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 + 1 6 = 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.
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 = + 5. 5) Write an equation for this graph in slope-intercept form.
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) 8 6 10 9 7 10 Points Scored (p) 1 9 1 1 11 15 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() = + 1. 1) 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. 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. 6 7 10y y 5 y 9) Use long division of polynomials to find the quotient. + 1 ( ) ( ) 10) Use synthetic division to find the quotient. + 1+ 15 + ( ) ( )
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. 5 6 1) y 6y + 8y ) 9 1+ 6 ) + 1+ 5) 0 6) y(y + (y 7) 9) 6 15 8 0 + 8) + 9 10) 10 11 6 + 0+ 50 11) 7 Simplify the following epressions. 1) 6 6 ) 5 81 16 ) ( )( 5 9 ) Simplify. 5) 5 + 9 1 8 Find the product and simplify the following epressions. 6) ( 7+ )( 7 ) 7) Simplify the following epression: 5 + 7 8) Write the epression using rational eponents. 10 7 9) Evaluate: 16 10) Simplify the epression: 1
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) + 11 + 7 = 1 1 5 = 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= 19 + 15i 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.