math final exam

find each product (multiplying and dividing fractions) chapter 5-4

find 3 2/3 x 1 4/5 find -1 1/2 divided by 2 1/4 make them improper fractions make them improper frac. divide the common factors multiply by reciprocal simplify divide the common factors simplify ex. 2 1/5 x (-1 1/11)

use the properties of similar triangles to calculate the side lengths (similar figures and scale drawings) chapter 6-3

similar triangles have have the same shape but not necessarily the same size. the symbol ~ means "is similar to" to solve: substitute the letters in for numbers write a proportion find the cross products divide each side simplify (look in the book for examples)

solve each equation. (solve equations with variables on both sides) chapter 7-5

solve 4(n-5) + 2= 3n- 4 4n-20 + 2= 3n - 4 4n - 18 = 3n -4 4n -3n- 18= 3n -3n - 4 n- 18= -4 n-18+18= -4+18 n=14

solve each equation (solving equations by multiplying and dividing fractions) chapter 5-8

solve -4 2/5x = 1 1/10 make the two fractions improper multiply each side by -5/22, the reciprocal of -22/5 divide common factors and simplify ex. 8x=12 and -4/5y= -1/3

solve each inequality (solving 2 step inequalities) chapter 7-6

solve and graph 2x+9>5 2x+9-9>5-9 2x>-4 2x>-4 2 2 x>-2

solve for the indicated variable

solve for 2(pie)r squared +2(pie)rh for h s- 2(pie)r squared = 2(pie) r squared + 2(pie) r squared s- 2(pie)r squared = 2(pie) r squared subtract, divide, simplify

solve each equation (solving equations by adding or subtracting fractions) chapter 5-7

solve h- 2 3/4 = -3 1/6 add 2 3/4 to both sides use a common denominator subtract -2 14/12 - 2 9/12 ex. h+3/4 = 7/8

simplify each expression (powers of products and quotients) chapter 5-9

(x to the power of 3 / -y to the power of 2) power of 5 raise both the numerator and the denominator to the power of five multiply exponents in the numerator. raise each factor to the power of 5 in the denominator. multiply exponents and simplify. ex.(3ab power of 3) power of 2 ex. (3x/5) power of 3

find the LCM

-11/20 and -22/40

write each decimal as a fraction or mixed number in simplest form (fractions and decimals) chapter 5-2

0.63----(6&3 repeating) 0.83-------(3 repeating) n=0.6333333333 n=0.833333333 100n=63.3333333 100n=83.33333 10n=6.333333 10n=8.33333 100n-10n= 63.3333-6.333333 -10n= -8.3333 99n=57 90n=75 99n/99=57/99 90n/90=75/90 n=19/33 n=15/18

find the LCM (comparing and ordering rational numbers) chapter 5-1

2/9 and 1/6

subtract each difference (adding and subtracting fractions) chapter 5-3

3 2/9 - 3 2/3

use <> and = for the LCM

5/9 and 11/21

write and solve an equation. (percents and equations) chapter 6-7

8 is 16% of what? 8=0.16% x n 8= 0.16n 0.16 0.16 n= 50 8 is 16% of 50. ex. what percent is 84 of 60

markup and discount chapter 6-9

A store pays $8 for a basketball. The markup is 60%. Later, they discount the basketball 25%. Find the original selling price and the sale price of the basketball. the markup is 60% of the cost. find 60% of $8 0.6(8)= $4.80 store's cost + markup= selling price 8+4.80= $12.80 the discount is 25% of the original selling price. find 25% of 12.80% 0.25(12.80)= 3.20 original price- discount = sale price 12.80- 3.20- 9.60 the sale price is $9.60

simple and compound interest chapter 7-8

B= p(1+r) to the power of n

find each unit rate (ratios and unit rates) chapter 6-1

One store has 6 packs for $.90. Another store has 8 packs for the same size juice cartons for $1.12. which is the better buy? 6 pack: price---------$.90 = $.15/ carton (divide top and bottom#) number------ 6 8 pack: price------$1.12 =$.14/ carton (divide top and bottom#) number--- 8 ex. $91 in 14 hours

whats the order of the metric system

Weight Length Inches Ounces Feet Cups Yards Pints Miles Quarts

circles 9-6

a circle is the set of all points in a plane that are the same distance from a given point, called the center of the circle. finding circumference c=pie(diameter) c=2(pie)(radius)

congruence 9-5

congruent figures have the same size and shape, and their corresponding parts have equal measures. identifying congruent triangles (sss) side-side-side (sas) side-angle-side (asa) angle-side-angle

relations and functions 8-1

graph the relation. (3,4) start at the origin (0,0). go right 3 units and 4 units up. (-1,-5) start at the origin (0,0). go left 1 unit and down 5 units.

find the probability. (probability) chapter 6-4

odds in favor of: number of favorable outcomes number of unfavorable outcomes odds against: number of unfavorable outcomes number of favorable outcomes ex. jar of 6 red socks, 4 blue, 14 white P(6)= 6---what u want 18----what u don't want (subtract the favorable from the possible amount of outcomes)

write a proportion then solve. (proportions and percents) chapter 6-6

what percent of 98 is 24.5? what ever is after the word "of" is on the bottom of the proportion so the proportion should look like this x/100 and the word "is" gives you the hint of the =, so x/100= 24.5/98 cross multiply then simplify

write each fraction as a percent (fractions, decimals, and percents) chapter 6-5

write 7/8 as a percent and 64% as a decimal divide 7 and 8 7/8= 0.875 move the decimal over 2 spots bc its out of 100 7/8= 87.5% 64% means 64 parts per 100 64/100 simplify the fraction 64%= 16/25 ex. 7/10 as a percent ex. 15% as a fraction

writing rules for linear functions 8-4

x f(x) also known as y -2 -12 0 -2 As the x values increase by 2, f(x) values 2 8 increase by 10. So m= 10/2= 5. When x=0 4 18 f(x)=-2. Substitute m= 5 and b =-2 into f(x)=mx+b. f(x)=5x+(-2) f(x)=5x-2--------rule

slope and y-intercept 8-3

you can find slope in 2 ways, by graphing and without graphing. slope= rise run if you graph slope, first you graph the coordinates given. then you start are the origin and find rise over run to get your slope. the second way without graphing is, slope= difference in y-coordinates difference in x-coordinates find the slope by subtracting the y's and x's from both coordinates. ex. (0, -2) and (4,1) slope= 1-(-2) = 3/4 4-0

find each percent of increase and decrease. (percent of change) chapter 6-8

find the percent of decrease from 85 to 60 85-60= 25 percent of decrease= amount of decrease original amount =25 85 ~0.294= 29.4% the percent of decrease is about 29.4% ex. 40 is increased to 45 ex. 60 is decreased to 15

graphing linear inequalities 8-8

graph y<2x-1 graph the boundary line y=2x-1. The y-intercept is -1 and the slope is 2. Since the inequality is <, the boundary line should be dashed (- - - -). QUICK NOTE: if the inequality is smaller than or equal to the boundary line should be straight (------). Try a text point. The origin is easy to use (0,0). y<2x-1 0<2(0)-1 0<-1 NO, if the answer isn't true you shade away from the origin, do not contain (0,0). But, if the answer is true ex. 0<3 then, you want to include (0,0).

equations with 2 variables 8-2

graph y=1/4x - 2 make a table of ordered pairs. then graph the ordered pairs and draw a line through the points. fill in the x column with small numbers. substitute and simplify y=1/4x - 2. fill in the (x,y) then graph.

convert from one unit to the other (using customary units of measurement) chapter 5-5

convert 36 oz to pounds 36 oz= 36 oz/1 multiply by 1/16 oz (multiply by a fraction that is equal to one and compares pounds to ounces) divide the common factors and units simplify ex. 12 fl oz to c

solving systems of linear equations 8-7

solve the system. check your solution. y=2x- 5 x-y=4 graph y=2x-5 solve x-y=4, for y add y to each side. (x-y+y=4+y) simplify. (x=4+y) subtract 4 from each side. (x- 4 = 4+y- 4) simplify. (x-4=y) graph y=x-4

solve each proportion (proportions) chapter 6-2

solve x/6 = 10/4 method 1: multiplication property of equality multiply each side by 6 simplify method 2: cross products cross multiply find the cross products divide each side by 4 (since the 4 crosses with the variable) simplify ex. 6/p = 18/42

points, lines and planes 9-1

a point is a location in space that has no size. a line is a series of points that extends in opposite directions without end. a plane is a flat surface with no thickness. it contains many lines and extends without end in the directions of all the lines. a segment is a part of a line. it have 2 endpoints a ray is a part of a line. it has exactly 1 endpoint. the endpoint is named first. parallel means 2 lines that will never meet. the sine II means "parallel" skew lines are lines that do not lie in the sam plane. they are not parallel and they do not intersect.

classifying polygons 9-3

a polygon is a close plane figure with at least 3 sides. acute triangle-3 acute angles less than 90 degrees right triangle-one right angle obtuse triangle-one obtuse triangle, bigger than 90 degrees but less than 180 equilateral triangle- 3 congruent angles isosceles triangle-at least 2 congruent sides scalene triangle-no congruent sides quadrilaterals quadrilateral- 4 sides trapezoid-exactly one pair of parallel sides parallelogram- both pairs of oppose sides parallel rhombus-4 congruent sides rectangle- 4 90 degrees angles square- 4 90 degrees angles and 4 congruent sides

angle relationships and parallel lines 9-2

adjacent angles share a vertex and a side but no points in their interiors. vertical angles are formed by 2 intersecting lines and are opposite each other. vertical angles have the same measure. congruent angles are angles that have the same measure. they are equal. if the sum of 2 angles add up to 180 degrees, the angles are supplementary. if the sum of 2 angles add up to 90 degrees, the angles are complementary. a transversal is a line that intersects 2 other lines. corresponding angles lie on the same side of the transversal and in corresponding positions. alternate interior angles are in the interior of a pair of lines and on opposite sides of the transversal.