MATH056 IMMERSION Dr Jason Samuels simplify the expression tutoring M-Th M1203

Transcription

1 MATH056 IMMERSION Dr Jason Samuels simplify the expression tutoring M-Th M1203 # identify every calculation that order of operations tells you to do in the next step # check your signs

2 solve for the given variable to solve for a variable (which appears as itself, no exponent) # get all of its terms to one side, then factor it out

3 simplifying expressions: turning fractions inside fractions into simple fractions # multiply by the LCD in both the numerator and

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5 solving equations involving fractions

6 simplifying expressions with fractions: multiplying & dividing

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10 simplifying expressions with fractions: adding and subtracting

11 simplifying expressions with fractions: multiplying and dividing

12 quadratics: factoring

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14 complex numbers

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16 combining techniques

17 # get rid of square root...square both sides # you get a quadratic equation, so solve it # check your solutions (square root sometimes removes one solution)

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19 radicals, simplifying radicals, rationalize the denominator # to make the radical in the denominator go away, multiply by the "irrational conjugate"

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21 exponents, fractional, in arithmetic exponents, in algebra

22 negative exponents simplify expressions involving exponents

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25 inequalities, one variable solving equations, two variables

26 solving equations with two variables, word problems ex) one family went to the movies and bought 3 adult tickets and 5 children tickets for $71. another family at the same theater bought 2 adult and 4 children tickets for $52. how much does each adult and child ticket cost? ex) Mike bought 9 stamps for $3.32. Postcard stamps are 28 cents and forever stamps are 48 cents. how many of each did he buy? ex) Rochelle buys 14 pieces of fruit for $7.35. Apples are $0.40 each, nectarines are $0.75 each. how many of each did she buy?

27 Absolute value equations & inequalities

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29 Lines definition - graph & formula slope - graph & formula intercepts - graph & formula to find slope of a line, given a formula, put in y = mx+b form (easiest)

30 to find slope, given the graph, count boxes, calcuate rise/run x-intercept: where graph crosses x-axis y-intercept: where graph crosses y-axis

31 combine ideas to graph the line, given "y=mx+b", mark the y-intercept, follow the slope up&over to mark another point, then draw a line

32 tricky application ex) find the equation of the line parallel to y=4x-1, through the point (3,2) ex) find the equation of the line perpendicular to 3x + 5y = 12 through the point (5,- 2)

33 ex) find the equation of the line parallel to 2x-7y=12, through the point (-3,-1) ex) find the equation of the line through (4,5) and (3,-1)

34 Logs ex) simplify log464 ex) simplify log216 ex) simplify log636 ex) solve for x: logx25 = 2 ex) solve for t: log5t = 3 ex) simplify: log

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36 Log rules 1) log b r x = x log b r 2) log b r + log b s = log b (rs) 3) log b r - log b s = log b ( r / s )

37 ex) simplify as one log term: ex) simplify as one log term: ex) simplify as one log term: ex) simplify as one log term:

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39 Trig relationships (ratios) in a right triangle

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42 lets see what this has to do with trig

43 extending trig to all angles the adjacent side wil be represented by an x-value. ~to the right, values are positive. to the left, values are negative (like the x-axis) the opposite side wil be represented by a y-value. ~to the top, values are positive. to the bottom, values are negative (like the y-axis) the hypotenuse is always positive

44 find the following values sin(225), cos(225), tan(225) you can fill in the pos/neg for the numbers right on the diagram sin(150), cos(150), tan(150) sin(-60), cos(-60), tan(-60) for a negative angle go "backwards" (clockwise) from 0 ex) find sin(300), cos(300), tan(300) ex) find all the sides

45 ex) if sinθ = -1/2, find tanθ if θ is in the a) 3rd quadrant b) 4th quadrant ex) if tan θ = 2/7, find sinθ and cosθ if θ is in the 3rd quadrant

46 ex) if sec θ = 5/4, find sinθ and tanθ if θ is in the 4th quadrant ex) you leave a building, walk 100 feet, then turn around and look up at the top of building at a 60 degree angle. how tall is the building? ex) you tie down a 12 foot pole (standing straight up) with a wire that makes a 45 o angle with the ground. how long is the wire?

47 more coverage: complex fractions graph the line literal equation multiply & divide rationals logs ex) solve for t: a 2 + mt = qt - x ex) solve for v: p = q + vt + 0.5at 2 ex) solve for v: K = 0.5mv 2

48 ex) for 2x-5y=10, find the slope & y-intercept and graph it ex) simplify: log 8 4 ex) rewrite as one log: -2log(x) + 1/ 3log(y) - 4log(z)