Sample Student Workbook Intermediate Algebra: Puzzles for Practice Written by Maria H. Andersen Muskegon Community College Prepared by Ann Ostberg Grace University
Table Contents: Intermediate Algebra Puzzles for Practice RNUM: Real Numbers Match Up on Fractions.. Signed Numbers Magic Puzzles. ALG: Algebraic Epressions Follow the Multiplication Road. Match Up on Like Terms and Distribution.. EQN: Solving Linear Equations and Inequalities Stepping Stones.... 7 Tic-Tac-Toe with Inequalities 8 ABS: Absolute Value Equations and Inequalities Matching Up the Different Cases.... 9 LINE: Lines and More Match Up on Slopes.... 0 Tic-Tac-Toe on Inequality Solutions SYS: Solving Systems Following the Clues Back to the System Equations.. Tic-Tac-Toe on Inequalities... SYS: More on Solving Systems Tic-Tac-Toe on Row Echelon Form..... Rowing to Freedom. EXP: Eponent Rules Match Up on Basic Eponent Rules.... Escape the Matri with Ten Power... 7 POLY: Simplifying Polynomials Caught in the Net..... 8 Match Up on Polynomial Division 9 FACT: Factoring and More The First Factoring Matchup..... 0 Escape the Matri by Solving Quadratic Equations. RAT: Rational Epressions and Equations Tic-Tac-Toe on Comple Fraction Pieces.. Match Up on Simple Rational Equations RAD: Radical Epressions and Equations Escape the Rational Eponent Matri..... Sail Into the Pythagorean Sunset QUAD: Quadratics Square Isolation Tic-Tac-Toe.... Match Up on the Discriminant.. 7 EXPF: Eponential Functions Eponential Workout..... 8 LOG: Logarithms and More Paint by Equivalent Equations. 9 Escape the Logjam. 0 CNC: Conics Name that Conic!...... SEQ: Sequences and More Paint by Factorials.
Match Up on Fractions Match-up: Match each the epressions in the squares the table below with its simplified value at the top. If the solution is not found among the choices A through D, then choose E (none these). A B C 7 8 D 0 E None these 7 7 0 8 8 8 + 8 8 0 9 0 + ( ) 8 9 0 + I thought we shared a common denominator, but he was only a fraction the person I thought he was. Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Signed Numbers Magic Puzzles Directions: In these magic puzzles, each row and column adds to be the same magic number. Fill in the missing squares in each puzzle so that the rows and columns each add up to be the given magic number. Magic Puzzle # 8 9 Magic Number = Magic Puzzle # 8 Magic Number = 0 Magic Puzzle # Magic Number = Magic Puzzle # Magic Puzzle # 9 7 8 7 9 8 8 7 Magic Number = Magic Number = Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Follow the Multiplication Road Match-up: Find your way from start to finish along the multiplication road by shading in matching pairs algebraic epressions. The first pair has been shaded for you! START a ( ) 7a ( ) ( ) z a ( ) ( 9) 9 z ( a ) ( 0.8 )( ). ( t )( ) a ( a) 0t ( t )( ) 9t ( ) 7a ( ) 9 9 z 8 z ( ) t 9t 7 ( ) 0 8 ( ) t t ( ) 7 7 FINISH Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Match Up on Like Terms and Distribution Match-up: Match each the epressions in the squares the lower table with an equivalent epression from the top. If the solution is not found among the choices A through D, then choose E (none these). A + y B + + y C + y z D + y+ z E None these ( y) z + + y + + + y+ ( + z) 8 ( + y) ( z) + y ( y+ ) ( ) + y + y + + ( + ) y ( + 8 y) ( y) + ( y+ ) y ( z y) ( + ) + y + ( z+ y) 8 + y+ z y + + + + + + y ( z+ y+ ) + ( ) Please! We realize you are all in the same Parentheses! Hang on and you will each get one! + y + y ( + y z) ( z y) ( z+ y) z ( y ) Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Stepping Stones Directions: Shade pairs equivalent epressions to create a path stepping stones from Start to Finish. Start 0 8 z z 8 z z z 0 8 u u 9u 9u u 9 7 u 7 Finish 7 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Tic-Tac-Toe with Inequalities Tic-tac-toe #: If the inequality in the square is true, then put an O on the square. If it is false, then put an X on the square. < 8> 8 > < < 7 7 a a 0< > Tic-tac-toe #: If the number in the square is a solution to the inequality, then put an O on the square. If it is false, then put an X on the square. < 7 9 < + 7 8> < + < 8 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Matching Up the Different Cases Directions: Begin by isolating the absolute value in each the equations and inequalities below. Then categorize the problem as one the four cases or a special case. The first one has been done for you. Let k be a positive constant and let X, X, and X be mathematical epressions. Case : Case : Case : Case : Special Case: X < k X > k X = k X = X If the constant is X k X k negative or zero. < < CASE a + > = + = = t + < + y < 0 > b = + + = + 0 + = d + < 9 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Match Up on Slopes Match-up: In each bo the grid below, you will find either a pair points that is on a line or the description a line in words. Match each line that is described with its slope in the choices A through E. If the slope is not found in A through E, then choose F (none these). A B C D 0 E undefined F None these ( 0,0 ) and (,0) (, ) and (,0) 0, and, (, ) and (, ) (, ) and (, ) ( ) ( 00,0) 00,00 and 7 0, and, 9 9 ( ) (.,.7).,.7 and (, ) and ( 8,0) ( 9,7 ) and ( 7,9 ) (, ) and (,) ( 8,8 ) and ( 7, ) The line is a vertical line. The line goes to the right unit for every units it goes up. The line is a horizontal line. The line goes down unit for every unit it goes to the right. 0 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Tic-Tac-Toe on Inequality Solutions Directions for Game #: If the ordered pair in the square IS a solution the inequality, then circle the ordered pair (thus putting an O on the square). If it IS NOT a solution, then put an X over the ordered pair in the square. + y< (,) y < + ( 9,) y > 0 (, ) y 0 > y+, (,) + y+ (,0) < ( 8,) (,9) y y (, ) Directions for Game #: If the ordered pair in the square IS a solution the graphed inequality, then circle the ordered pair (thus putting an O on the square). If it IS NOT a solution, then put an X over the ordered pair in the square. y (, ) (, ) (, ) (, ) ( 0., ) ( 0,0 ) (, ) (, ) ( 7, 7) Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Following the Clues Back to the System Equations Directions: In each crime-scene below, you are shown the graph a system equations. Use your mathematical powers reasoning (and detective skills) to determine what the system equations must have been to result in this graph.. y. y. y Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Tic-tac-toe on Inequalities Directions for Tic-tac-toe #: If the ordered pair in the square IS a solution the system inequalities shown below, then circle the ordered pair (thus putting an O on the square). If it IS NOT a solution, then put an X over the ordered pair. System Inequalities: y< + y (, ) (, ) (, ) (, ) ( 8, ) (, ) (,0 ) ( 0, ) ( 0, ) Directions for Tic-tac-toe #: If the ordered pair in the square IS a solution the graphed system inequalities, then circle the ordered pair (thus putting an O on the square). If it IS NOT a solution, then put an X over the ordered pair. y (, ) (,0 ) (, ) ( 8, ) (, ) ( 0, ) (, ) (, ) (,0 ) Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Tic-Tac-Toe on Row Echelon Form A matri is in row echelon form if it has s down its main diagonal and a zero below its main diagonal. Directions: If the matri in the square is in row echelon form, then circle it (put an O on the square). If the matri is not in row echelon form, then mark it with an X. 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Rowing to Freedom Directions: Begin with the matri in the bo marked Start. Follow each the given row operations and shade the bo that contains your result for each one (each row operation is carried out on the previous answer). At the pit stop you ll get a new matri to use. You can escape this matri by rowing your way to freedom! R R R + R R R + R R R R.... START 0 0 0 0 0 0 0 0 0 0 0 R + R R R R (P.S.) R R R + R R.. 7. 8. ( ) 0 PIT STOP 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9. R + R R 0. R R. R R R R. 0 0 0 0 0 0 0 0 9 0 0 0 0 0 9 0 0 0 0 0 9 0 0 0 0 0 0 0 0 You ve successfully rowed to freedom! Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Match Up on Basic Eponent Rules Match-up: Match each the epressions in the squares the grid below with an equivalent simplified epression from the top. If an equivalent epression is not found among the choices A through D, then choose E (none these). A B C 9 D E None these ( )( ) ( ) + ( )( )( ) ( 7 ) + ( ) I haven t made it home yet, but I ve made it to third base to like the 0th power. ( )( ) ( )( ) + ( ) ( ) ( ) ( ) ( ) + ( ) 8 + Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Escape the Matri with Ten Power Directions: Begin at the bo marked START. By shading in pairs adjacent squares that represent equal numbers, you will eventually find the path to escape this matri boes. The first step in the path and two the middle steps in the path have been shaded for you. START 0.000. 0 0,000,000 7. 0. 0 00,000 7.0 0 0 0 I ve got TEN power! 789 0 7.89 0.0. 0 8 9 0 90, 000, 000 7.90 0 0.90 0. 0 8, 000, 000 0 0. 0 0.000 0,00.0 0.0 0.0 0,000 0 0. 0 0.00 0.000 0.89 0 89 89 0 0 0 0.0 0.0.0.0 0 ESCAPE the Matri 7 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Caught in the Net Directions: Which fish get trapped between the two nets? Graph y = + and y = + 0 (the nets ) to find out. 9 y 0 J 8 0 8 8 0 K G M 8 0 L H 8 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Match Up on Polynomial Division Directions: Match each the epressions in the squares the grid below with an equivalent simplified epression from the top. If an equivalent epression is not found among the choices A through D, then choose E (none these). Be careful you may have to simplify rational epression terms. A + B C + + D E None these + + + 7 + + 8 + + 7+ 8 + + 9 ( ) ( ) ( + ) ( + ) ( + 7+ ) ( + ) y+ y abc abc y 8abc 9 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
The First Factoring Matchup Directions (READ them): In each bo the grid, you will find an epression that needs to be factored. Once you have factored each epression, look to see whether the factor appears in the list at the top. If it does, list that letter, if none the factors are listed, then choose F (none these are factors). The first one has been done for you. Some boes may have more than one answer. A + B C + y D y E + F None these are factors + y y ( ) + y( ) ( + y)( ) Ans: C y + 9y y + 8y y + y 8 + + y+ y y + 0y + y+ y yz yz y + y 0 7y y + + + + y y ab+ ab 0 y 0 9y + y + y + y + y + y y+ y y y y + 0 0 0 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Escape the Matri by Solving Quadratic Equations Directions: In each bo the grid, you will find a quadratic equation that needs to be solved. Once you have solved the equations, use pairs matching solution numbers to navigate your way out the matri. The first one has been done for you. For eample, the repeated solution leads you to the bo on the right, with solutions and. To move the net step on the escape route, you need to find an adjacent bo with a solution and something else. START HERE Solve: ( + ) = 0 Solutions: and Solve: = 0 ( )( ) + =0 Solutions and Solve: 8 8= 0 Solve: ( + ) = 0 Solve: + 8=0 Solve: = 0 Solve: 8+ =0 ( )( ) Solve: = 0 Solve: Solve: + = 0 Solve: 9+ =0 + = Solve: + =0 ( )( ) ESCAPE the Matri Solve: + 8+ = 0 Solve: = 0 Solve: 0 + = Solve: = Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Tic-Tac-Toe on Comple Fraction Pieces Directions: In every bo in the tic-tac-toe grid, there is a rational epression and a simplified form. If the two are equivalent, then circle the simplified form (thus placing an O on the square). If the epression has not been simplified correctly, then put an X over the incorrect simplification. Tic-tac-toe Game#: ( ) Tic-tac-toe Game#: ( ) ( ) 8 9 8 + + ( ) ( ) ( 8 ) 9 9 8 + + ( ) + ( ) ( ) + + 9 0 ( ) + + y y y 8 ( ) 0 + 7 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Match Up on Simple Rational Equations Directions: Solve each rational equation and check the result. Then choose the letter that corresponds to this result. Some problems may have more than one answer. If there is no solution, then choose E (No Solution). If the result is not among the choices, then choose F (None these). The first one has been done for you. A B C D E No Solution F None These Nice try, but you can t just erase the hard parts. + = + + = + ( ) + = + 8 = = ( C) = + 8 = = + + + = + + = + + = + 7 = + ( + )( + ) + = 7 + Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Escape the Rational Eponent Matri Directions: Assume all variables represent positive numbers. Begin at the bo marked START. By shading in adjacent pairs squares that contain equivalent epressions, you will eventually find the path to escape this matri boes. The first step in the path and a couple steps in the middle have been taken for you. START ( b ) 8b 9b + 7 b b y 9 y y ( ) 9y ( ) 7 7 y y 7 8 0 y y y 7 7 y 9 y ( + ) 9 + 0 y y y ESCAPE 0 y 00 y Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Sail Into the Pythagorean Sunset Directions: Almost all the triangles in the figure below are right triangles. Using the sparse information you are given and the Pythagorean Theorem, work out the lengths all the missing sides in the sailboat below. You should be able to work out the sides the non-right triangles by piecing together the information you find from the right triangles. It might be helpful to start by finding the measure a. g a = b = c = d = e = f = g = k 9 n 7 7 m 9 0 p 8 h h = j = k = m = n = p = a j c c c d 0 f 7 e 0 8 b 8 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Square Isolation Tic-Tac-Toe The square root property can be used to solve a quadratic equation if ) you can isolate the part the equation that is written as a square. ) the only variables in the equation are in the squared part. Directions: If the equation can be solved easily with the square root property using the rules above, then isolate the squared part, and circle the equation (placing an O on the square). If the equation cannot be easily solved with the square root property, then place an X on the square. ( + ) = 0 7 = ( ) = ( ) = = + 7 + 8 + 8 0= 0 9 = ( ) + = 0 + = ( + ) Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Match Up on the Discriminant Find the discriminant: b -ac. Negative Zero Positive The solutions are two different imaginary comple conjugates. The solution is one rational number. The solutions are two different real numbers. Non-perfect Square The solutions are two different irrational numbers. Perfect Square The solutions are two different rational numbers. Directions: In each bo, find the discriminant and then classify it. A Two different rational numbers 0+ = 0 ( ) ( )( ) B d = 0 = 0 C 9 = Two different irrational numbers C + = 0 = 0 One rational number D Two different imaginary numbers + =0 + = ( ) + = + = + = + = 7 + = 0 8 + = 7 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Eponential Workout Directions: For each epression, simplify and then find and shade the bo with its equivalent form in the grid.. ( e )..... 0 0 e 7 7. ( e ) / 8. ( ) 9. 0. 7 7 0 0. 99 ( ).. 0 e 9 e. ( ). ( 9 ) /. 0.00( 0 ) 7. 0 0 8. ( ) / e 9. + 8 0. ( ) 8.. e e e e 99 7-9 e 9 0 99 0 e 8 9 8 0 9 00 8 9 - e e.8 9 8 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Paint by Equivalent Equations Directions: Write each logarithmic equation as its corresponding eponential equation. Write each eponential equation as its corresponding logarithmic equation. Shade in your answers in the grid to reveal the picture. The first one has been done for you.. = log =. = 8. log =. log =. = 7. log = 8. log = 0 9. =. = 9. log000 =. log =. 0 =. 0 = 00 0. =. = 9 log 9 = log 9 0 = = 0 log = 8 9 log = log = 0 log = 00 = = log log = log/ = log = 00 log/9 = log 0 log 8 = log = log = 0 0 = = = = = = 8 log = log = 9 0 = 000 = log = log = = = 9 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Escape the Logjam Directions: Begin at the bo marked START. Either solve the equation or simplify the epression. Look for the result in the movement grid to the right. If your result is not in the movement grid, that s a BAD sign. For eample, the answer to = 7 is.77, so we move to the right. Net solve log =. ( ) Move Left 0.00. Move Right.77 0.7.0 0.09 Move Down.90.098 0.790 8 997 0.77 START = 7 =.t e =. e = log 8 log 0 log( ) = 0 e + e = 7 log = log ( 7) + log =.8 e =. + = = + = 8 = log = log log log = 0. = 7 e = 9 ln log = = log log = = + = 7 900 log = 900 log( + ) = log ln = + = 9 y = z+ ln e z ESCAPE the logjam 0 Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Name that Conic! y = y = 0 -... Conics are the BEST!!!!!! Match-up: Match each the equations in the squares the grid below with the conic classification. You may have to rearrange or simplify equations to determine their classification. A Circle B Ellipse C Parabola opening up or down D Parabola opening right or left y = 9 = y + E Hyperbola opening right and left F Hyperbola opening up and down G Something else + y = + ( y ) =9 ( ) + y = ( y ) y ( ) = y + = 9 9 y + = = ( ) ( ) ( y ) + + 9 = + y = + y + y = ( ) + + + = y + 00 y = 00 y + = Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.
Paint by Factorials Directions: Evaluate each the factorial epressions by simplifying first. Then shade in the bo in the grid that corresponds to the simplified epression. 8! 87 Eample: = = 87! = = 8 7 =. Evaluate:!. Evaluate: 00! 99!. Evaluate: 99! 00! 00 7. Evaluate:! 0! 00 0. Evaluate:. Evaluate:!! 7. Evaluate: 8. Evaluate: 0! 8! 0 8! ( ) 9!! 9! ( )!!! 0 0 0! 9. Evaluate:! 9!! 0. Evaluate: 9! 8! 7!0! 0! 8 undefined Cengage Student Activities for Intermediate Algebra, M. Andersen, Copyright 0.