FC: ACT SKILLS 3 | By: Daniel Clemments
1: Table of Contents | Page 1- Laws of Exponents Page 2-y=mx+b Page 3- Arrangements Page 4- SohCahToa Page 5- Beyond SohCahToa Page 6- Probability Page 7- Anything times zero is zero Page 8- y= ax2 + bx+ c Page 9- Circles Page 10- Weird circle factoid Page 11- Absolute Value Page 12- Sequences Page 13- Fahrenheit/Celsius conversions Page 14- Most Common errors 1 Page 15- Most Common errors 2 Page 16- Weird numbers Page 17- Logs Page 18- Not so complex numbers Page 19- How to think like a math genius 1 Page 21- How to think like a math genius 2
2: CAMPING | What a beautiful view! | 2n + n = 3n n- = 1/ n^2 | When adding with matching bases and exponents, add coefficients. A negative exponent means take the reciprocal. For a fractional exponent the top number is the power and the bottom number is the root.
4: If Sawyer charges $20 per bottle of water and a flat fee of $25 to discuss, which of the following equations expresses Sawyers total fees. A. y=45x B. y=25x+20 C. y=5x D y=20x+25 E. y=45x | 1. Choose a number between 1 and 10. 2. Multiply number by 9. 3. Take results and add the the digits. 4. Subtract 5 from that number. 5. | The fee for each, $20, goes next to x. And 25 dollars is a fixed fee, so y=20x+25 | Y= mx+b | In y= mx+b, m is the slope and b is the intercept.
5: Steps for arrangements 1. Draw a blank for each position. 2. Enter number of possibilities. 3. Multiply numbers of possibilities | Multiply the numbers to get the number of arrangements 4x3x2= 24 | Arrangements
6: SohCahToa | SohCahToa means 1. Sin= opposite over hypotenuse 2. Cos= adjacent over hypotenuse 3.Tan= opposite over adjacent The hypotenuse is the longest side and opposite and adjacent are based on being opposite or adjacent to the hypotenuse. | If 5 is the hypotenuse then the opposite is 4 and the adjacent is 3 so tan equals 3/4 or 0.75.
7: Beyond SohCahToa | Reciprocals cosecant= 1/sin Secant= 1/cos cotangent= 1/tan | The problem wants us to find the angle measure. The best way to do this problem is plug in the answers for the unknown and see which one comes out between 0 and 360. In this case the correct answer was 270.
8: Probability | Probability is equal to what you want divided by the total amount of things to choose from. Always use this equation when you see the word probability. EXAMPLE | Since there are 14 that are not pink you divide that by the total which is 18 so the answer is K 7/9.
9: Anything Times Zero is Zero | On these problems the best thing to do is use the answers. If you get a problem like (x- 3)(x+ 2) = 0 you should plug in the given answers for x to see what gives you zero. | When you see this problem use the answers. When you determine x = -4 you should try all the problems that use -4 for the first x. In this case there are two. Answer A -4 and 4 does not work but E, -4 and 3 comes out to equal 0.
10: Y= ax2 + Bx +C | Standard Form ax2+bx+c a indicates if graph is up or down c is the point where the graph crosses the y axis Vertex Form y= a(x-h)2+k h and k are coordinates of the vertex. The equation can also be written as y-k=a(x-h)2
11: Circles | To determine the equation of a circle use (x-h)2+(y-k)2=r2 - (h,k) is the center of the circle and r is the radius. | The center is (4,2), h=4, k=2 and the radius is 5. When you plug this into the equation you get (x-4)2+(y-2)2 so the answer is E.
12: Weird Circle Factoid | A triangle that is formed by three points of a circle where one side of the triangle is the diameter is always a right triangle and the right angle is opposite of the diameter | Since NO is the diameter we know M is the right angle. Since NMO= 90 degrees the 2 sides will equal 45 degrees so the answer is G.
13: Absolute Value | |\If you see -3 in brackets then it means the absolute value of negative of -3 so in these brackets a negative number becomes a positive number. | When you plug in the answers -2 and -8 become to and 8 so since 2 works the answer would be 2 and -2.
14: Sequences | Arithmetic sequence is where a certain number is added to each term like 3,7,11,,15 Geometric sequence where certain number is multiplied to each term 3,-6,12,-24 | The first thing you need to do is find the number being used. In this problem it is -7. When you use this number F,G,H,J are correct so the answer will be k since the common ratio is not -7.
15: Fahrenheit/Celsius conversions | If your given degrees Celsius to convert just plug in the numbers and simplify. For Fahrenheit you can just plug in the answers | For this problem you set the given formula equal to 357 degrees and simplify. Then you can use the answers for C to get the answer.
16: Most Common Careless Errors | 1. Be relaxed and work quickly 2. (2x)2 = 4x2 square the 2 and the x 3. -2(3x-3)=-6x+6 not -6x-6 Distribute the -2 to both numbers. 4. 5x+20/5=x+4 not x+20 Divide 5 by 5x and 20 | This just means the number in parenthesis is plugged in for x. SO the equation would be 3(2p)2 so the answer would be J.
17: COMMON ERRORS 2 1. When foiling make sure to include the middle term. 2. 2(3)2=18 not 36 remember to use PEMDAS 3. Always finish the questions. Make sure the answer you get is the final answer. 4. (x2)(4x5)(3x)= 12x8 not 12x7 if the x does not have an exponent it has an implied one. 5. Make sure you convert the units if the problem wants you to go from one unit to another. | Make sure you divide the feet and inches by two separately that so you have the correct units
18: WEIRD NUMBERS | 1. Small fractions multiplied by small fractions get smaller. 2.The larger the digits of a negative number, the smaller it is. 3. Subtracting a negative number is like adding. 4.Squaring a negative eliminates it. 5.Anything times 0 equals 0. | To work this problem choose a number like 0.5 and plug it in for each solution. When you find the one greater than zero and less than one that is your answer.
19: LOGS | A log is another way of writing an exponent. The log of 25 is two because 5 squared is 25. Log expansion is adding or subtracting logs. When you add logs you multiply the numbers, when you subtract you divide them. | Log 16 means what squared is equal to 16. So the answer would be 4. Then you have to raise it the the fourth power so the answer is E 64.
20: NOT SO COMPLEX NUMBERS | These numbers have a regular part like a whole number and an imaginary part like the square root of a variable. Just treat it like a normal equation when factoring these. | To solve this problem you just have to FOIL. Just multiply the first outer inner and last variables to get the answer.
21: How to Think Like a Math Genius | 1. When you see variables in the question use the answers. 2.When you see x= use algebra or answers. 3. What is y in terms of x means get y by itself. 4.The word mean is the same as average. 5.Calculate angle measures for vertical angles and linear pairs. 6. When parallel lines cross 8 angles are formed. 7. Triangles with 2 equal sides angles are 60 degrees. 8. Underline math vocab. 9. Use answers for least common multiple and LCD. 10. Slope is the change in y over the change in x. 11. y=mx+b is the slope intercept formula.
22: MATH GENIUS CONTINUED | 12.f(3) means plug 3 in for x. 13.f(g(m)) means plug g(m) in for x. 14. When a question with variables is too theoretical make it real. 15. Memorize basic formulas such as perimeter, area, and volume. 16.
23: THINK LIKE A MATH GENIUS 2 | 1. Use any diagrams to estimate answers. 2.If diagram is not drawn to scale redraw it. 3.When you see a right triangle try a2+b2=c2 4. SImilar triangles have sides that are proportional. 5. Translate word problems into math. 6. Memorize the law of exponents. 7. When something can be factored FOIL reduce or simplify. 8. SohCahToa When you see the word probability use formula want over total.