7.12 The student will represent relationships with tables, graphs, rules, and words.

Transcription

1 7.12 The student will represent relationships with tables, graphs, rules, and words. HINTS & NOTES Relation- is a set of ordered pairs. Remember to always start from the origin. Origin is (0,0) Move horizontally ( ) first and then move vertically ( ). Ordered pair (x, y) Practice 1. Which equation is true for all values in the table. X Y A. y 3 x B. y 3x C. y 3x II I D. y x 4 2. Create a table to match the coordinates given in the picture below. III IV X Y Rules- describe a relationship between two sets of numbers with a table, graph, word sentence or equation. 3. The output value(y) of a function is equal to the input value(x) divided by three. Write an equation to represent this relation. Y= Describe and represent relations and functions, using tables, graphs, rules, and words. Given one representation I can represent the relation in another form. Math SOL Review Guide (Grade 7) 1

2 7.13 The student will a) write verbal expressions as algebraic expressions and sentences as equations and vice versa; and b) evaluate algebraic expressions for given replacement values of the variables. HINTS & NOTES PRACTICE 1. Which represents the phrase shown? The product of three and a number, decreased by 2 Sum add Total add Increased by add Difference subtract Less than subtract Decreased by subtract Product of multiply Times - multiply A. 3(x - 2) B. 3(2 x) C. 2 3x D. 3x 2 2. Which phrase best represents the following? 4x 6 Quotient of divide Twice multiply by 2 REMEMBER 7 less than a number means n-7 NOT 7-n An expression is like a phrase, while an equation is like a sentence. Equation a statement in which two expressions are shown to be equal. Inequality a comparison of two expressions that uses one of the symbols,, <, >, and. Expression a group of numbers, variables, and operations that express a numerical relationship. 3. F. Six less than four times a number. G. Four times a number less than six. H. Six less than a number squared. J. A number squared less than six. Which best represents the sentence above? A. B. C. D. Twice the number of students in Tim s class divided by five is ten. 2 j j2 2 j j2 = 10 = Select all the expressions below.. Identify all the statements that are false. Math SOL Review Guide (Grade 7) 2

3 6. What phrase best represents the following? 2x + 7 F. Seven more than twice a number G. Seven more than a number squared H. A number squared more than Seven J. Two plus a number seven. 7. Evaluate three more than twice x, if x=-4. Write your answer in the box provided. 8. Write an expression for five less than one-third x, in the box. 9. Evaluate 2x ( x) 4, if x=-8. Write your answer in the box. 10. Create your own word sentence and then write the equivalent equation. Write verbal expressions as algebraic expressions. Expressions will be limited to no more than 2 operations. Write verbal sentences as algebraic equations. Equations will contain no more than 1 variable term. Translate algebraic expressions and equations to verbal expressions and sentences. Expressions will be limited to no more than 2 operations. Identify examples of expressions and equations. Apply the order of operations to evaluate expressions for given replacement values of the variables. Limit the number of replacements to no more than 3 per expression. Math SOL Review Guide (Grade 7) 3

4 7.14 The student will a) solve one and two-step linear equations in one variable; and b) solve practical problems requiring the solution of one and two-step linear equations. Hints & Notes Practice To Solve Isolate the variable Use inverse operations. An operation that is performed on one side must be done on the other side as well. To Check Plug it in! Plug it in! For any problem involving solving an equation or an inequality, plug in all of the answer choices until you find the one that works. 1. What is the value of k that makes the following true? k (-2) = 6 A. -8 B. -4 C. 4 D Which equation is represented by the model below? F. 3x=9 G. 1x + 2x = 9 H. x-3=9 J. 2x + 3 = 9 3. Solve each equation below and write your solution in the box. a. 4f=28 b. -3y=-1 c. -11=n-2 4. Identify all equations below that have a solution of -2. Represent and demonstrate steps for solving one and two-step equations in one variable using concrete materials, pictorial representations and algebraic sentences. Solve one and two-step linear equations in one variable. Solve practical problems that require the solution of a one or two-step linear equation. Math SOL Review Guide (Grade 7) 4

5 7.1 The student will a) solve one-step inequalities in one variable; and b) graph solutions to inequalities on the number line. Hints & Notes Practice To Solve Isolate the variable Use inverse operations. An operation that is performed on one side must be done on the other side as well. 1. Solve x < 4, and graph on the number line provided. 2 A. x < -8 B. x > -8 C. x < -2 D. x > -2 If you MULTIPLY or DIVIDE both sides of an INEQUALITY by a NEGATIVE number you must REVERSE the comparison sign 2. Select all the values for t that make the following true? t To Check Plug it in! Plug it in! For any problem involving solving an equation or an inequality, plug in all of the answer choices until you find the one that works. 3. Solve each of the following inequalities and write your answer in the box provided and graph on the number line. Represent and demonstrate steps in solving inequalities in one variable, using concrete materials, pictorial representations, and algebraic sentences. Graph solutions to inequalities on the number line. Identify a numerical value that satisfies the inequality. Math SOL Review Guide (Grade 7)

6 7.16 The student will apply the following properties of operations with real numbers: a) the commutative and associative properties for addition and multiplication; b) the distributive property; c) the additive and multiplicative identity properties; d) the additive and multiplicative inverse properties; and e) the multiplicative property of zero. HINTS & NOTES PRACTICE Commutative switches places (commutes) a + b = b + a a b = b a Associative switches groups (associates w/ different people ) a + (b + c) = (a + b) + c a (b c) = (a b) c Distributive a(b + c) = ab + ac Identity the starting identity does not change. a + 0 = a a 1 = a Inverse adding or multiplying by the opposite or reciprocal a + -a = 0 a a 1 = 1 Multiplicative Property of Zero if you multiply by 0 then your answer is 0. a 0 = x = 1 If the number sentence is true, then x is the A. additive identity B. additive inverse C. multiplicative identity D. multiplicative inverse 2. Which number sentence illustrates the commutative property of multiplication? F (10 ) = 12 + ( 10) G (10 ) = 10 + (12 ) H (10 ) = ) J (10 ) = ( ) 3. Choose the number that completes this statement of the Associative Property. 16 (24 1) = (16 24) A. 1 B. 16 C. 24 D Jane is simplifying the following expression. Write the property she used the box to the right of each step. Identify properties of operations used in simplifying expressions. Apply the properties of operations to simplify expressions. Math SOL Review Guide (Grade 7) 6