There are so many math questions you have to practice and learn for the ACT! So, what kind of problems will show up? I’ve gathered some of the most common math skills that will show up on the exam and how often they will appear. So, buckle up and take some notes because we’re in for a long ride.

### Guaranteed Math

**Fractions** – All four operations. Mixed numbers.

**Average** – Arithmetic mean. There is always a basic version and usually an advanced one, like the average sum trick (see below).

**Probability** – Know the basic part:whole versions. There is usually a harder one also (like one with two events).

**Percents** – Know all basic variations. More advanced ones are common also.

**Exponents** – All operations. Fractional and negative exponents are very common too (see below).

**Linear Equations and Slope** – Find the slope when given two points. Be able to isolate y (to create y = mx + b). All the standard stuff from 8th grade Algebra.

**Solving Equations** – Be very comfortable with ax + b = cx + d. Distribute. Combine like terms. You also need to be able to create these equations based on word problems.

**Picking Numbers** – You never have to use this but it will be a useful option on every test.

**Ratio** – Part:part, part:whole

**Quadratic skills** – Factor. FOIL. Set parenthesis equal to zero. Graph parabolas.

**Area/Perimeter of basic shapes** – Triangles, rectangles, circles.

**Negatives** – Be comfortable with all operations.

**SOHCAHTOA** – Every variation of right triangle trig, including word problems.

**Plug in answers** – Like picking numbers, it’s not required but it’s often helpful.

### Extremely Likely Math (> 80% chance)

**Function shifts** – Horizontal shifts, vertical shifts. Stretches. You should recognize y = 2(x+1)^2 – 5 right away and know exactly what to do.

**Average sum trick** – 5 tests, average is 80. After the 6th test, the average is 82. What was 6th test score?

**Rate (like mph)** – The concept of speed in miles per hour shows up every time.

**Median** – 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?

**Radicals** – Basic operations. Translate to fractional exponents.

**System of Equations** – Elimination. Substitution. Word problems.

**Angle chasing** – 180 in a line. 180 in a triangle. Corresponding angles. Vertical angles.

**Time** – Hours to minutes, minutes to seconds.

**Pythagorean Theorem** – Sometimes asked directly, other times required as part of something else (like SOHCAHTOA or finding the distance between two points).

**Apply formula** – they give you a formula (sometimes in the context of a word problem) and you have to plug stuff in.

**Factoring** – Mostly the basics. Almost never involves a leading coefficient.

**Factors** – The basic concept and greatest common factor, with numbers and variables.

**Matrices** – Adding, subtracting, multiplying. Knowing when products are possible.

### Very Likely Math (> 50% chance)

**Absolute Value** – Sometimes basic arithmetic, sometimes an algebraic equation or inequality.

**Use the radius** – A circle will be combined with another shape and you have to use the radius to find the essential info about that other shape.

**3:4:5** – Recognize 3:4:5 right triangle relationships.

**Fractional Exponents –** Rewrite radicals as fractional exponents and vice versa.

**Multistep conversion** – For example, they might give you a mph and a cost/gallon and then ask for the total cost.

**Probability, two events** – If there’s a .4 probability of rain and a .6 probability of tacos, what is the probability of rain and tacos?

**Difference of two squares** – (x + y)(x – y) = x^2 – y^2

**Remainders** – Can be simple or pattern based: If 1/7 is written as a repeating decimal, what is the 400th digit to the right of the decimal point?

**Midpoint** – Given two ordered pairs, find the midpoint. Sometimes they’ll give you the midpoint and ask for one of the pairs.

**Weird shape area** – It’s an unusual shape but you can use rectangles and triangles to find the area.

**Periodic function graph** – The basics of sine and cosine graphs (shifts, amplitude, period).

**Circle equations** – (x-h)^2 + (y-k)^2 = r^2. Sometimes you have to complete the square.

**Negative exponents** – Know what they do and how to combine them with other exponents.

**Composite function** – As in g(f(x)).

**Shaded area** – The classic one has a square with a circle inside.

**Counting principle** – License plate questions.

**Logarithms** – Rewrite in exponential form. Basic operations.

**Imaginary numbers** – Powers of i. What is i^2? The complex plane.

**Lowest Common Multiple** – In word problems. In algebraic fractions.

**FOIL** – The opposite of factoring!

### Math Worth Knowing (>25% chance)

**Ellipses** – Know how to graph basic versions.

**Weird shape area** – It’s an unusual shape but you can use rectangles and triangles to find the area.

**Scientific notation** – Go back and forth between standard and scientific notation. All four operations.

**Vectors** – Add, subtract, multiply (scalar), i and j notation.

**Permutation** – You have 5 plants and 3 spots. How many ways can you arrange them?

**Volume of a prism** – Know that the volume = area of something x height. Sometimes the base will be a weird shape.

**c = product of roots, -b = sum of roots** – Use when in x^2 + bx + c form. Usually not required but often helpful.

**Arithmetic sequence** – Usually asks you to find a specific term, sometimes asks you to find the formula.

**Law of Cosines** – They almost always give you the formula. Then you just have to plug things in.

**Triangle opposite side rule** – There is a relationship between an angle and the side across from that angle?

**Change the base** – If 9^x = 27^5, what is x?

**Similar triangles** – Relate the sides with a proportion.

**Probability with ‘or’** – 3 reds, 5 blue, 6 green. Probability of picking a red or blue?

**Probability with ‘not’** – 3 reds, 5 blue, 6 green. Probability of picking one that’s not red?

**30:60:90** – Know the basic relationships. Sometimes required for advanced trig questions.

**Volume of a cylinder** – They’ll usually give it to you but not always.

**Trapezoid** – Usually basic area questions.

**Domain** – Usually you can think of it as ‘possible x values’.

**Conjugates** – Rationalize denominators that include radicals or imaginary numbers. Know that imaginary roots come in pairs.

**Exponential Growth/Decay** – Be comfortable with this: Final = Initial(1+/- rate)^time.

**Weighted average** – 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?

**Inverse trig** – Use right triangle ratios to find angles.

**Parallelogram** – Know that adjacent angles add to 180. Area formula.

**Value/frequency charts** – They’ll tell you the value and frequency and then ask about mean or median.

**Algebra LCD** – Find the lowest common denominator, then combine the numerators.

**5:12:13** – Recognize 5:12:13 right triangle relationships.

**System of equations with three equations** – Usually a word problem. Involves substitution.

**Compare numbers** – Radicals, fractions, decimals, absolute value.

**Translate points** – Images, reflections.