For questions 5-8, solve each inequality and graph the solution set. You must show work for full credit. (2 pts each)
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1 Alg Midterm Review Practice Level 1 C 1. Find the opposite and the reciprocal of 0. a. 0, 1 b. 0, c. 0, 1 0 d. 0, 1 0 For questions -, insert <, >, or = to make the sentence true. (1pt each) A a. < b. > c. = A. 7 a. < b. > c. = B a. < b. > c. = For questions 5-8, solve each inequalit and graph the solution set. You must show work for full credit. ( pts each) A 5. + k 8 + k 8 k k a. k b. k c. k d. k
2 C. ( 5) < 10 ( ) 5 < 8 10 < 8 < 0 < 0 A 7. 5 < 17 or 5 + > 1 5 < 17 < 1 < OR 5 + > 1 5 > 5 > 5 C 8. Solve the inequalit. Graph the solution OR Find the slope of the line = 10 (1pt) = = 10 = + so slope
3 A 10. Classif the sstem: 7 + = = 7 + a. inconsistent b. independent c. dependent 7 + = compare to = 7 + = 7 + Same slope; different -intercept parallel = inconsistent 11. Skip 1. Find an equation for the line through (, ) and parallel to = + 5. Write it in slope-intercept form. What is the -intercept? slope is and through (, ) using point-slope: = = + 8 = intercept: (0, 11) using slope-intercept: = m + b 1. Graph the following numbers on a number line. (pts) 1,,.75, = + b = 8 + b 11 = b = + 11 =.75 slope is parallel = same slope
4 B 1. Solve the sstem b graphing: = = a. solution (,0) b. solution ( 0, ) 1 st line: = = + = nd line: = = + 1 = c. solution (, 0 ) d. solution ( 0, )
5 15. Evaluate the epression for b =. () + () + () = 1 1. Evaluate the epression ( ) 1 + ( ) ( 1) = 8 1 b + b + b ( h ) 1+ h for h = 17. Suppose f = 8. Find f ( ). (1pt) f ( ) = ( ) 8 = 1 0. Solve + 7 = 5 + = 1 + = + = You must have both answers. (The or indicates that the solution can be either number.) 1. = S S 5 = 5r 5r S t = 5r 8 = = = 5r t Solve for t. r t or + = = 0 = Solve 17 = 17 = = 15 = 5. Is the relation a function? Eplain full! 1,, 0,1,, 1,, { } There are no repeated -values so it must be a function. (Ever has a unique -value.) 19. Simplif ( ) Function? X es no
6 . The graph shows a scatterplot of (attendance, graduation rate) data. B a. The relationship shown describes a (circle one): a. Weak, positive correlation b. Strong, positive correlation c. Weak, negative correlation d. Strong, negative correlation b. What does the graph tell ou about the relationship between attendance and graduation rate? As attendance increases the graduation rate increases. + =. Use elimination to solve: = 7 + = = 7 = 15 = 5 5 = 7 = 1 = Or + = 1 = 1 = = = 7 1 = 7 = 5 5. Solve the sstem b substitution: = = = 1 = 10 = 0 = = 1 + = 1 1 = 0 Solution: ( 5, ) Solution: (,0)
7 . Is the relation a function? Wh or wh not. (1pt) Can t have two -values for 1 -value Or fails vertical line test. 7. Solve the following sstem. 5 + = = One option: Multipl 1 st equation b. Multipl nd equation b = 1 9 = 1 19 = 0 = 0 0 = = = Solution: ( 0, ) 8. Graph the absolute value equation. (pts) = Graph the absolute value inequalit. (pts) < + 5 Test (0,0): 0 < < 5 0 < NO Note: line segments should be dashed! (Not equal) 0. Graph the linear inequalit. (pts) Test (0, 0): YES
8 1 1. Solve the sstem b graphing: > > 0 0 >. Write the equation of the line that passes through (7, 8) and (, ). Write our answer in standard form. 8 m = = = ( ) ( ) = ( ) 5 0 = + 5 = 5 = or = 5 5 ( ) ( ) = ( ) 5 10 = = 5 = 8 10
9 The actual eam will be broken up into parts: Multiple Choice, Short Answer and Graphing. This review sheet is organized differentl so that ou ma organize our thoughts, our note cards and make connections. A. Simplif: Remember ou must follow the order of operations!!! You will also need these skills when solving equations. 1. Replace the with >, = or < > 1 1 > 1. Simplif 8 using the imaginar number i. ii i. Simplif (7 i) ( 5 + i) 7 i + 5 i 1 7i. Write 50 9 in the form a + bi. 5i i 7. Determine whether the function is linear or quadratic. Identif the quadratic, linear, and constant terms. f = (5 + 1)( ) 5. Simplif ( i)( 10 i) 0i 0 simplif 1 st! 5 ( ) + 1( ) quadratic function quadratic term: 10 linear term: 17 constant term:. Simplif ( + i)(1 8 i) (1 8 i) + i(1 i) + i + i 1i + i i i
10 B. Factoring: You need this skill to solve quadratic equations. 1. Factor Factor 5 9. (Hint: this is a special case) ( ) 7 5 GCF u v = u + v u v (5 ) () = C. Solving: The goal is alwas to find the value(s) that make the sentence(s) true. Man times this involves isolating the and/or the term containing the. 1. Solve the quadratic equation b factoring. + 8 = 0 ( ) ( ) = 0 ( ) ( ) ( )( + 7) = = 0. Solve = 0 ( ) ( ) = 0 ( ) ( ) ( + )( + 8) = = 0 ( ) = 0 = ( ) + 7 = 0 = 7 + = 0 = or + 8 = 0 = If ou can t factor. Solve the quadratic equation using the quadratic formula = 0 ( 1)( 1) = ± = ± 1 = ± i = ± = ± i. Solve ( ) + 1 = 0 ( ) ( )( 1) = ± 1 1 = ± 8 = ± 1 = ± 1 = + = = 1 or 1 1 = = 10
11 5. Solve 5 = 10 5 = 1 5 = 8 5 = 8 = 1 5 = =. Solve ( ) = for. 7 5 = 5 ( ) 7 5 = = 11 8 = = 7. Solve 5 = 50 5 = 50 = 10 = ± Solve the sstem b substitution or elimination. If there is one solution, write that solution. If there is no solution write no solution. If there is infinitel man solutions write infinitel man. 8. Solve + = 0 + = 0 = = = ± i = ± i + 5 = 7 5 = = 7 5 = 5 = 1 = + 5 = = 7 5 = 19 = 19 5 or 5 = 5 5 = 5 5 = 19 = The volume of a clinder is given b the formula V = π r h. Solve this equation for h. V π r V π r r h π = π r = h D. Problems That Relate to Graphs. 11
12 1. Find the slope of the line that passes through (, 5) and (, ). 5 8 = =. Identif the verte, ais of smmetr, and points corresponding to P and Q. Verte: (, 7) Ais of Smmetr: = P (0, -9), Q (5, ) Q P. Is this the graph of 8 = ( ) = + () 8() = = No verte not at (, ) = + 8? 8 10 Application. You are at the top of a building that is approimatel 1000 feet tall. The function = 1t + 10t models the height in feet of an object t seconds after it is launched from the top of the building. a. What is the maimum height of the object? b. When will the object hit the ground? ( 10) ( ) = = 5 1 = + + = feet 1(5) 10(5) 1000 ( 10) ( ) ( 10) ( 1)( 1000) ( ) = ± = ± = ± 9.5 = seconds 1
13 E. Graphing. You must show how ou determined points on the graph for full credit! 1. Graph = 9. Graph pt = 9 = + or intercept ( 0,5 ) shade 0 (0) + 5 true shade toward (0, 0) = 5. Solve b graphing 8 + = 8 + = = 8 + = + 1 graphed b slope-intercept form OR pt = =
14 . Graph ( ) = + 5. Graph = + verte (, ) ( ) = = 1 = + () () = = Graph = 5 V-shape flipped shifted right and up. OR = Write the equation that is the translation of = right units and down 5 units. =
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