College Pre Calculus A Period. Weekly Review Sheet # 1 Assigned: Monday, 9/9/2013 Due: Friday, 9/13/2013

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1 College Pre Calculus A Name Period Weekly Review Sheet # 1 Assigned: Monday, 9/9/013 Due: Friday, 9/13/013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT. 1. What is the simplest form of 4 1 x 8 1 x x?. Write the quadratic equation, with no fractions, with the sum of the roots equal to 4 9 and product equal to What is the domain of the function shown below in interval notation? 4. What is the equation of the trigonometric function graphed below? Be sure to justify your answer here: Be sure to justify your answer here: 5. What is the range of the function shown below in interval notation? 6. In the right triangle shown below, what is the measure of angle S, to the nearest degree? Be sure to justify your answer here:

2 7. What is the middle term in the expansion 8. What is the equation represented by the graph 6 of ( x below? y)? x 9. Express x simplest form x with a rational denominator in Solve for x: ( x ) If g ( x) x 4x 1, evaluate g ( x ) 1. Solve algebraically for x: ( log 7 x 1) Express the product of cos 30 and sin 45 in simplest radical form. 14. If g( x) ( ax 1 x) form., express g(10) in simplest cot xsin x 15. Express as a single trigonometric sec x function, in simplest form, for all values of x for which it is defined. Use this space to show work for #15:

3 College Pre Calculus A Name Period Weekly Review Sheet # Assigned: Monday, 9/16/013 Due: Friday, 9/0/013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT. 1. Write an equation for the graph of the trigonometric function shown below:. 3. Solve for x: 3x + x = 0 4. Factor Completely: 3a 48b 4 5. Simplify the complex fraction: x 3 x 9 6. What is the solution set for the equation 5x 9 x 3

4 Solve 10 x algebraically and express the x result in simplest radical form Evaluate ( x 9) when x = 6. Express your answer in fractional form. 10. Solve for x: 4 8 x 5 3x 11. Solve for x: log 5 x 4 1. What is the radian measure of the smaller angle formed by the hands of a clock at 7 o clock? 13. Simplify the expression What is the range of the function ( x 4) 7? (give answer in interval notation) 15. Jasper invests $5,000 in an account that pays 4.75% annual interest compounded continuously. rt Using the formula A Pe, where A = amount in the account after t years, P = principal invested, and r = annual interest rate, how many years, to the nearest tenth, will it take for Jasper s investment to triple? Show all work for #15 here:

5 College Pre Calculus A Name Period Weekly Review Sheet # 3 Assigned: Monday, 9/3/013 Due: Friday, 9/7/013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT. 1. Solve for x: x + 4 = 3. Factor: 4x 0x Solve for x and write answer in interval notation: x + 3 > 4 4. Solve for x and write answer in interval notation: x 1 < 4 5. Find the equation of the line passing through the point (-1,-) and parallel to x y + 3 = 0 6. Factor: 15 64x 3 7. Find the distance from the point (4,) to the line 6x 8y + 1 = 0 8. Find the distance between the parallel lines 3x y + 1 = 0 and 3x y = 7

6 9. Find all values of x if the distance from A (-3, 1) and B (x, 6) is If the midpoint of AB is (-8,6), with A (3,4), find the coordinates of B. 11. Find the length of AB if A (3,-7) and B(-1,4). 1. Solve and give answer in interval notation: x 3 3x Factor: 5x 10x Factor: 15x 11x What is the 3 rd term in the expansion of 3 4 ( x 3y ) Use this space to continue to show your work for question #15

7 College Pre Calculus A Name Period Weekly Review Sheet # 4 Assigned: Monday, 9/30/13 Due: Friday, 10/4/13 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT. 1. Solve and write answer in interval notation x 9 5x 3. Write the equation of the line passing through the point (,-5) and perpendicular to the line 4x + 3y + = 0 in general form. 3. Factor: 7 y Factor Completely: 16 64x 3 5. Factor: x 4 10x 9 6. Find the distance between the two parallel lines 5x 4y = -5 and 5x 4y 7 = 0 7. Factor: x 6x 9 y 8. Algebraically find the domain of 1 x 3 9. Find the range of g ( x) 5 x Algebraically find the domain of h ( x) x 7

8 1 11. Algebraically find the range of h ( x) x 7 1. Find the distance from the point (4,-7) to the line 3x y = 5 in simplest radical form. 13. What is the equation of the horizontal line passing through the point (-7,6)? 14. Write the equation of the line parallel to the line segment with endpoints (-3,5) and (4,7) and contains the point (-1,6) in general form 15. Find the midpoint of AB with coordinates of A, and B, Find the (x, y) table of values for each part of the function, sketch the piecewise graph and then find the domain and range. [10 Points] x, x 0 x 1, x 0 Domain: Range:

9 College Pre Calculus A Name Period Weekly Review Sheet # 5 Assigned: Monday, 10/7/013 Due: Friday, 10/1/013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT. 1. Find all values of x if the distance from A (x,3) to B (5,7) is 5.. Factor: 64 7x Factor: 9x 18x x 4. Find the range of g ( x) x 5 (Note If you are using a graph to answer this question, it must be a complete graph) 5. Algebraically find the domain of 1x x 7 6. If x 5 and g ( x) x, f find (x) g 7. If x x 6 and g ( x) x 9, find ( f g)( x) 8. Write the equation of the line parallel to 3y x = 5 and passing through the point (6,-1) in general form.

10 9. Complete the square to write the equation of g ( x) 5x 10x 6 in standard form of a quadratic equation for graphing 10. Find the distance from the point (-,) to the line 5x 3y +1 = 0 Part II: 0 Points 11. An object 160 feet above the ground is shot straight up with an initial velocity of 48 ft/sec. a. Write the general formula for projectile motion b. Write the equation that would be used to represent this problem c. Draw the graph that represents the problem situation: d. When will the object reach is maximum height? e. What is the maximum height? f. When will the projectile hit the ground?

11 College Pre Calculus A Name Period Weekly Review Sheet # 6 Assigned: Monday, 10/1/13 Due: Friday, 10/5/013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT. 1. Determine the number of real zeros of the. Solve and write the answer in interval notation quadratic function 3x 5x 7 5x Algebraically find the range of 4 x x 3 4. Draw a complete graph and find the range of ( x 6) ( x Hint: look at the window on test # 3) 5. What is the equation of the line, in general form, passing through the points (5,-4) and (-3,)? 6. Find the distance from the point (-3,) to the line x 5y 1 = Factor completely: 8x 1x x 3 8. Complete the square and find the vertical shift of the function x 8x 6

12 9. Write the equation of the function that would be used to represent the area of a sidewalk with a uniform width x surrounding a rectangular garden that is 19 feet wide and 7 feet long. 10. A rectangular fence is used to enclose a plot of land with an existing wall as one side. If only 750 feet of fencing is used, write the equation used to find the area of the plot of land. 11. Graph the function from #9 above and find the width of the sidewalk if the area of the sidewalk is 350 square feet. [8 Points] 1. Graph the function from #10 above and find the maximum area of the plot of land and the dimension of the plot that produces that maximum area. [8 Points] Maximum Area: Width of sidewalk: Dimensions of the plot: Part II: 14 Points 13. Complete the square on the quadratic equation y x 14x 5 and list all transformations from the graph of y = x, then find the vertex, axis of symmetry, domain and range List all transformations: Vertical stretch or shrink: Reflect over x axis? Horizontal Shift: Vertex: Domain: Vertical Shift: Equation of Axis of Symmetry: Range:

13 College Pre Calculus A Name Period Weekly Review Sheet # 7 Assigned: Monday, 10/8/013 Due: Friday, 11/1/013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT. 1. Evaluate: ( x h) 5 (Write the answer for this question neatly along the bottom of the answer sheet it s really long). Evaluate: 3 4 ( 3a 5b ) (Write the answer for this question along the bottom of the answer sheet it s really long, too) 3. Find the difference quotient for 7x 14x 5 4. Find f "( x) if 6x 5 3x 4 x 6x Identify the domain and range of y x 3 6. Express as a single fraction, ( f g)( x) if ( 5) x 3 and g ( x) x 4

14 7. Solve graphically x 8x 7 8. Solve by completing the square 4x 0x Find the distance between the parallel lines 4x y 5 0 and 4x y Algebraically find the range of 5x 7 y x Factor: x 4 13x Solve and write answer in interval notation 3x Complete the square and identify the vertical shift of the graph of y 3x 1x What is the horizontal shift of the graph y 3x 1x 1? (use your work from #13) 15. Write the equation of the line perpendicular to 3x 4y 0 and passing through the point (1,-5) in general form Continue work for #15 here:

15 College Pre Calculus A Name Period Weekly Review Sheet # 8 Assigned: Monday, 11/4/013 Due: Friday, 11/8/013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT. 1. Graphically find the solution to 3 x 5x 3x 7in interval notation. Solve using sign patterns and write answer in interval notation: x 3 + x 6x > 0 Zeros: Answer: 3. Factor: 7 xy 7 4 x y Find the center and the radius of the circle x y 1x 8y Find the value(s) of x if the distance between A (1, 14) and B (x,) is equal to Find the inverse, f -1 (x), if 3x, x 5 x 5

16 7. Solve using sign patterns and write answer in 3 x interval notation: 0 x 5x 8. Find the solution to the compound inequality 4 3x The cost equation for manufacturing calculators is c( x) x 10x 31where c(x) is the cost in thousands of dollars for x units. Graphically find the number of units for a cost of 535 thousand dollars. 10. If (x, ) is in relation to 3x y 1 139, find all values of x 11. An object 30 feet above the ground is shot straight up with an initial velocity of 50 feet per second. For what period of time will the object be at least 550 feet the ground? (15 Points) Identify variables and write equation here: Graph the problem situation here: Completely answer the problem here:

17 College Pre Calculus A Name Period Weekly Review Sheet # 9 Assigned: Monday, 11/18/013 Due: Friday, 11//013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT. x 3x. Find the inverse, f 1 ( ) 1. Use a sign chart to solve 0 x, if 5 x 3x 7 ; x 4 x 4 3. Determine all real zeros of 3 x 11x x 11 by factoring 4. Find the difference quotient of 3x 5x 6 3 x 5x 5. Solve for x: Find the equation of the line perpendicular to x + 5y 6 = 0 and passing through (-3,7) in general form 7. Solve by completing the square 3x 9x 1 0giving answer in simplest radical form 8. Complete the square and identify the horizontal shift of 4x 1x 5.

18 9. Find the center and radius of x y 8x 10y Find the coordinates of the x-intercept(s) of 4x + 9y = Draw a complete graph and find all intervals where f (x) is increasing and decreasing if 4 x x 5x 6 (5 Points) 1 Draw a complete graph and find all local extrema of 3 x 7x 7x 15 (5 Points) Increasing: Local Maxima: Decreasing: Local Minimum: 13. A candy box (probably to hold some chocolate for Mrs. Wiech) is to be made out of a piece of cardboard that measures 1 inches by 15 inches. Squares of length x will be cut from each corner and then the ends will be folded up to create the box. Find the value of x that will allow the maximum volume of the candy box created ( holding the maximum amount of chocolate ) Draw picture here: Draw a graph of the problem situation here: Identify variables and write equation here: Completely answer the problem here:

19 College Pre Calculus A Name Period Weekly Review Sheet # 10 Assigned: Monday, 1//013 Due: Friday, 1/6/013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT. 1. Write the equation of a circle in general form. Use Horner s Algorithm to find the quotient that has a center of (5,-6) and a radius of. and remainder when 3 x 13x 17 is divided by x. 3. Find the remainder when 3 x x 6x 4 is divided by x Find the domain of ( f g)( x) if x and g ( x) x 1 x 7 5. Given the function,, what x 4x 1 is the equation(s) of the vertical asymptote(s)? Given: 3x 5x 7x x 3, find f "( x). 7. The graph of x 3 5x is symmetric with respect to: 8. Solve for x and give answer in interval notation: 5 14 x 49 7 a. x-axis b. y-axis c. origin d. has no symmetry

20 9. Write the equation of the absolute value function whose graph has a vertical stretch of, reflects over the x-axis, a horizontal shift left of 5 and vertical shift down of Express as a single fraction, ( f g)( x) if ( 3) x and g ( x) x Graph x x 5x and find all zeros, local maximum and local minimum, and intervals where f(x) is increasing and decreasing a. Draw a complete graph of f(x): b. Find all zeros: Zeros: c. Find all local extrema: Local minima: Local maxima: d. Intervals where f(x) is increasing and decreasing: Increasing: Decreasing: 1. For the piecewise function, find (x, y) values, graph and find domain and range and identify intervals where x x, x 1 f (x) is continuous and discontinuous if x, x 1 Domain: Range: What type of discontinuity does f(x) exhibit? Continuous: Discontinuous:

21 College Pre Calculus A Name Period Weekly Review Sheet # 11 Assigned: Monday, 1/9/013 Due: Friday, 1/13/013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT. 1. What is the equation of the quadratic function. Solve by completing the square, giving answer whose roots are 5 6i? in simplest radical form: 3x 1x Given p x, find the production level, x, is the price, p, is $ If 16x 81 and g ( x) 4x 9, f find (x). g 5. Determine the number of negative real roots for 4 3 the function 3x x x 6 6. Factor: 7a b 9 7. Algebraically, find the range of 3x 3 5 x 4 8. What is the equation of the line, in general form, which is perpendicular to the line x 5y 6 0 and passes through the point (-3, 7)

22 9. Find the inverse, f 1 ( x ), if x ; x 5 x What is the upper bound of 3 x 4x x 3? (be sure to justify your answer) 11. Find the distance from the point (5, 3) to the line 6x y + 4 = 0 1. Simplify: 1 a 4 1 a 13. What is the local maximum of the function 3 x 4x 6x 4? Be sure to include a complete graph 14. Find the difference quotient for the function 3x x Evaluate ( x 4y )..show all work and clearly identify your answer on the bottom of the answer sheet. (5 Points no partial credit) Continue your work for #15 here: Draw Pascal s Triangle here:

23 College Pre Calculus A Name Period Weekly Review Sheet # 1 Assigned: Monday, 1/6/14 Due: Friday 1/10/14 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT. 1. Find the reciprocal of form i 3 i in simplest a bi. Solve for x and y: ( x y) (3x y) i 15 4i 3. When the polynomial f(x) is divided by x 1, the quotient is x x 4 and the remainder is 3. Find f(x) 4.Write a polynomial of degree 3 with zeros of 5 and 3 i 4 4 a b 5. Simplify: a b 6. Solve using sign patterns: x x 1 3 x 3 7. Given the function x 3x 5x 6, determine the number of possible negative real roots. 8. Find the equations of the vertical and 5x 7 horizontal asymptotes for x 4 9. Find all zeros of x 15x Solve for x in fractional form: 64 3 x x

24 5 x 4x Solve Graphically: 6 3 x Given the function: x 4 1 x 3 x a. Use the first derivative and a sign chart to find interval(s) where f(x) is increasing and decreasing. Be sure to clearly identify your answers. First Derivative: Sign Chart for Finding Interval(s) of Increasing and Decreasing Clearly identify interval(s): Increasing: Decreasing: b. Using the sign chart from above, find all local extrema in fractional form of f(x) Local Maxima: Local Minima:

25 College Pre Calculus A Name Period Weekly Review Sheet # 13 Assigned: Friday 1/13/14 Due: Friday 1/17/14 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE SEPARATE ANSWER SHEET. NO WORK = NO CREDIT, EVEN IF THE ANSWER IS CORRECT. 1. Solve for x: log x. Solve for x: log 5 x 1 3. Solve for x: log x What is the 3 rd term in the expansion of 4 5 ( 3x 5y ) x 9 5. Use a sign chart to solve 0 x 6. Find 1 ( x 3x 4 f ) if ; x 1 x 1 7. Find the distance from the point (-,5) to the line 3x y 1 = 0 8. Algebraically find all the real zeros of 4 3 g ( x) 3x x 4x 8 9. Write the equation of the line that passes through the points (3,-3) and (5,-) 10. What is the remainder when x 6x 3x 7x is divided by (x + 1)

26 11. What is the domain of h ( x) 5 x 1 1. What is the center and the radius of the circle x y 8x 6y What is the domain of y x x 3 x Write the equation of the 3 rd degree function that has roots of 4 and 3 5i 15. Find f "( x) if 3x 5x Solve for x: ( x 7) If 5x 3 and g ( x) x x 7, find ( g f )( x) 18. Find the difference quotient for 3x 5x How long will Logan need to leave $45 in an account at 5.5% interest compounded quarterly for the investment to reach $1500? 0. Graph maxima. f x ( x) (8x) and find the local

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