Math Pre-Calc 20 Final Review

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1 Math Pre-Calc 0 Final Review Chp Sequences and Series #. Write the first 4 terms of each sequence: t = d = - t n = n #. Find the value of the term indicated:,, 9,, t 7 7,, 9,, t 5 #. Find the number of terms in each sequence:, 7 5,,..., 8 4-5, -0, -0,, -040 #4. Write the general term (t n ) for each sequence: -8, 4, -, -5, -0, -5, #5. The 0 th term of an arithmetic sequence is and the nd term is 48. Find the first term and the common difference. #6. Write out the first three terms of the geometric sequence whose fifth term is 48 and whose seventh term is 9. #7. Find the sum of each series: S 9 #8. Find the sum of the infinite geometric series: #9. Suppose that each year a tree grow 90% as much as it did the year before. If the tree was.5 m tall after the st year, how tall would it eventually get? #0. A man walks 5km in week, 8 km in week, km in week and so forth. How many km would he walk in total over 0 weeks?

2 Chp Trig #. Sketch the angle and name its reference angle: 4 #. Find the eact value of the following without using a calculator: Cos 0 Sin 5 #. A point P(4,-) lies on the terminal arm of an angle Ѳ in standard position. Determine the eact trigonometric ratios for Sin Ѳ, Cos Ѳ and Tan Ѳ. #4. If Sin Ѳ = 5, Ѳ is in Q, find the Cos Ѳ and Tan Ѳ. #5. Find the quadrant where Cos Ѳ < 0 and Tan Ѳ > 0. #6. Solve for Ѳ if 0 Ѳ 60. Sin Ѳ = #7. Find each measure indicated: #8. Solve each triangle Δ ABC. B = 7, A =, b = 5 a = 6, b = 7, c = 8 #9. Determine how many ABC triangles satisfy the following conditions. A = 65, a = 9. cm, and b = 0.7 cm A = 4, a = 5, and b = 7 #0. Two boats leave a dock at the same time. Each travels in a different direction. The angle between their courses is 54. If one boat travels 80 km and the other travels 00 km, how far apart are they?

3 Chp Quadratic Functions #. Find the verte of each quadratic: y = y + = y = ( + ) + #. Write each of the following in verte-graphing form by completing the square: y = + 4 y = + y = - + #. Answer the following questions for each quadratic function: verte equation of the ais of symmetry concavity (faces up or down) d) maimum or minimum value e) domain and range f) and y intercepts g) sketch the graph i) y = -( + ) + ii) y = #4. Write a quadratic equation in verte graphing form for each of the following: a = verte is (-, ) verte is (, ) and passes through the point (, -) #5. Write the new equation of the parabola y = after the following: ( marks) a horizontal translation units to the left and a vertical translation unit up a vertical translation units down and a reflection across the -ais a multiplication of the y-values by - and then a horizontal translation unit to the right #6. A bridge has the shape of a parabola. Its width is 50m and its height is m. Find the quadratic equation for this bridge. #7. The height, h, in metres, of a flare t seconds after it is fired into the air is given by the equation h(t)=-4.9t + 6.5t. At what height is the flare at its maimum height? How many seconds after being shot does this occur? #8. A farmer has 00m of fencing material to enclose a rectangular field adjacent to a river. No fencing is required along the river. Find the dimensions of the rectangle that will make its area a maimum. What is the maimum Area? (Hint: a diagram of the situation is given below) 00 ~~~~~River~~~~~

4 Chp 4 Quadratic Equations #. Solve the quadratic equations by factoring: 6 = = = 4 #. Solve the quadratic equations by completing the square: (Write answers in Eact Form) = = 0 = 0 #. Solve the quadratic equations using the quadratic formula: (Write answers in Eact Form) = 0 = 4 (Hint: Same as 0 4 = 0) #4. Find the zeros of the function f() = #5. Find the quadratic equation with the roots of, #6. Find the discriminant and state the nature of the roots: 4 5 = 0 = = 0 #7. The hypotenuse of a right triangle is. If the sum of the legs is 7, find the legs. (Hint: Let one leg be and the other is therefore 7- since the sum is 7.) #8. If h(t) = 5t 0t + 45, find t when h = 0. (Hint: 0 = 5t 0t + 45)

5 Chp 5 Radicals #. Simplify: y #. Change each mied radical into an entire radical: 4 #. Simplify: Squares Cubes Fourths #4. Multiply (Epand) the following and simplify: ( 6 )( ) ( ) d) ( )( ) ( 4 ) y 6y e) ( + ) f) ( 5) g) ( + )( ) #5. Divide the following and be sure to rationalize all denominators: d) e) f) g) 9 #6. Solve the radical equations: = = + 5 = 5 d) + 4 = e) y 5 + y = 5

6 Chp 6 Rationals #. Simplify: y 5y #. Multiply/Divide the following and simplify: m f 5c 5cf 4m 8y y y y 4y y y y + a 6 6a 4a a + 6a a + 7a + #. Add/Subtract the following and simplify: m + n c a 5 a y 0 y y 4 y+ d) e) + #4. Solve each rational equation and list all the restrictions: + 4 = 5 = 9 = 6 4 d) d = d + 4 d d + + d 4 d #5. The sum of two numbers is. The sum of their reciprocals is 9 4. Find the numbers. #6. Two hoses are used to fill up a pool. If one hose fills the pool in 6 hrs and the other fills the pool in hrs, how much time would it take the fill the pool using both hoses?

7 Chp 7 Absolute Value and Reciprocal Functions #. Evaluate: 6 4 d) () #. Solve each equation: = = = 7 d) + = 5 e) + = 4 #. Use the graph of y=f() to sketch the graph of y= f() 5 4 y=f() y 5 4 y y=f() #4. Sketch the graph of: y = y = #5. Epress y = as a piecewise function. #6. Sketch the graph of y = + and y =. State the invariant points. + #7. Sketch the graph of y = 6 and = 6. State the invariant points. y

8 Chp 8 Systems #. Solve by graphing. Give approimate solutions if needed. Verify your solutions. y = ½+ y + + = 8 #. Solve algebraically. Verify your solutions. y = + y = #. Solve algebraically. Verify your solutions. + y = 0 y + = 0 #4. Solve algebraically. Verify your solutions. y = 4 + y = Chp 9 Quadratic Inequalities #. Solve by graphing: y < + y 6 #. Solve: + < 0 > < d) < 5 #. Solve by graphing: y < ( ) y +

On a separate sheet of paper, answer the following questions by showing ALL of your work.

Final Exam Review Cummulative Math 20-1 Ch.1 Sequence and Series Final Exam Review On a separate sheet of paper, answer the following questions by showing ALL of your work. 1. The common difference in