MIDTERM REVIEW NAME DATE Write an algebraic expression to represent the following verbal expressions. 1) Double the difference of a number and 7. 2) Find the value of the expression 24 − 20 ÷ 4 . Solve each equation.

3)

14− 2x5

= −2

4) −2y

3+ 1

6= − 3

2

5) −7(x +8) = 21 6) Solve A = bh

2 for b.

7) A(n)____________________is a mathematical sentence stating that two mathematical expressions 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 mn, 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) 4 5 12x+ = 2) 3 2 19 3c− + = 3) Evaluate the expression 2 2x − y if x = -2 and y = 3. Solve the following inequalities. 4) 2(3 1) 26w− ≤ 5) 22 5 3x> − − 6) Write (DO NOT SOLVE) an inequality for the following: Thirteen more than a number is less than 48.

Algebraic expression Equation Integers Irrational Number Rational Number Real Numbers Variables    

7) Graph 1x ≥ − on the number line. 8) Write the inequality 6x > − using both set builder notation and interval notation. Set builder notation: Interval notation: Solve the following inequalities. 9) 12 5 9y− ≤ − < 10) −4x −1≤ 35 or 3x + 7 < −8 11) For 2 0x− ≤ < : Graph the solution set on the number line.

12) Write the solution set of 6 5x− < ≤ using interval notation. 13) Solve the inequality x − 8 ≥ 6 . Match the correct term to its definition. 14) 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 {(-2, -7), (-6, 4), (-3, 1), (-3, 7)}. 2) 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: 3) slope = 1, passes through (2, 5).

4) passes through (-4, 2), parallel to the line whose equation is 5.2xy = +

5) Write an equation for this graph in slope-intercept form.

4

2

2

absolute value empty set union intersection

Evaluate if 2( ) 13f x x= − and g(x) = 1− x . 6) f (2b) 7) (3)g For questions 8– 10, use the set of data in the table.

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 20 field goals are attempted. 11) Graph ( ) 1f x x= + . 12) Graph

2 , if 1( ) .

1, if 1x x

g xx

≤ −⎧= ⎨ > −⎩

13) Graph 1y x≥ − − .

14) 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 x-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 x-coordinates is called the _______________________________of a line. 18) The ____________________________can be used to determine if a relation is a function.

Field Goals Attempted (a) 8 6 10 9 7 10 Points Scored (p) 12 9 14 14 11 15

Word Bank Absolute value Domain Greatest integer Line of best fit Parallel Perpendicular Range Slope Vertical line test y-intercept  

 

2) Solve the system of equations by using substitution. Write the solution as an ordered pair.

2 53 3 3x yx y+ =− =

3) Solve the system of equations by using elimination. Write the solution as an ordered pair.

3 4 74 19

x yx y

+ = −− =

Simplify the following expressions using only positive exponents. 1) ( )0x 2) ( )234x 3) Add: ( ) ( )2 23 4 2 6z z− + −

4) Subtract: ( ) ( )2 25 6 5 7 3 3x xy x xy+ − − + + Multiply the following polynomials. 5) ( )( )4 2 5x x+ + 6) ( )26x + 7) ( )( )3 1 3 1x x+ − 8) Divide the following polynomial. The quotient should be simplified, written with only positive exponents.

2 6 7 3

5 2

10 42

x y x yx y−

9) Use long division of polynomials to find the quotient. ( ) ( )22 3 14 2x x x+ − ÷ − 10) Use synthetic division to find the quotient. ( ) ( )23 14 15 3x x x+ + ÷ +

5 5

6

4

2

2

4

1) Solve the system of equations by graphing. Write the solution as an ordered pair.

 

11) ________________________ are monomials that contain no variables. 12) The monomials that make up a polynomial are called the _________________ of the polynomial. 13) _____________________ are polynomials that have two unlike terms.  Factor each polynomial completely. If the polynomial cannot be factored, write “prime.” 1) 4 5 2 6 34 6 8x y x y x y− + 2) 2 9x − 3) 2 12 36x x− + 4) 2 14 24x x+ + 5) 2 3 40x x− − 6) 3 (2 3) 4(2 3)y y y− + − 7) 3 26 15 8 20x x x− + − 8) 210 11 6x x− − 9) 2 49x + 10) 22 20 50x x+ + 11) 3 27x − Simplify the following expressions.

1) 3 664x 2)

2581

3) 16x44 4)

2 −3x3( ) 5 9x3( )

Simplify. 5) 5 3 9 12 2 48+ − Find the product and simplify the following expressions. 6) ( )( )7 3 2 7 3 2+ −

7) Simplify the following expression: 5 73

+

8) Write the expression using rational exponents. 10 7x

9) Evaluate: 16 3

4 10) Simplify the expression: x34

x13

binomials coefficients constants polynomials terms

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) 4 4 2 6x − + = 12) 11 7 4x + + =

13) x12 − 5 = 0

Find the product and simplify. 14) 4i i11i 15) (2 4 )(3 7 )i i− + 16) Simplify: 25i Solve the following equations and write your solution using imaginary notation, when necessary. 17) 23 75 0x + = 18) Find the values of x and y that makes the following equation true. (7 2) (2 3) 19 15x y i i− + + = +

19) A solution of a transformed equation that is not a solution of the original equation is a(n)_________________________ solution. 20) When a number has more than one real root, the _________________root is the non-negative root. 21) 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. 22) In the expression xn , n is the __________________________.  

conjugates extraneous imaginary index principal rational exponent