CP Pre-Calculus Summer Packet

Transcription

1 Page CP Pre-Calculus Summer Packet Name: Ø Do all work on a separate sheet of paper. Number your problems and show your work when appropriate. Ø This packet will count as your first homework assignment and is due on first day of school. - True or False. To find the x-intercept of the graph of a linear equation, let y = 0.. An equation of the form y = (x ) is in slope-intercept form. -4 Choose the word or term that best completes each statement or phrase.. The process of adding or subtracting equations to remove a variable and simplify solving the system of equations is called ( substitution, elimination) 4. If a system of equations in three variables has one solution, the graphs of the equations intersect in a ( point, plane) 5-7 Simplify each of the following expressions without using a calculator. 5. [(+ 6) ] Evaluate each expression if x + xy w w y+ w 9 9. ( ) w=, x= and y= 4 without using a calculator.

2 Page 0-5 Name the property illustrated. You may use the same choice more than once. 0. (4 + x) + y= y+ (4 + x). ( x+ 5) = x ( x+ 5) = ( + x) + 5. a = a 4. a+ 0 = a a. Commutative prop. b. Associative prop. c. Distributive prop. d. Identity prop. e. Transitive prop. f. None of these 5. if a = b and b = c then a = c 6- Solve each equation or inequality 6. + k = x = x x 4 ( x 5) = 0 9. x ( ) > 9 0. x =. 5+ x 8. < 7x 5 9. x + x 0 4. x + x = 5. x +8 = 0 6. x 4x 5x = 0 7. x 9 x + 8 = x + 8 = 9 9. x 5 x > 8 0. x = 7. log ( 4x ) = 4-4 Given: {(,6),(,9),( 4,65),(,),(,)}

3 Page. Find the domain of the relation. Find the range of the relation 4. Is the relation a function? ( yes or no ) 5-6 Find each value if 5. f (4) 6. g( ) f x x and g x x ( ) = ( ) = f ( ) 4g() Graph each equation or inequality 8. y = x 9. x+ y = 40. y = x 4. y> x 4. x + if x < f( x) = x if x Equations of a line. 4. Find the slope of the line that passes through the points (5, ) and (4,6) Write the slope-intercept form of an equation of the line that satisfies each condition. 44. has slope: and y-intercept: passes through (, 5) and (8, ) 46. parallel to the graph of y = x and passes through (,).

4 Page perpendicular to the graph of y = x and passes through (,). Systems of linear equations. 48. Solve the system of equations by substitution, or elimination. x+ y= 8 x + y = Solve the system of equations by substitution, or elimination. 7x+ 6y = 4 x+ 4y = 8 Matrices 50. Solve the equation x = 5y Perform the indicated matrix operation. If the matrix does not exist write impossible Find the value of each determinant: Solve the system 5x y = 0 x + 8y = by Cramer s rule or by matrix equation.

5 Page 5 Quadratic Functions Given: y= x + ( ) 55. Find the coordinates of the vertex 56. Find the equation of the axis of symmetry 57. Find the x-intercept(s) 58. Find the y-intercept 59. Does the parabola open up or down? 60. Graph the function Given: 5x + 8x = 6. Find the value of the discriminant 6. How many real solutions ( x-intercepts) 6. Solve the equation. Give exact value(s) 64. Write the equation y= x + x + 6 in vertex form. 65. Solve the following quadratic inequality : x x Use synthetic division to determine whether x + is a factor of x x 5x + 6. Function Notation and Operations 67-7 Given: f (x) = x and g(x) = x Find:

6 Page f ( ) 68. g(5) 69. f (x) g(x) 70. g( f (x)) 7. Is f(x) -? 7. Is g(x) -? 7. Are the following two functions inverses of each other ( hint: show that f(g(x)) = g(f(x)) = x) f (x) = x + amd g(x) = x Conic Sections Classify each equation as a parabola, circle, ellipse, or hyperbola 74. x + 5x + 6y 4 = x +0y + x y + 4 = Given: (x + 5) 5 + (y ) 4 = 76. Find the coordinates of the center 77. Find the coordinates of the foci 78. Find the coordinates of the endpoints of the major axis. 79. Graph the equation 80-8 Given: (x + 5) 5 (y ) 4 = 80. Find the coordinates of the center 8. Find the coordinates of the foci

7 Page 7 8. Find the coordinates of the vertices. 8. Graph the equation Given: y = ( 8 x + ) 84. Find the coordinates of the vertex 85. Find the coordinates of the foci 86. Equation of the directrix 87. Equation of the axis of symmetry 88. graph the equation. 89. Write the conic section x + y + 8x 4y +6 = 0 in standard form ( in the form (x h) + (y k) = r ) Radical expressions Simplify. Use absolute value when appropriate x 4 y 6 9. ab 6a b (b / ) / Complex numbers.

8 Page Write in i-form: Add. (+ 4i) + ( 7i) 99. Subtract. (+ 4i) ( 7i) 00. Multiply. (+ 4i)( 7i) 0. Divide. + 4i 7i 0. evaluate : i i Rational Expressions 0-05 Perform the indicated operation. Give simplest answer x x 7 4 x 49 x + 4x x + 5 c d + cd x 7x + x Direct and Inverse Variation. 06. If y varies directly as x and y = 6 when x = 4,find y when when x is. 07. If y varies inversely as x and y = 4 when x = 4,find y when when x is 4. Word problems. 08. Two numbers are in the ratio of : and their sum is 5. Find the numbers. 09. If there is a 6% tax on clothing, find the tax on a suit that costs $ The time required to drive a given distance is inversely proportional to the speed. If it takes 7.5 hours to cover a distance at 84 km/hr, how long will it take at 90 km/hr?

9 Page 9. A collection of 77 quarters and dimes is worth $.50. How many quarters are there?. The sum of two numbers is 6 and their difference is 6. Find the numbers.. Two trains leave a station at the same time, heading in opposite directions. One train is traveling at80 km/hr, the other at 90 km/hr. How long will it take for the trains to be 45 km apart? 4. A rectangle is 8 cm longer than it is wide. The area is 40 square cm. Find the dimensions. 5. How many different pairs of letters from the English alphabet are possible? 6. An airline is hiring 5 flight attendants. If 8 people apply for the job, how many different groups of 5 attendants can the airline hire?!