foci:__________ Asymptotes:________ Asymptotes:________ 14. ( ) ( 15. ) ( ) ( ) Center:____________ Center: ____________ Vertices:___________ Vertices:___________ Foci:__________ Foci:__________ Asymptotes:________ Asymptotes:________ Find the standard form of the equation of each hyperbola. 16. Foci (0, ), vertices (0, ) 18. Endpoints of transverse axis: (0, Asymptotes: y = x 17. Vertices ( 4, 0), Asymptotes: ) 19. Foci (0, 1), length of transverse axis 1 Convert the equation to standard form by completing the square. 20. Graph the parabola and identify the vertex, directrix, and focus. 21. 22. Vertex: _______ Vertex: _______ Dir: _______ Dir: ____________ Focus:___________ Focus:_________ 23. ( ) ( ) 24. ( Vertex: _______ Vertex: _______ Dir: ___________ Dir: __________ Focus: ________ Focus:________ ) Write an equation in standard form for the parabola satisfying the given conditions. 25. Focus: (8, 0); Directrix: x = -8 26. Vertex: (2, -3); Focus (2, -5) Find the equation for the parabola whose graph is shown. 27. 28. Convert the equation to standard form by completing the square. 29. Chapter 11 – Sequences & Series Find the first five terms of the recursively defined sequence. 1. ; 3. Find the sum: 2. 4 k 2 ; 4. Write the sum using sigma notation: k 1 Determine whether the sequence is arithmetic or geometric. Identify the common difference or the common ratio. 5. 6. 2, 4, 6, 8, … 7. Determine the common difference, the fifth term, the nth term, and the 100th term of the arithmetic sequence -12, -8, -4, 0, … 8. The 12th term of an arithmetic sequence is 32, and the fifth term is 18. Find the 20th term. 9. Which term of the arithmetic sequence 1, 4, 7, … is 88? 10. Find the partial sum of the arithmetic sequence that has . A partial sum of an arithmetic sequence is given. Find the sum. 11. ( ) 12. 20  1  2n n 0 13. An arithmetic sequence has first term and common difference this sequence must be added to get 2700? . How many terms of 14. Determine the common ratio, the fifth term, and the nth term of the geometric sequence 15. The first term of a geometric sequence is 3, and the third term is . Find the fifth term. 16. Which term of the geometric sequence 2, 6, 18, … is 118,098? 17. Find the partial sum of the geometric sequence 1 + 3 + 9 + 18. Find the sum of the infinite geometric series 19. Express as a fraction. + 2187. Use the Binomial Theorem to expand. 21. ( 22. ( ) ) 23. Find the eleventh term in the expansion of ( 24. Find the term containing ) . in the expansion of (√ ) . Chapter 12 – Limits 1. For the function g whose graph is given, state the value of the given quantity, if it exists. a) ( ) b) ( ) c) d) ( ) e) ( ) f) g) g(2) h) ( ) ( ) ( ) i) g(0) Find the limit algebraically. 2. 5. (𝑥 𝑥 𝑥 )(𝑥 3. 𝑥) 𝑥 𝑥 6. 𝑢 𝑢 𝑢 4. √ 7. ℎ 𝑥 𝑥 𝑥 (𝑥 𝑥 𝑥 𝑥 ) 𝑥 8. Evaluate the limits using the function below. ( ) a) { ( ) b) ( ) c) ( ) d) ( ) e) ( ) Find an equation of the tangent line to the curve at the given point. Use: 9. ( ) at (1, 1) 10. ( ) at -1 12. ( ) Use the power rule to find the derivative of the function 13. ( ) 14. ( ) 𝑓(𝑎) 𝑎 at (-1, 1) ( ) Find the derivative of the function at the given number. Use 11. 𝑥 𝑓(𝑥) 𝑎 𝑥 𝑓(𝑎 ) 𝑓(𝑎) ℎ at 3 ( ). Then find ( ). 15. ( ) √

Math Pre-Calc Semester 2 Final Exam Review

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