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S: ACT MATH PROJECT

FC: ACT Math Project Matt Knight 1st Period Feb 21st, 2012

1: Table of Contents 2/3..................................ACT skill 31 4/5.................................ACT skill 32 6/7.................................ACT skill 33 8/9..................................ACT skill 34 10/11.......................ACT skill 35 12/13..............................ACT skill 36 14/15...........................ACT skill 37 16/17...........................ACT skill 38 18/19...............................ACT skill 39 20/21.............................ACT skill 40 22/23...............................ACT skill 41 24/25..........................ACT skill 42 26/27............................ACT skill 43 28/29..............................ACT skill 44 30/31.............................ACT skill 45 32/33..........................ACT skill 46 34/35..............................ACT skill 47 36/37................................ACT skill 48

2: When adding with matching bases and exponents, you'll simply add the coefficients. 2n^2 + n^2 = 3n^2 | they won't combine if the exponents and/or coefficients do not match 2n + n^2

3: if you get a negative exponent, just take the reciprocal n^-2 = 1/n^2 | when you have a fractional exponent, rewrite it so that the top # is the exponent and the bottom is the root n^4/3 = 3sqrt n^4

4: in y=mx+b, m = slope, and b = y intercept | the y and the x are a given set of coordinates

5: slope is equal to the rise over the run | the y intercept is where the line intercepts the y axis

6: a lot of questions will ask how many ways a group of things can be arranged | take each number of choices and multiply them

7: chevrolet lets you pick the color, audio system, and sunroof options for an SUV. you can get red, blue, white or black. a standard sound system, or an aftermarket one, and no sunroof/small sunroof/large sunroof. 4x2x3 = 24 therefore there are 24 possible configurations

8: sohcahtoa means sin - opposite hypotenuse cos - adjacent hypotenuse tan - adjacent opposite | when trying to find the sin/cos/tan of a triangle based on leg length, you'll use sohcahtoa

9: sohcahtoa is a way of remembering how to use the leg lengths to get the sin/cos/tan | sin = opposite/hypotenuse cos = adjacent/hypotenuse tan = adjacent/opposite

10: when dealing with cosecant, secant, and cotangent, sohcahtoa doesn't help | cosecant = 1/sin secant = 1/cos cotangent = 1/tan

11: cosecant = hypotenuse/opposite secant = hypotenuse/adjacent cotangent = adjacent/opposite | these are just the reciprocals of sin/cos/tan

12: probability can be simply expressed as the amount you want, over the amount that you have in total | there are 5 blue marbles, 2 red marbles, and 9 yellow marbles in a bag. what are the odds of randomly picking a blue one?

13: 5 blues/16 total

14: Anything multiplied by 0 is equal to 0 | if a problem says something like this: (x+2)(x-4)=0 use the answers!

15: Take your answers and plug them into the formula until you get a product of zero | as long as one set of parenthesis will be equal to zero, the whole equation will multiply out to zero

16: When x^2 is in an equation, the graph will be called a parabola | it looks like a big curvy line

18: Circles have a formula too, and some question relating to it is almost always on the ACT | (x-h)^2 + (y-k)^2 = r^2

19: (h,k) is the center of the circle | This is always ranked as a medium or hard question because nobody has the formula memorized, but it's really easy

20: The ACT loves to use triangles formed by the sides of circles | its always a right triangle, with the hypotenuse forming the diameter of the circle

21: the right angle is always opposite of the diameter of the circle

22: absolute value is expressed by a pair of bars around a number or set of numbers | it means that regardless of sign, the number will be positive

23: you can't just drop the sign, you have to do the math inside the bars, then make it positive

24: sequences can be arithmetic or geometric | arithmetic sequences will repeatedly add a number

25: geometric sequences will multiply | you'll usually just have to predict the next in a sequence

26: fahrenheit to celcius conversions are usually on the ACT | the formula is F=9/5C+32

27: just plug in whichever one you have and solve the equation

28: Focus, but relax | if something is in parenthesis and has an exponent, multiply everything inside the parenthesis

29: remember to foil parts of equations | the denominator will apply to every part of the numerator

30: Remember the middle term when you FOIL | Remember PEMDAS

31: Anything without an exponent has an implied exponent of 1 | Don't get tripped up by strange units of measurement

32: fractions multiplied by fractions get smaller, not bigger | the higher negative number that you have, the lower the number

33: subtracting a negative number is the same as adding a positive | anything times zero is zero

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