ALGEBRA 2 MIDTERM REVIEW Evaluating Expressions: 1.) -3 + 3(-2+ 5) 2 2.) ( -5 ) 2 3.) -5 2 Simplify and evaluate the expression for the given value of the variable: 4.) f(x) = x 2 + x 8; find f(-2) 5.) f(a) = 3a 2 + a 2a 2; find f(3) 6.) f(n) = 2( n + 1) 4 (n 2); find f(-1) Solve the equation: 7.) 8.) 3(2x-1) = -4(-x + 1) + 5 9.) Convert 1.7 yards per minute into feet per second Solve the formula for the indicated variable: 10.) Solve for y: 2x 3y = 6 11.) Solve for l: P = 2l + 2w 12.) Solve for h: A =
Solve the inequality and draw it s graph : 13.) 3x + 1 > 2x + 3 14.) Solve the compound inequality and graph its solution: 15.) 3x + 1 < -2 or 2x + 9 > 1 16.) - 4 < -2x + 4 < 12 Solve the absolute value equation or inequality. Evaluate the function when x = 5.
Find the slope of the line passing through the points. 23.) (4, -3) and (6,5) 24.) (2, 0) and (8,0) 25.) (5, 8) and (5, 14) Tell whether the two lines are parallel, perpendicular or neither. 26.) Line through (-5,3) and (8,4) 27.) Line through (5,-9) and (-2,5) Line through (2,7) and (1,20) Line through (6,3) and (9,9) Graph the following equations: 28.) 3y + 2x 15 = 0 29.) 2x - 4 y = 0 30.) 1 x 5 if f (x) = 2 x < 2 5x + 4 if x 2 31.) Write the equation of the line that passes through the given point and has the given slope. (5, -1); m = (6,0); m = 0 ( 4, 5); undefined slope 32.) Write the equation of the line that passes through the points ( -2, 5) and (-6, 8). 33.) Write the equation of the line that is parallel to the line y = 2x -1, but passes through the point ( 6,7,)
34.) Write the equation of the line that is perpendicular to the line y = 2x-1, but passes though the point (6,7) 35.) The table shows the number p (in thousands) of patents issued to U.S. residents where t is the number of years since 1985. Draw a scatter plot of the data and describe the correlation shown. Then approximate the best-fitting line for the data. t 0 1 2 3 4 5 6 7 8 9 10 p 43.3 42.0 47.7 44.6 54.6 52.8 57.7 58.7 61.1 64.2 64.4 Based on your best-fit line equation, predict the number of patents that will be issued to U.S. residents in the year 2015. 36.) The table shows the average fuel consumption F (in gallons) of a passenger car between 1970 and 2002 where t is the number of years since 1970. Find a model using the quadratic regression feature of your graphing calculator. t 0 5 10 15 20 25 26 30 32 F 760 695 576 559 520 530 532 544 600 Based on your quadratic regression model equation, in which year was the average fuel consumption the lowest? Graph the following inequalities: 37.) 38.) y 5 < -x 39.) x + 4 > -3
Graph the following absolute value inequalities: 42.)Solve the system of equations by graphing: x + 2y = -4 3x + 2y =0 43.) You want to burn 380 calories during 40 minutes of exercise. You burn about 8 Calories per minute inline skating and 12 Calories per minute swimming. How long should you spend doing each activity? 44.) Solve the following system of equations. x + y + z = 3 x + y z = 3 2x + 2y + z = 6
Graph the following systems of inequalities: 45.) 46.) 47.) 48.) Perform the indicated operation. 49.) Solve the matrix equation for x and y. Find the product of the following matrices. 50.) 51.)
Find the determinant of the following matrices. 52.) 53.) Find the inverse of the following matrices. 54.) 55.) Use matrices to solve the following system of equations. 56.) -2x + 4y = 22 57.) x + 2y 3z = 10 3x y = -13 2x 3y + 4z =-10-2x + 3y -5z = 13 ********************MEMORIZE****************** The inverse of A = is The determinant of a 2 x 2 matrix Det = ad - cb
58.) Use a table of values to graph the following quadratic function. y = x 2-2x + 1 x y vertex What is the vertex? What is the axis of symmetry? What is the discriminant? What does the discriminant tell you? Find the x-intercepts by factoring. 59.) Use a table of values to graph the following quadratic function. y = -2x 2 +8x -5 x y What is the vertex? What is the axis of symmetry? What is the discriminant? What does the discriminant tell you? Find the x-intercepts by using the quadratic formula.
***************MEMORIZE THE QUADRATIC FORMULA***** ********** x = b ± b 2 4ac 2a to solve equations in the form 0 = ax 2 + bx + c for x. Solve the following equations for x using the quadratic formula. 60.) x 2-8x + 5=0 61.) 9x 2 = 1-7x 62.) 3x 2-5x= -1 Solve the following equations for x by factoring. 63.) x 2-4x -21=0 64.) 2x 2 = 200 65.) 2x 2 + 3x + 1= 0 66.) The path of a diver is given by where y is the height in feet and x is the horizontal distance x from the end of the diving board (in feet). How high is the diving board from the water? Find the maximum height of the diver. How far is the diver from the diving board when he reaches his maximum height? How far is the diver from the diving board when he hits the water?
Write the expression as a complex number in standard form. 67.) (4 3i) (2 + 5i) 68.) ( 7 + 3i)(2 - i) 69.) Simplify the following expressions. 70.) 71.) Perform the indicated operation. 72) 73) 74) Find the solutions of the equation by setting equal to zero and factoring 76.) 77.) 78.) Find all roots for each function. 78.) 79.)
80.) If f(4) = 0, find all of the real zeroes of the polynomial function f (x) = x 3 2x 2 11x +12 81.) If f(-1) = 0, find all of the real zeroes of the polynomial function f (x) = 3x 4 5x 3 5x 2 + 5x + 2 82.) Write a polynomial function of the least degree that has real coefficients, the given zeroes and a leading coefficient of 1. a.) i, 3 b.) 4, 6, -7 c.) 2, 1+ i
Other Important Terminology Is the Graph a Function? Function Not a Function Graphically: passes vertical line test Graphically: fails vertical line test Each x-value must produce a unique The same x-value produces more y output. than one y-output (2,4) (3,4) (4,4) (3,5) (3,6) (4,7)