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Name: _________________________________ Midterm Review Questions Date: ______________ Graph the following numbers on a number line: 1.) 6 2.) 5 3 Put the following numbers in order: 3.) 9, -3, 10 , 1 , 5, 2 4.) Evaluate the following variable expression where x = 7: 3.) _________________________ 5.) Evaluate the following variable expression where y = -3: -x + 15 6.) Evaluate the following expression where n = 4: 12y 7.) Evaluate the following variable expression where x = 2 and y = 4: x 32 48 n 3y 2 Solve: 8.) 4x + 7 = 27 9.) 2x – 9 = 0 10.) 15n + 9 = 21 11.) 2b + 11 = 15 – 6b Solve: 1 5 1 19 12.) x x 2 3 2 4 13.) 5n + 11 = 7n - 9 Rewrite the following formulas for the given variable: 14.) Investment at Simple Interest Solve for P: I=PRT 15.) Area of a Triangle 1 Solve for b: A bh 2 16.) Volume of a Cone 1 Solve for h: V r 2 h 3 Identify the five steps to solving a word problem (in order): 17.) Step 1: 18.) Step 2: 19.) Step 3: 20.) Step 4: 21.) Step 5: Complete the following word problem (showing all five steps), and being sure to answer the question at the end. 22.) You have borrowed $529 from your parents to buy a mountain bike. Your parents are not charging you interest, but they want to be repaid as soon as possible. You can afford to pay them $20 per week. How long will it take you to repay your parents? Solve and graph the following inequalities: 23.) 5-2x 27 24.) 2(4 – x) > 8 Solve and graph the following inequalities: 25.) x – 8 > -4x -3 26.) 3x – 7 < 5 27.) -7<6x – 1<5 28.) -16 3x 4 2 29.) 3x + 2 < -10 or 2x – 4 > -4 30.) Simplify the expression: 5(n 2 n) 3(n 2 2n) Solve the following absolute value equations and inequalities: 31.) -|x – 4| = 5 32.) |2x + 1| = 5 33.) |4x – 12| > 16 34.) |3x -+ 2| < 7 35.) Name the quadrants of the following coordinate plane correctly. 36.) Is the following input/output table representative of a function? Explain. Input -2 -1 0 1 2 Output 6 8 10 12 12 Evaluate the following functions using the number provided: 37.) f(x) = 5 + 3x – 17; x = 12 38.) f(x) = -x – (5x + 7); x = -2 39.) Find the slope of the line that goes through points (3, -4) and (1, -6). Show all work! 40.) Are the following lines parallel, perpendicular, or neither? Show all work! Line 1: (4, -3); (-8, 1) Line 2: (5, 11); (8, 20) Find the x-intercepts and y-intercepts for the following problems: 41.) y = x - 3 42.) y = 4x + 8 43.) 5y = 2x - 3 44.) Write the equation of the line that has a slope of 3 and goes through the point (1,0). 45.) Write an equation of the line that passes through (1, -1) and is parallel to the line 1 y x6 2 46.) The variables x and y vary directly. Write an equation that relates the variables. X = 0.8; y = 1.6 47.) Using the equation above, what is the value of y if x = 5? 48.) Draw a scatterplot of the data. Then approximate the best-fitting line by giving me the line equation. x y -2 4 -1 3 0 2.5 0.5 2.5 1 2 2 0.5 2.5 -1 3.5 -3 Graph the following inequalities. Make sure to shade appropriately. 49.) y > 3x – 4 50.) y < 1 x2 2 4 -2.5 5 -2.5 Graph the following inequalities. Make sure to shade appropriately. 51.) y 2 52.) y 2x + 1 53.) In the following absolute value equation, what is the vertex of the graph? y = |x – 4| + 2 54.) In the following absolute value equation, would the graph open “up” or open “down”? y = 3|x + 5| - 1 55.) In the following absolute value equation, would the graph be wider, narrower or the same width as y = |x|? 1 y | x 3 | 4 2 Graph the following absolute value equations: 56.) y = 2|x| 57.) y = -|x – 3| + 1 Match the following linear equations, linear inequalities and absolute value equations to the letter of their appropriate graphs: 58.) x 1 __________ 63.) y 3 1 59.) y x 2 3 __________ 64.) y = 2|x| 60.) y -3x + 2 __________ 65.) y __________ __________ 1 x 1 2 __________ 61.) y = |x - 2| __________ 66.) y = 2x + 4 __________ 62.) y = -|x – 2| + 1 __________ 1 67.) y | x 1 | 2 2 __________ A B C D E F G H I J 68.) Decide if the point (3, 0) is a solution for the linear system below: -x + 2y = 3 10x + y = 30 69.) Graph the following linear system to find the solution: 3x – y = 12 -x + 8y = -4 70.) Find the solution to the following sets of of linear systems using the substitution method. 9x – 5y = -30 x + 2y = 12 71.) Find the solution to the following sets linear systems using the elimination method. x + 3y = -2 x+y=2 Graph the system of linear inequalities: 72.) y -4 y < -2x + 10 73.) y > 2x - 7 4x + 4y < -12 Complete the following word problem: 74.) The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 16 vans and 5 buses with 417 students. High School B rented and filled 10 vans and 8 buses with 480 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry? 75.) Graph the following quadratic equation using standard form: y = x 2 – 2x - 1 Axis of symmetry is ___________ Vertex is ____________________ x-intercepts are _______________ y-intercept is _________________ 76.) Graph the following quadratic equation using intercept form: y = -(x + 2)(x – 4) Axis of symmetry is ___________ Vertex is ____________________ x-intercepts are _______________ y-intercept is _________________ Additional point (if necessary) ______________ 77.) Graph the following quadratic equation using vertex form: y = -(x – 2) 2 - 1 Axis of symmetry is ___________ Vertex is ____________________ x-intercepts are _______________ y-intercept is _________________ Additional point (if necessary) ______________ 78.) Write the equation of the quadratic function that has a vertex (0, 0) and contains the point (4, 8). Factor the following quadratic expressions completely! 79.) x 2 11x 24 80.) 2 x 2 3x 1 81.) 18 x 2 2 82.) 81x 2 198 x 121 Simplify or solve: 83.) 168 84.) 85.) 6 8 86.) x 2 100 30 2 Also complete the following multiple-choice questions and list the answers here. Show the work on separate paper and attach by the due date. Pg 62 Pg 134 Pg 191 1.) __________ 1.) __________ 1.) ___________ 2.) __________ 2.) __________ 2.) ___________ 3.) __________ 3.) __________ 4.) ___________ 4.) __________ 4.) __________ 6.) ___________ 5.) __________ 5.) __________ 6.) __________ 6.) __________ 7.) __________ 7.) __________ 8.) __________ 8.) __________ 9.) __________ 9.) __________ 10.) _________ 10.) _________ 11.) _________ 11.) _________ 12.) _________ On page 192 please complete the following problems and attach the work to the back. 2.) ________ 36.) ________ 4.) ________ 38.) ________ 6.) ________ 40.) ________ 8.) ________ 42.) ________ 10.) ________ 44.) ________ 12.) ________ 46.) ________ 14.) ________ 48.) ________ 16.) ________ 50.) ________ 18.) ________ 52.) ________ 20.) ________ 54.) ________ 22.) ________ 56.) ________ 24.) ________ 58.) ________ 26.) ________ 60.) ________ 28.) ________ 62.) ________ 30.) ________ 64.) ________ 32.) ________ 74.) ________ 34.) ________ On page 394 please complete the following problems and attach the work to the back. 44.) ________ 58.) ________ 46.) ________ 60.) ________ 48.) ________ 62.) ________ 50.) ________ 64.) ________ 52.) ________ 66.) ________ 54.) ________ 68.) ________ 56.) ________