Topic 1: Order of Operations, Integer Exponents

Transcription

1 ESM Materials Topic : Order of Operations, Integer Exponents Objective #: Master Order of Operations (Understand misleading nature of PEMDAS ) Objective #: Simplify expressions involving Integer Exponents Objective #: Evaluate formulas, expressions and functions Order of Operations Step : Grouping Symbols: [( )],, ab. value inside-out Step : Exponents Step : Multiplication/division Left Right Step : Addition/subtraction Left Right Example Example Example () 0 () ( ) 0 () + 0 () + 0 () () [ ] [ 0] I. Perform the operations - no calculator! Simplify completely. ) ( ) ( + ) + ( 0) ) ( ) ( ) ( ) ) + + ) + + ) + [ () ] ) + ) + ) ) + 0) ( ) ( ) + ) 0 + ) ( ) ) ) ( ) ) ( ) ) ) ) + ) + 0) ) 0 0

2 ) ) ) ) + ) 0 ) ( ) ) ) ( ) 0) 0 ) ) + ) ) + ) ( ) ) ( ) + ) ) ( ) ) + ( ) ( )( ) 0) + () ( ) ( ) ()( ) ) + () ()( ) ) ( ) ()( ) () ) () ( ) ( ) ()( ) II. a, b: Evaluate each formula or expression at the given value(s). For c, solve for unknown value. ) F = C+ ; a) C = 0 b) C = c) F = 0 ) C = ( F ) ; a) F = b) F = 0 c) C = ) ) ) K S = mv = ; a) m ; v n a = = b) m= 0; v= c) K = 0; v= ; a) ; a a = n = b) a = ; n= x yz ; a) x ; y ; z = = = b) x= ; y = ; z = ) y z xy a) x= ; y = ; z = b) x= ; y = ; z = III. Evaluate each function at the given value; write result as an (Ordered, Pair). ) gx ( ) = x ; x = ) hx ( ) = x x +. ; x = 0. ) rt () = t+ ; t = ) ) f( x) =.x+ 0. ; x = 0. ) hx ( ) x x =, x = f( x) = x + x ; x = ) f( x) = x x ; x = ) hx ( ) x x = ; x =

3 IV. Simplify: express answer with positive exponents. a) 0 a b b) x yz c) ( n ) d) ( n ) e) ( n ) f) ( n ) g) ( n ) 0 h) p i) pm pm j) abc abc k) nw l) nw km k m m) a b c( abc ) n) 0 x w z( x w z ) o) ( 0 a b ) p) ( x y ) q) a b ( a b ) Topic : Place Value, Rounding, Fractions Objective #: Identify place-value by name and exponential equivalent Objective #: Express numbers in written form; round numbers Objective #: Perform operations with fractions I. a) Place Value name; b) Values in decimal form; c) Values in fraction form; d) Values in 0 n form a) b) c) d). II. a) Round,, to the nearest: ten thousand hundred ten thousand million ten million hundred thousand b) Round.0 to the nearest: unit thousandth ten hundredth tenth ten-thousandth hundred III. Express each number in written form. Examples: Acceptable Unacceptable a) 0.0 sixty-two thousandths point zero, six, two b). two and fifteen hundredths two point fifteen c).00 seventy-four and five hundred two ten-thousandths

4 Number ) 0.00 ). ). ) 0. ).0 ) ) 0. ) 0.00 Written form IV. Simplify the following fractions. ) ) ) ) 0 0 ) 0 ) 00 V. Write each improper fraction as a simplified mixed number, e.g., = ) ) ) ) ) ) VI. Perform the operations; simplify. ) 0 ) ) 0 ) ( ) 0 0 ) ) 0 ) ) + ) 0) + ) + ) 0 ) + ) ) ( ) ) 0 ) 0 ) ) + 0) ) + ) ) 0 0 ) ( ) ) 0 + ) + ) + ) ( ) + ) ( ) 0) ( ) ( ) VII. Determine the unknown part of each circle. ) ) ) / / / / / / / /

5 Topic : Fractions, Decimals, % and Scientific Notation Objective #: Improve computational skills with fractions, decimals and per cents Objective #: Develop mental math skills and number sense Objective #: Convert numbers to Scientific Notation/Standard forms I. Determine the unknown part of each circle. ) ) ) ) ) ).%.% % % %.0%.%.%.% II. Perform the operations; simplify. ) ).0 0. ) ).0 0. ) ) ) ) ). + ( 0.) 0). ( 0.) ) ( 0.). )(.) ( 0.) 0 ) (.) (. ) ) ( 0. ) (0.) ) ( 0.).( 0.) ) ( 0.) ( 0.) + ( 0.) III. Divide by moving the decimal point(s), then simplifying fraction. (Do not use long division.) ). ) 0. ) ). ) ) ). IV. Express each fraction as a decimal and a per cent. ),000 ) ) ) 00 ) ) ) ) ) 0,000 0) 0 V. Express each decimal as a per cent and a simplified fraction. ) 0. ) 0. ).0 ). ). ). ) 0.0 ) 0.0 ) ) 0.0

6 VI. Express each per cent as a decimal and as a simplified fraction. ) % ) 00% ) % ),% ) 0.% ).% ) % ) 0% ) 0.0% 0).% ) % ) % ) % ) 0 % VII. Express each per cent as a simplified fraction. (Hint: Avoid long division) % ) % ) % ) % ) % ) VIII. Mental Math Find the following without a calculator. Look for patterns.. a) 00% of lbs. b) 0% of lbs. c) % of lbs.. a) 00% of $, b) 0% of $, c) % of $,. a) 0% of feet b) 0% of feet c) 00% of feet. a) 0% of cm b) % of cm c) 0.% of cm. a) % of,000 students b) 0% of,000 students c) 0.% of,000 students. a) 0% of $.0 b) % of $.0 c) % of $.0. a) 0% of $0.0 b) % of $0.0 c) % of $0.0 IX. Convert to Scientific Notation. Round answers to nearest hundredth. Example: is written as. 0. ),00,000 ),00 ), ) ), ) 0.00 ) 0. ) ) ). ) 0.0 ),. X. Convert to standard form. ). 0 ). 0 ).0 0 ) ). 0 ). 0 ). 0 ) 0 0 XI. Perform the operations. Write answers in Scientific Notation, rounded to nearest hundredth ) ( ) + ( ) ) ( ) + ( ) ) ( ) ( ) ) ( 0 ) (. 0 ) ) (. 0 ) ( 0 ) ) (. 0 ) (. 0 ) ) (. 0 ) ) ( ). 0 ) ). 0 0 XII. True or False a) ( ) = b) ( + ) = + c) = d) e) = f) ( ) = g) = h) = 0 (0 ) =

7 Topic : Applications to Fractions, Decimals, and % Suggestion: In problems,,, and, organize the given information into a chart, diagram, etc. ) At a school of students, 0 are girls. Ten of the students who play hockey are boys. a) How many boys attend the school? b) How many girls play hockey? c) How many students do not play hockey? d) What simplified fraction of the hockey players are girls? e) What simplified fraction of the girls plays hockey? f) What simplified fraction of the boys plays hockey? g) What % of the girls plays hockey? ) In a business of 0 employees, are men. Eight of the employees that are accountants are women. a) How many women work in the office? b) How many male accountants are there? c) What simplified fraction of the employees is male? d) What simplified fraction of the accountants is female? e) What % of the employees works in accounting? f) What % of the men does not work in accounting? ) Fifty people were asked to name their favorite ice cream. The results of the survey are below. Other a) What % chose Other? Chocolate, % Vanilla, % Strawberry, 0% b) What simplified fraction named strawberry? c) What simplified fraction chose vanilla? d) How many selected: vanilla? chocolate? ) A sports club has 0 members, % of whom surf. Two-thirds of the surfers snow board; other club members also snow board. a) How many of the club members surf? b) What simplified fraction of the members does not surf? c) How many of the surfers snow board? d) What simplified fraction of the members does not snowboard? e) What % of the members snow boards? ) Malin polled a group of students. Her findings: 0% of the students had registered to vote; eightfifteenths of the students support the Democratic candidate, and of the supporters of the Democrat are male. a) How many of the students are registered to vote? b) What simplified fraction of the students is registered to vote? c) What % of the students is not registered to vote? d) How many of the students prefer the Democratic candidate? e) What simplified fraction of the students do not prefer the Democrat? f) How many of the supporters of the Democrat are female? g) What % of the supporters of the Democrat are male? h) What % of the supporters of the Democrat are female?

8 Topic : Expressions, Equations, Formulas Objective #: Determine whether an expression or equation Objective #: Simplify expressions; solve equations Objective #: Solve a formula for the indicated variable. I. Classify as expression/equation; simplify/solve, as appropriate.. a) nn b) n =n. a) (a) ( a) = a+ b) (a) ( a) + a+. a) c c+ 0 = b) c c+ 0. a) a+ a b) a+ = a. a) y y = y+ b) y y y 0 0. a) 0. p 0.0 p+ 0. b) 0. p 0.0 p+ =0.. a) r r b) r. =. + 0.r. a) 0.(x+ ) =. x b) 0.(x+ ). x. a) 0.y0.0y =. b) 0.y0.0y +. II. Simplify the expressions; solve the equations. b ) y 0.y ) = 0.. ) ) [ n ] k = ) [ w + (w ) ] ( ) = 0 ) y = ) m m ) v = v 0 0 r r+ (r+ 0) = 0 0) n = 0 ) c c + ) 0.r0.r.. ) ( ) ) ( ) ( ) ) n+ n = ( n) ) y 0.y = 0. n n + n + ) ( cd ) d(c+ ) ) c c + = ) y+ = y ) 0) 0.r+ r 0.0 =0.0 ) (y) y( y)(y+ ) ) xy xy y + y ( a b) a(a b) III. Solve for the indicated variable. ) y = mx + b; x ) L+ W = P; W ) V = Ah A ) as S = a n ; S ; y y ) m= ; y ) x x ab + c K = mv ; m ) PRT = A P; P ) L= ; n b

9 Topic : Applications Objective: Develop a structured approach for solving comparison application problems. The length of a rectangular garden is four feet longer than the width. The garden s perimeter is feet. a) Express in terms of x: width = length = c) Find the dimensions of the garden; use correct units.. A piggy back contains coins, all nickels and quarters. There are three times as many nickels in the bank as quarters. a) Express in terms of x: # nickels = # quarters = c) Find the number of nickels and the number of quarters in the bank.. A piggy back contains coins, all dimes and pennies. The number of dimes in the bank is three more than one-half the number of pennies. a) Express in terms of x: # pennies = # dimes = c) Find the number of pennies and the number of dimes in the bank.. The number of girls in a certain first grade class is five less than twice the number of boys; there are students in the class. a) Express in terms of x: # girls = # boys = c) Find the number of boys and girls in the class, respectively.. The number of boys at a basketball camp is four less than three-halves the number of girls in attendance; children attend this camp. a) Express in terms of x: # girls = # boys = c) Find the number of boys and girls at the camp, respectively.. The largest angle in a triangle is twice the measure of the smallest angle, while the other angle is eight degrees larger than the smallest angle. a) Express in terms of x: smallest = other = largest = c) Find the measure of each angle.. The smaller of two complementary angles is 0 degrees more than one-third the measure of the larger angle. a) Express in terms of x: smaller = larger = c) Find the measure of each angle.. The larger of two supplementary angles is degrees less than four times the measure of the smaller angle. a) Express in terms of x: smaller = larger = c) Find the measure of each angle.

10 Topic : Lines Objective #: Graph a line using slope and y-intercept Objective #: Determine a line s slope, x- and y-intercepts Objective #: Find the equation of a line in y = mx + b form Objective #: Identify/manipulate Slope-Intercept. Point-Slope and Standard forms I. a) Graph all five lines on the given xy-plane. Use a straight-edge! Label! b) Identify slope of each line. c) Find each line s x- and y-intercepts, when possible; write as (Ordered, Pairs). A: y = x slope = x-int.: (, ); y-int.: (, ) B: y = x slope = x-int.: (, ); y-int.: (, ) C: x = slope = x-int.: (, ); y-int.: (, ) D: y = x+ slope = x-int.: (, ); y-int.: (, ) E: y = slope = x-int.: (, ); y-int.: (, ) II. a) Write the line in slope-intercept form, y = mx + b. b) Find the x- and y-intercepts; write as (Ordered, Pairs). c) Graph the line. ) x y = ) x+ y = ) y+ = ( x ) ) x y = 0 III. Given a line s slope and a point on the line, find the equation of the line in y = mx + b form..,.,.. m = ; point: ( ) m = ; point: (, ). 0. m = ; point: ( ) m = ; point: (, ). m = ; point: (, ) m = ; point: (, ) IV. Given two points, find the equation of the line in y = mx + b form.,,. ( 0, ), (, 0 ). (, ), ( ). ( ), (, ). (, ), (, ). (, ), (, ). (, ), (, ). (,. ), (,. ). (,. ), (, ) V. Write in Ax + By = C form, where A, B and C are Integers.. y = x. y = x. y = x+. y =.x+.. y = 0.x+ 0.. y = ( x 0). y+ = ( x+ ). y = ( x+ ) 0