Analysis of math from the last 10 ACTs

	A	B	C
1	Visit mathchops.com to practice the most common questions on the ACT through customized games.
2	Tag Name	Frequency	Description
3	fractions	57	All four operations. Mixed numbers.
4	Area/Perimeter of basic shapes	44	Triangles, rectangles, circles.
5	average	38	Also called the arithmetic mean. There is always a basic version and usually an advanced one, like the average sum trick (see below).
6	probability	34	Know the basic part:whole versions. There is usually a harder one also (like one with two events).
7	percent	29	Know all basic varations. More advanced ones are common also.
8	exponents	28	All operations. Fractional and negative exponents are very common (see below).
9	slope	28	Find it when given two points. Be able to isolate y (to create y = mx + b).
10	solving equations	27	Be very comfortable with ax + b = cx + d. Distribute. Combine like terms.
11	pick numbers	25	You never have to use this but it will be a useful option on every test.
12	ratio	25	Part:part, part:whole.
13	quadratic	24	Factor. FOIL. Set parenthesis equal to zero. Graph parabolas.
14	negatives	20	Be comfortable with all operations.
15	SOHCAHTOA	18	Every variation of right triangle trig, including word problems.
16	plug in answers	16	Like picking numbers, it’s not required but it’s often helpful.
17	function_shifts	16	Horizontal shifts, vertical shifts. Stretches. You should recognize y = 2(x+1)^2 - 5 right away and know exactly what to do. Ellipses, circles, periodic functions also.
18	mph	15	The concept of speed in miles per hour shows up every time.
19	median	14	Middle when organized from low to high. Even number of numbers. What happens when you make the highest number higher or the lowest number lower?
20	radicals	14	Basic operations. Translate to fractional exponents.
21	system of equations	12	Elimination. Substitution. Word problems.
22	avg_sum_trick	12	5 tests, average is 80. After the 6th test, the average is 82. What was 6th test score?
23	angle chasing	12	180 in a line. 180 in a triangle. Corresponding angles. Vertical angles.
24	time	11	Hours to minutes, minutes to seconds
25	pythagorean theorem	11	Sometimes asked directly, other times required as part of something else (like SOHCAHTOA or finding the distance between two points).
26	apply formula	10	They give you a formula (sometimes in the context of a word problem) and you have to plug stuff in.
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28	composite functions	10	As in g(f(x)).
29	factoring	10	Mostly the basics. Almost never includes a leading coefficient.
30	matrices	10	Adding, subtracting, multiplying. Knowing when products are possible.
31	absolute value	9	Sometimes basic arithmetic, sometimes an algebraic equation or inequality.
32	fractional exponents	9	Rewrite radicals as fractional exponents and vice versa
33	multistep conversion	9	For example, they might give you a mph and a cost/gallon and then ask for the total cost.
34	probability with two events	9	If there's a .4 probability of rain and a .6 probability of tacos, what is the probability of rain and tacos?
35	remainder	7	Can be simple or pattern based, as in “If 1/7 is written as a repeating decimal, what is the 400th digit to the right of the decimal point?”
36	midpoint	7	Given two ordered pairs, find the midpoint. Sometimes they’ll give you the midpoint and ask for one of the pairs.
37	weird shape area	6	It’s an unusual shape but you can use rectangles and triangles to find the area.
38	periodic function graph	6	Periodic function graph – The basics of sine and cosine graphs (shifts, amplitude, period).
39	circle_equation	6	(x-h)^2 + (y-k)^2 = r^2. Sometimes you have to complete the square.
40	negative_exp	6	Know what they do and how to combine them with other exponents.
41	shaded area	6	The classic one has a square with a circle inside.
42	counting principle	6	License plate questions.
43	logarithms	6	Rewrite in exponential form. Basic operations.
44	imaginary numbers	6	Powers of i. What is i^2? The complex plane.
45	LCM	6	Straight up. In word problems. In algebraic fractions.
46	FOIL	6	This has to be automatic.
47	ellipses	5	Know how to graph basic versions.
48	scientific notation	5	Go back and forth between standard and scientific notation. All four operations.
49	vectors	4	Add, subtract, multiply (scalar), i and j notation.
50	permutation	4	You have 5 plants and 3 spots. How many ways can you arrange them?
51	volume of a prism	4	Know that the volume = area of something x height. Sometimes the base will be a weird shape.
52	c = product of roots, b = -sum	4	Use when in x^2 + bx + c form. Usually not required but often helpful.
53	difference of two squares	4	(x + y)(x - y) = x^2 - y^2
54	arithmetic sequence	4	Usually asks you to find a specific term, sometimes asks for a formula.
55	law of cosines	4	They almost always give you the formula. You generally just have to plug the numbers in.
56	triangle opposite side rule	4	There is a relationship between an angle and the side across from that angle?
57	change base	4	If 9^x = 27^5, what is x?
58	similar triangles	4	Relate the sides with a proportion.
59	probability_or	4	3 reds, 5 blue, 6 green. Probability of picking a red or blue?
60	probability_NOT	4	3 reds, 5 blue, 6 green. Probability of picking one that’s not red?
61	factors	4	The basic concept and greatest common factor, with numbers and variables.
62	30_60_90	3	Know the basic relationships. Sometimes required for advanced trig questions.
63	volume of cylinder	3	They’ll usually give it to you but not always.
64	trapezoid	3	Usually basic area questions.
65	domain	3	Usually you can think of it as “possible x values”.
66	conjugates	3	Rationalize denominators that include radicals or imaginary numbers. Know that imaginary roots come in pairs.
67	exponential_growth	3	Be comfortable with this: Final = Initial(1+/- rate)^time.
68	weighted average	3	Class A has 8 kids and an average of 70. Class B has 12 kids and an average of 94. What is the combined average of the two classes?
69	inverse trig	3	Use right triangle ratios to find angles.
70	parallelogram	3	Know that adjacent angles add to 180. Area formula.
71	use radius	3	A circle will be combined with another shape and you have to use the radius to find the essential info about that other shape.
72	value frequency	3	They’ll tell you the value and frequency and then ask about mean or median.
73	3_4_5	3	Recognize 3:4:5 right triangle relationships.
74	algebra LCD	3	Find the lowest common denominator, then combine the numerators.
75	5_12_13	3	Recognize 5:12:13 right triangle relationships.
76	three equations	3	Usually a word problem. Involves substitution.
77	compare numbers	3	Radicals, fractions, decimals, absolute value.
78	Translate points	3	Images, reflections.
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