# ACT MATH

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ACT Math 1

### Slide 2:

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

### MATH Plug it In :

MATH Plug it In 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. 3 Time Saver

### Example Plug it in :

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

### MATHPLUG IT IN :

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

### Plug it in Example :

Plug it in Example 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 Plug in a number that fits the definition.

### Math #2 – Process of Elimination :

Math #2 – Process of Elimination 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. 7 Time Saver

### Example POE :

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

### GOOD SENSE :

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.

### Math Order of Process :

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…

### POWER in your HAND :

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

### ON THE TEST :

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.

### Math #3- Geometry Triangles :

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

### Triangles :

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

### Example Triangles :

Example Triangles 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 15 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. A=1/2BH H….? B=10 1 2 3 4 5

### Example Triangles :

Example Triangles 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° 16 22 N 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 1 2 3 4 5

### Math #3- Geometry Angles :

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

### Angles :

Angles 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 18 A B C D B A D C H G F E

### Example Angles :

Example Angles 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° 19 Because angle AXZ and angle YXZ are complimentary angles they add to 180 Find XZY by subtracting YXZ(50) and XYZ(45) from 180 50 1 2 3 4 5

### Math #3- Geometry Lines :

Math #3- Geometry Lines 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) Y X rise run B= 20

### Example Lines :

Example Lines 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) 21 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) 1 2 3 4 5

### Math #3- Geometry Circles :

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

### Example Circles :

Example Circles 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 23 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

### Math #4 - Algebra :

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-First I-Inner O-Outer L-Last x*x M*x x*N M*N Simplify the remaining variables for your answer 24

### Example Solving FOR X :

Example Solving FOR X 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 25 2(1-2y)+y=5 or 2-3y=5 -3y=-3 so y=1 X+2(1)=1 so X=-1 0.375 +0.065 0.440/2= 0.22 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. The answers are in decimal form so change 3/8 to 0.375 and add it to 0.065 then divide by 2

### Algebra :

Algebra Exponents 10^5( add 4 0’s to right ) becomes 100,000 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 Radicals 26 Time Saver

### Example Exponents CONTINUED :

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

### Examples Square Roots :

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

### Math #5- Trigonometry :

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

### “Trick”onometry :

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

### Example Trig :

Example Trig 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 31 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 X 1 2 3 4 5