MIDTERM REVIEW. Write an algebraic expression to represent the following verbal expressions. 1) Double the difference of a number and 7.

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1 NAME MIDTERM REVIEW DATE Write an algebraic epression to represent the following verbal epressions. 1) Double the difference of a number and 7. ) Find the value of the epression 0. Solve each equation. 1 = ) 5 y = 5) 7( + 8) = 1 6) Solve A = bh for b. Algebraic epression Equation Integers Irrational Number Rational Number Real Numbers Variables 7) A(n) is a mathematical sentence stating that two mathematical epressions are equal. 8) A(n) is a symbol, usually a letter, used to represent an unknown quantity. 9) are all numbers used in everyday life; the set of all rational and irrational numbers. 10) A(n) is any number m n, where m and n are integers and n is not zero. The decimal form is either a terminating or repeating decimal. 11) A(n) contain at least one variable. Solve each absolute value equation. When applicable, identify the empty set with. 1) + 5 = 1 ) c + 19= Evaluate the epression y if = - and y =. Solve the following inequalities. ) (w 1) 6 5) > 5 6) Write (DO NOT SOLVE) an inequality for the following: Thirteen more than a number is less than 8.

2 7) Graph 1 on the number line. 8) Write the inequality > 6using both set builder notation and interval notation. Set builder notation: Solve the following inequalities. 9) 1 y 5 < 9 Interval notation: 10) 1 5 or + 7 < 8 11) For < 0: Graph the solution set on the number line. 1) Write the solution set of 6< 5using interval notation. 1 Solve the inequality 8 6. Match the correct term to its definition. absolute value empty set union intersection 1) A number s distance from zero on the number line. 15) The graph of a compound inequality containing and. 16) The solution set for an equation that has no solution. 1) Identify the domain and range of the relation {(-, -7), (-6, ), (-, 1), (-, 7)}. ) Is the graph in #1 a function? Why? NO EXPLANATION = NO CREDIT! Write an equation in slope-intercept form for the line that satisfies each set of conditions: slope = 1, passes through (, 5). ) passes through (-, ), parallel to the line whose equation is y = ) Write an equation for this graph in slope-intercept form.

3 Evaluate if f( ) 1 = and g() = 1. 6) f (b) 7) g ( For questions 8 10, use the set of data in the table. Field Goals Attempted (a) Points Scored (p) The table above shows the relationship between the number of field goals attempted and the number of points scored by one basketball player over a 6-game period. 8) Sketch a scatter plot for the data. 9) Use two ordered pairs to write a prediction equation. 10) Use your prediction equation to predict the number of points scored when 0 field goals are attempted. 11) Graph f() = ) Graph, if 1 g ( ) =. 1 Graph y 1. 1, if > 1 Word Bank Absolute value Domain Greatest integer Line of best fit Parallel Perpendicular Range Slope Vertical line test y-intercept 1) The graph of a(n) function forms a V- shape. 15) Two lines in the same plane having the same slope are. 16) The set of all -coordinates of the ordered pairs of a relation is the. 17) The ratio of the change in the y-coordinates to the corresponding change in - coordinates is called the of a line. 18) The can be used to determine if a relation is a function.

6 1) Solve the system of equations by graphing. Write the solution as an ordered pair. 5 5 ) Solve the system of equations by using substitution. Write the solution as an ordered pair. + y = 5 y = Solve the system of equations by using elimination.

4 6 1) Solve the system of equations by graphing. Write the solution as an ordered pair. 5 5 ) Solve the system of equations by using substitution. Write the solution as an ordered pair. + y = 5 y = Solve the system of equations by using elimination. Write the solution as an ordered pair. + y = 7 y = 19 Simplify the following epressions using only positive eponents. 1) ( ) 0 ) ( ) Add: ( z ) + ( z 6) ) Subtract: ( 5 + 6y 5) ( 7 + y+ Multiply the following polynomials. 5) ( + )( + 5) 6) ( + 6) 7) ( + 1)( 1) 8) Divide the following polynomial. The quotient should be simplified, written with only positive eponents y y 5 y 9) Use long division of polynomials to find the quotient. + 1 ( ) ( ) 10) Use synthetic division to find the quotient ( ) ( )

5 binomials coefficients constants polynomials terms 11) are monomials that contain no variables. 1) The monomials that make up a polynomial are called the of the polynomial. 1 are polynomials that have two unlike terms. Factor each polynomial completely. If the polynomial cannot be factored, write prime ) y 6y + 8y ) ) ) 0 6) y(y + (y 7) 9) ) ) ) 7 Simplify the following epressions. 1) 6 6 ) ) ( )( 5 9 ) Simplify. 5) Find the product and simplify the following epressions. 6) ( 7+ )( 7 ) 7) Simplify the following epression: ) Write the epression using rational eponents ) Evaluate: 16 10) Simplify the epression: 1

6 Solve the following equations for real solutions. Check your answers to determine whether the solutions are real numbers. If there is no real solution, write NRS. 11) + = 6 1) = = 0 Find the product and simplify. 1) i i11i 15) ( i)( + 7 i) 16) Simplify: 5 i Solve the following equations and write your solution using imaginary notation, when necessary. 17) + 75= 0 18) Find the values of and y that makes the following equation true. (7 ) + (y+ i= i conjugates etraneous imaginary inde principal rational eponent 19) A solution of a transformed equation that is not a solution of the original equation is a(n) solution. 0) When a number has more than one real root, the root is the non-negative root. 1) Binomials of the form a b + c d and a b c d where a, b, c, and d are rational numbers are called of each other. n ) In the epression, n is the.

ALGEBRA SUMMER MATH PACKET

Algebra Summer Packet 0 NAME DATE ALGEBRA SUMMER MATH PACKET Write an algebraic epression to represent the following verbal epressions. ) Double the sum of a number and. Solve each equation. ) + y = )