5A Quiz Review Learning Targets 4.4 5.5 Key Facts Graphing one-variable inequalities (ex. x < 4 ) o Perform algebra steps to get x alone! If you multiply or divide by a negative number, you must flip the direction of the inequality o Shade in the number line to represent solutions to the inequality! Draw a closed circle if or! Draw an open circle if < or > Graphing equations of lines o If the equation is in slope-intercept form ( y = mx + b ), m gives the slope of the line (rise/run) and b gives the y-intercept o If the equation is in any form, you can plug in x = 0 to find the y-intercept and plug in y = 0 to find the x-intercept Graphing two-variable inequalities (ex. y > 2x 3) o Graph the line as if it was an equation (=)! Draw a dashed line if < or > o Test a point to determine which half of the grid to shade Solving systems of equations graphically o o Graph both lines The point where they intersect is the solution to the system! If the lines are parallel, there is no solution! If the lines are the same, there are infinitely many solutions Graphing a system of two-variable inequalities o Graph the solution to each inequality as described above o The final solution is where the shaded areas overlap (shade this darker or with a new color) Make sure your homework is up-to-date: #1-7 in your workbook should be done. Learning Targets: 4.4 I can solve quadratic equations using the quadratic formula and use the results to solve projectile motion problems. 4.5 I can find the vertex of a quadratic equation and use the results to solve projectile motion problems. 4.6 I can write complex numbers in terms of i. 4.7 I can add, subtract, and multiply complex numbers and simplify the results. 4.8 I can divide complex numbers and simplify the results. 5.1 I can solve one variable inequalities and graph the solution on a number line. 5.2 I can graph linear equations. 5.3 I can represent and interpret the solutions to a two-variable inequality on the coordinate grid. 5.4 I can solve systems of linear equations by graphing. 5.5 I can represent and interpret the solutions to a system of two variable inequalities on the coordinate grid. 1
LT 5.1 5.5 Practice 1. Simplify and shade the solutions to each inequality on the number line provided. Show all your work and label the number line with appropriate numbers. a. 3x > 9 b. 2x 1 3 c. 4 2x < 2 d. 1 x 4 1 2. Graph the following equations or inequalities. a. y = 2x + 3 b. 2x y = 6 2
c. y > 1 3 x 1 d. y 3x 5 3. Solve the following systems of equations by graphing. Be neat and check your solution by plugging into both equations if you are unsure. a.! y = x " # y = 2 x + 2 3 b. " y = 2x 1 # $ 3y 6x = 9 Solution: Solution: 3
c. " 2x 5y = 20 # $ y = 2 x 4 5 d. " 4x =12 3y # $ y = 3x + 9 Solution: Solution: 4
4. Graph the solutions to the following systems of inequalities on the grids below. Be neat and make sure it s clear what the final solution is (shade darkly or use a different color). a. $ y 4x % & y 1 x + 5 2 b. # y > x + 2 $ % y 2 3 x 2 Is (4, 5) a solution to the system? Is (-2, 2) a solution to the system? Explain why or why not in writing: Explain why or why not in writing: 5
LT 4.4 4.5 Practice 5. Rosheen is catapulting a bowling ball from a height of 3 meters. The initial speed of the bowling ball is 22.8 m/s at an angle of 37.87. Variable Known? Variable Known? x i v xi x f v yi y i g y f t a. Fill in the table with any known information. You may round to the nearest whole number. b. Use the quadratic formula to determine when the ball hits the ground. Show your work. c. When does the ball reach its highest point? Show your work. d. What is the highest point that the ball reaches? Show your work. 6
LT 4.6 4.8 Practice 6. Write each of the following in terms of i. a. 49 b. 38 7. Simplify each of the following expressions. Show your work. a. 2 + 3i + 3 2i b. 4 + 5i (1 6i) c. 3 + 6i 4 2i d. 5!i 4!3i 7
Answers 1. a. x > 3 b. x 2 5 5 0 5 5 0 c. x > 1 d. x 8 5 5 0 0 5 10 2. a. b. c. d. 3. a. (6, 6) b. No solution, the lines are parallel. 4. a. b. c. Infinitely many solutions, the lines are identical. d. (3, 0) 8
5. a. Variable Known? Variable Known? x i 0 v xi 18 m/s x f? v yi 14 m/s y i 3 g -10m/s 2 y f? t t b. The ball lands after 3 seconds. c. The ball reaches its highest point after 1.4 seconds. d. The highest point the ball reaches is 12.8 meters. 6. a) 7i b) i 38 7. a) 5 + i b) 3 + 11i c) 24 18i d)!"!!"!!" 9