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ACT Math

ACT Math. ACT Math. Geometry(38%) Algebra(55%) Trigonometry(7%) 60 Minutes 60 Questions. NOT 1 Question per minute …the questions get harder as the test goes on and take more time. MATH Plug it In . Time Saver. Type 1 If you are given a value for a variable.

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ACT Math

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  1. ACT Math

  2. ACT Math Geometry(38%) Algebra(55%) Trigonometry(7%) 60 Minutes 60 Questions NOT 1 Question per minute…the questions get harder as the test goes on and take more time.

  3. MATH Plug it In Time Saver Type 1 • If you are given a value for a variable. • Plug the given answer back into the problem and see which answer fits the question. • Start plugging with the middle answers first( B/C/G/H) then move to the others.

  4. Example Plug it in PLUG the answer back into the variable(x). 15^2(15x15)=225 25^2(25x25)=625 35^2(35x35)=1225 Solve the equation X^2=625 if X>0. A. 12 B. 15 C. 25 D. 35 E. 50

  5. MATHPLUG IT IN Time Saver Type 2 • Insert or “SUBSTITUTE” YOUR OWN Value Into the Problem • This only works in the following type of problem. (See Example)

  6. Plug it in Example Plug in a number that fits the definition. If x and y are both odd numbers, which of the following MUST be an odd number? A. x + y B. xy C. xy + 1 D. 2xy E. 2x + 2y 3 5 3+5=8 3*5=15 3*5+1=16 2(3*5)=30 2(3)+2(5)=16

  7. Math #2 – Process of Elimination Time Saver POE or Process of Elimination is your best tool on the math section. Eliminate ridiculous and outlying answers to give yourself better odds on each question. This method is very helpful for tougher questions.

  8. Example POE Prime numbers cannot be divided by whole numbers. 1, 2, 3, 4, 5, 6 5,7 8. How many numbers from 1-10 are prime numbers? F. 1 G.2 H. 4 J. 5 K.10

  9. GOOD SENSE • Once you’ve eliminated answers • If you get stuck…don’t panic • Look at the problem….some give you the answer if you just think about it logically. • If it makes SENSE it could be correct.

  10. Math Order of Process • If you know how to do the question. Do it. • If you are unsure or think it will be hard: • POE • Plug Rule • Get beyond the math and think about which answer makes sense…

  11. POWER in your HAND 2 3 4 1 5 Look at your Hand 1. (Pinky) POE 2. (Ring) Plug Rule 3. (Middle) Good Sense 4. (Pointer) 1 min. rule 5. (Thumb) Stay Positive

  12. ON THE TEST In our experiences these are the most crucial types of problems found on the test with solutions. Not all types of problems are covered.

  13. Math #3- GeometryTriangles H B Isosceles Triangle -Two sides are identical making the two adjacent angles equal If A=A then x=x C Hypotenuse is always C (long side). A B A A X X *Angles inside any triangle add up to 180 degrees Area of a Triangle ½(Base*Height) Pythagorean Theorem A^2 + B^2 = C^2

  14. Triangles Time Saver 60 2 Know all the dimensions of these two triangles. If you memorize these two rules you will save valuable time on the test. 1 30 √3 45 √2 1 45 1 30-60-90 Rule 1-2- √3 45-45-90 Rule 1-1-√2

  15. Example Triangles 1 2 3 4 5 A=1/2BH H….? B=10 In order to find the area you must have a way to find ½ Base x Height. In this case there is no way to find the height of line AD. In the figure below AB≠AC and BC is 10 units long. What is the area, in square inches, of ABC ? F. 12.5 G. 25 H. 35 J. 50 K. Cannot be determined from the given information

  16. Example Triangles 1 2 3 4 5 N 22 In an isosceles triangle 2 sides are equal in length and the two angles will be equal also. So since all angles of a triangle = 180, 2N-22=180 or N=79 The triangle below is isosceles and is drawn to scale. What is the measure of angle N ? A. 22° B. 68° C. 78° D. 79° E. 89°

  17. Math #3- Geometry Angles A B A B Complementary Angles - When any line intersects a right angle A+B=90° Y - RULE - When any line intersects a straight line A+B=180°

  18. Angles A C D B A B C D E F G H X - Rule - two intersecting straight lines A+C(or D)=180 B+C(or D)=180 A=B, C=D Z – Rule - 2 parallel lines intersected by a straight line -B, C, F, G are equal -A, D, E, H are equal -A/C, D/B, E/F, G/H are complimentary and add to 180

  19. Example Angles 1 2 3 4 5 Because angle AXZ and angle YXZ are complimentary angles they add to 180 50 Find XZY by subtracting YXZ(50) and XYZ(45) from 180 In the figure below, X is on line AY, Angle XYZ measures 45°, and AXZ measures 130°. What is the measure of Angle XZY ? F.  45° G.  60° H.  85° J.   95° K. 105°

  20. Math #3- Geometry Lines Y B= X rise run Equation of a line y=mx+b m=slope(rise/run) b=y intercept Finding a line intercept Solve to find both x & y (X,Y) x + y =10 and y = 4 x=6 y=4 (6,4)

  21. Example Lines 1 2 3 4 5 Don’t be fooled by this type of question solve for X, they’ve given you the value of Y. (X,Y) x+(7)=5 X=-2, Y=7 (-2,7) When graphed in the (x,y) coordinate plane, at what point do the lines x + y = 5 and y = 7 intersect? A. (–2,0) B. (–2,7) C. (0,7) D. (2,5) E. (5,7)

  22. Math #3- Geometry Circles Radius(r) Diameter(d) Circumference and Area Diameter=2(R) Area=r^2 Circumference=2ror D LEARN MORE ABOUT CIRCLES ON THE MATH HELP DVD

  23. Example Circles 1 2 3 4 5 Radius= Hypotnuse 5^2 + 12^2 = C^2 25+144=169 169=C^2 13^2=C^2 C=13 r 5 24 A Chord is 24 inches long from the center of a circle, as shown below. What is the radius of the circle to the nearest tenth of an inch? • 29.0 • 24.5 • 16.9 • 13.0 • 10.9

  24. Math #4 - Algebra Know the function of a variable(x) *Its simply a number you don’t know Know how to solve for (x) *Get X on a side by itself Know how to use FOIL *When given a problem in this format (x+M)(x+N) Simplify using the FOIL method F-FirstI-InnerO-Outer L-Last x*x M*x x*N M*N Simplify the remaining variables for your answer

  25. Example Solving FOR X 1 2 3 4 5 Solve for x in the first equation and then plug it in and solve for y in the second equation. 2(1-2y)+y=5 or 2-3y=5 -3y=-3 so y=1 X+2(1)=1 so X=-1 The answers are in decimal form so change 3/8 to 0.375 and add it to 0.065 then divide by 2 0.375 +0.065 0.440/2= 0.22 If x + 2y = 1, and 2x + y = 5, then x + y = ? F. 1 G. 2 H. 3 J.  4 K. 5 What is the average of  3/8 and 0.065 ? A. 0.05125 B. 0.1825 C.0.22 D. 0.375 E. 0.5125

  26. Algebra Time Saver Radicals Exponents 10^5( add 4 0’s to right ) becomes100,000 10^-5( add 4 0’s to the left or 1/10^5 ) becomes 0.00001 Square Roots (round non perfect SR’s to closest SR) √65 = est. 8 √145= est. 12 MORE ON EXPONENTS SEE THE MATH HELP DVD

  27. Example Exponents CONTINUED 1 2 3 4 5 0.0 0 0 30 Negative exponents= add one minus exponent number of zeros to the left of the number preceded by a decimal 3 x 10 – 4 = ? F. –30,000 G. –120 H. 0.00003 J. 0.0003 K. 0.12

  28. Examples Square Roots 1 2 3 4 5 Estimate - knowing that √49 = 7 & √81 = 9. Thus (7)(9)=63 What integer most nearly approximates (√50)(√80)? A.    20 B.    40 C.    63 D.   200 E. 2,000

  29. Math #5- Trigonometry Opposite Hypotenuse hypotenuse Adjacent Hypotenuse Opposite Hypotenuse Opposite X Hypotenuse Adjacent Adjacent Opposite Adjacent Adjacent Opposite Know the following terms: Sin x- Cos x- Csc x- Sec x- Tan x- Cot x-

  30. “Trick”onometry Time Saver • SOH-CAH-TOA or “SOCK-A-TOWA” • SOH is Sin=Opp/Hyp • COH is Cos=Adj/Hyp • TOA is Tan=Opp/Adj

  31. Example Trig 1 2 3 4 5 X Sin x=opposite/hypotenuse Find Hypotenuse A^2+B^2=C^2 7^2+24^2=x^2 or 625=x^2 or x=25 Sin x=24/25 In right triangle ABC below, what is the sine of A ? A. 7/24 B. 7/25 C. 24/7 D.24/25 E. 25/24

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