Algebra Honors Summer Review 07-08 Label each problem and do all work on separate paper. All steps in your work must be shown in order to receive credit. No Calculators Allowed. Topic : Fractions A. Perform the indicated operations. Simplify if possible... 5. 7. 5 + 9. 8 9. 8 6 + 9 6. 7 5 0 6 8. 5 + 8 7 9 5 5 8 8 6 B. Perform the indicated operations. Simplify if possible. 9... 5. 7. 5 6 0. 5 7. 9 8 9 0. 8 6. 5 5 8. 6 5 5 7 8 7 8 7 8 8 C. Perform the indicated operations. Simplify if possible. 9... 7 7 9 6 8 6 7 5 5 0 7 0... 7 5 + 9 8 6 + 6 5 + 6 Topic : Decimals A. Change the fractions to decimals.. 5. 5 B. Perform the indicated operations. Simplify if possible...57 + 0.6.. -.7 5. 5.6 + 9. + 7.
C. Perform the indicated operations. Simplify if possible. 6. (0.00)(6) 7. (9.6)(5) 8. 0.8 0.8 9..906. Topic : Proportions and Percents A. Solve each proportion... 8 m =. 6 7 8 6 =. 5 x z 8 = 5 6 = 0 c 5. x 5 6 x = 6. = 5 8 00 B. Applications: Solve Each Proportion 7. If 6 feet of rope weigh 0 pounds, how much will 80 feet of the same rope weigh? 8. If pounds of turkey costs $.98, what should pounds cost? 9. Katie and Jenna traveled 9 miles in 7 hours. If they travel at the same rate, how long will it take them to travel 78 miles? 0. Three loaves of bread cost $.87. How much do loaves cost? C. Solve each percent.. 0% of 0 =. 5% of 5 =. % of 5 = 5. % of 75 = 5. 0% of = 5 6. 80% of = 56 7. % of 5 = 6 8. 80 % of = 6 9. The purchase price of a camera is $8. The carrying case is % of the purchase price. Find the total cost of the camera and the carrying case. 0. A test has 50 questions. Marissa got 80% of them correct. How many did she get correct?. Diet soda contains 90% less calories than regular soda. If a can of regular soda contains calories, how many calories does a can of diet soda contain?. A salesman makes a 5% commission on all he sells. How much does he have to sell to make $500?
Topic : Signed Numbers A. Perform the indicated operations.. 8.6 + (.7). ( 0) + ( ). 0+ ( 9). 5+ ( 8) + ( ) 5. [ 7+ ] + ( 9) + 8 6. [ 8+ 9] + 7+ ( 5) 7. + 7 + ( ) 8. 6 9. 6 ( ) 0. 6 ( 7). 5.. ( 0 ). 6 5 + B. Evaluate when x=, y= 6, and q= 5. x+ y+ q 6. y q x 7. y+ y+ q 8. x+ y q C. Combine like terms. Simplify if possible. 9. a+ a+ 0. 7x x+ y+ 57. x y+ x+ y. 9m m n+ n D. Perform the indicated operations.. ( 5)( ). ( 8) 5. ( )( 5) 6. ( ) 7. ( ) 8. 9. 0 5 0. ( )
.. 6. ( ) ( )( )( ) 6 ( 8) ( ). 0 00 8 + + + 5 ( ) ( ) 5. 5( 0) 6. 0 7. 8. 7 0 Topic 5: Basic Review A. Choose the numbers from the following set which belong in each category.,0,,,,6,7, 5, 7, π. Natural numbers. Whole numbers. Integers. Rational numbers 5. Irrational numbers 6. Real numbers 7. Imaginary numbers 8. Prime numbers 9. Composite numbers 0. Even numbers. Odd numbers B. Determine whether the following statements are true or false.. is a real number. Every rational number is an integer. 5 is an irrational number 5. 8 is a rational number 6. 0 is a natural number. 7. is an integer. C. Name the Property that justifies each statement. 8. If = x and x = y, then = y 9. (x + y) = x + y 0. (a + b) + c = a + (b + c). 5 + ( 5) = 0. If a = b, then b = a. a + b = b + a. ab = ba 5. 6 6. ( ) = 6 = 7. (ab)c = a(bc )
D. Find the absolute value. 8. 0 9. 0.. 0 E. Write the opposite and reciprocal of each number.. 8 Opposite: Reciprocal:. 0 Opposite: Reciprocal:. Opposite: Reciprocal: 5. Opposite: Reciprocal: F. Find the roots. 6. 6 7. 0 8. 6 5 9. G. Insert <, >, or = between each pair of numbers to form a true statement. 0. 5. 6 8..5.05. 7 8 G. Translate each statement using mathematical symbols. Use the variable x to represent each unknown number. Do not simplify or solve. Some may be expressions and some may be equations/inequalities.. Three less than eight times a number 5. Twice the sum of four and a number. 6. The sum of 5 and a number is greater than or equal to 7. 7. The difference of half a number and amounts to. 8. Three more than the product of and a number is 7. 9. Four times the sum of 5 and a number is not equal to the opposite of 5. H. Perform the indicated operations. Simplify if possible. 50. 8 5. 0 ( 0 ) 5. ( ) ( ) 6+ 6+ 9 5. 8 5 5
5. + 55. 8 8 56. 6 ( 6 + ) 0 + i8 57. ( ) 5 58. Change to scientific notation: 0.0000097 8 59. Change to standard notation: 9. 0 60. Classify as a monomial, binomial or a trinomial: + x+ x 6. If Px () = x + x, find P( ). 6. Evaluate when x = and y = : 6. Evaluate when x = 9 and y = : x y x+ y y x x y Topic 6: Equations, Inequalities and Absolute Values A. Solve each equation.. 5n + =. 5 y = 5. 8 x =. 5 = 5 0 n 5. 5 = b 6. 8m m+ 7 = 9 7. 7 x x 7 5x 7 = + = 8. ( ) 9. x+ ( x+ 5) = 0 0. ( x ) 9 + 5=. ( 5+ m) = 0. ( ) x 7 = B. Solve each inequality.. t+ > t 7. y 9> 5. x 5 x 0 < + 6. ( x ) + < x+ 7. 5x ( x ) 8. m ( m ) + 6 > 9 9. ( t+ ) 5( t+ ) > 0 0. x ( x ) ( x) + 5+ +
C. Solve each absolute value equation.. a + =. x 6 =. x =. x + 6 = 5. x + 6= 6. 6x + + 6= 9 7. x = 8. 6 x + = D. Solve each absolute value inequality. 9. x < 9 0. x + > 7. x 5. x 5. x <. x + + 8< 5. x + 5< 6 Topic 7: Polynomials A. Perform the indicated operations.. ( x x+ 7) + ( x + x+ 5) ( x x+ ). ( 5x + x+ ) ( x + x+ 7). ( a b) ( a 5b) +. ( 6x x x) ( x 6x+ ) 5. ( b a) + ( 8b 5a+ c) 6. ( 7x 9y+ ) ( 5x 8y+ 6) 7. a+ ( a b) ( a b) 8. x ( 6x y) + ( x 7y) 9. ( a 5) + ( a ) ( a+ ) 0. ( 7m+ ) + ( 6m+ ) ( m+ 7). ( x x+ ) + ( 5x x+ 7) ( x + 6x 5). ( 7a 5) ( a ) + ( a+ ) B. Perform the indicated operations.. 6 ( 5 ) 5. ( b) ( 6b) a a. 7b ( b) 6. ( x y )( x y ) 7. ( 7 )( ) mn mn 8. 7ab ( a b)( ab) 9. ( x )( x 5) 0. ( x )( x+ ). ( 7x )( x ). ( x+ )( x+ 9). ( x 5)( x ). ( x )( x ) 5. ( x+ )( x + 7x ) 6. ( 8a 7)( a + 5a+ )
C. Factor each polynomial completely. 5 7. 6a 5a 8. ab + 6ab 5 5 9. x x x 0. x + x x. x + 5x + 6x. x 8x+ 5. x + x. + x x 5. x + 7x+ 6. x 7x + 6x 7. 8x 8. 6 a + 6a 9 9. 5x 5 0. xy + y x 8 D. Solve each quadratic equation.. x + x= 0. x x 6= 0. x 7x+ = 0. x 5x 6= 0 5. x = 00 6. x 8x 9= 0 Topic 8: Graphing A. Find the slope of the line containing the given points., ;, 5. P( ) Q ( ). R( 5, ); S(, ). T(, ); V(, 7). M(, ); R(,) 5. C( 0,0 ); D(,) 6. P( 0, ); S( 6,) 7. E( 6, ); F( 6,9) B. Use the slope and the y-intercept to graph each equation. 8. x+ y = 9. y x = C. Determine if the lines are parallel 0. x+ y= and 6x+ y=. x y= and 6y+ x= 8. x y= 0 and x y= 0. y+ 6= 0 and y = 0 Topic 9: Systems of Equations A. Solve by the addition or substitution method.. x+ y = y = x+. x+ y = 7 x y =. a+ 5b= 0 a+ b= 8
. x+ y = 9 x+ y = 6 5. x+ y = 9 x+ y = 6. x+ y = 0 x+ y = 7 Topic 0: Word Problems A. Integer Problems. One number is 5 times another. The sum of the numbers is 7. Find the numbers.. One number is less than another. The sum of the numbers is 0. Find the numbers.. The sum of two consecutive integers is -7. Find the integers.. Find three consecutive integers whose sum is 8. 5. The sum of two consecutive odd integers is. Find the integers such that the sum of the first and third is 0. B. Measurement Problems 6. The length of a rectangle is 7 times its width. The perimeter of the rectangle is 6 centimeters. Find the dimensions of the rectangle. 7. The lengths of the sides of a triangle can be represented by three consecutive even integers. The perimeter of the triangle is 96 meters. Find the lengths of the sides of the triangle. 8. The length of a rectangle is 8 inches more than twice its width. The perimeter is inches. Find the length and width of the rectangle. C. Age Problem 9. Anna is now four times as old as her brother Ramon. In years, Anna will be twice Ramon's age then. How old is each now? D. Distance Problem 0. Two automobiles start at the same time at the same place and travel in opposite directions. One travels at a rate of 5 kilometers per hour and the other at a rate of 0 kilometers per hour. In how many hours will they be 5 miles apart? Sketch the given information first, then write the equation and solve. E. Problems Using Two Variables. The sum of two numbers is 5. The difference of the same two numbers is 0. Find the numbers.. Two angles are supplementary. The measure of one angle is 0 more than twice the other. What is the measure of each angle?