System of equations with three equations Most systems of equations problems only involve two equations, but occasionally they’ll include three equations, often in the form of a word problem. For these problems, students need to isolate two different variables in two of the equations. These then need to be substituted in for each other in…
Lowest Common Denominator The Lowest Common Denominator is the smallest number that can be a denominator for two separate fractions. Another way to think of it is that it’s the smallest number that both original denominators can factor into. This is why the most common way to find the LCD is simply to multiply the…
Pythagorean Triplets There are a few common triangles that appear on the ACT math section that are called “Pythagorean Triplets”. These are right triangles where if a student knows two of the sides, they also can know the third side automatically without having to use the Pythagorean theorem. These triangles are known as 3,4,5 and…
Value/frequency charts Frequency charts summarize data sets by showing how often each data point appears within a set. This can be displayed as either a table or a graph. Questions about these charts will generally focus on the mean/median of the data set. Students should be comfortable calculating the mean/median from either of these two…
Use the radius Any time a circle appears in a problem, the first thing to think about is the radius of the circle. It is the core piece of information about the circle, and it is the thing that is most commonly used to calculate or infer information about things that appear in the rest…
Parallelogram Parallelograms are an important thing to review for the ACT, because they tend to be something students are less familiar or comfortable with. Problems involving parallelograms can therefore become an easy place for students to lose points. Some key things to remember about parallelograms are as follows. Adjacent Angles Area Formula The area of…
Reciprocal vs. Inverse trig Reciprocal Trig Functions The normal trigonometric functions are sine, cosine, and tangent. However, there are also expressions for the reciprocals of these functions. These functions are secant, cosecant, and cotangent. They are equal to the reciprocals of the ratios from SOHCAHTOA: Secant = 1Cosine=HypotenuseAdjacent Cosecant =1Sine=HypotenuseOpposite Cotangent=1Tangent=AdjacentOpposite The easiest way to remember this is that…
Weighted average Weighted averages are a way to combine the averages of two data sets of different sizes. This is similar to calculating sum totals on a histogram. For example, two classes are described. Class A has 10 students who had an average test score of 75. Class B has 15 students with an average…
Exponential Growth/Decay The Exponential Growth/Decay formula is one of the most common equation forms to see on the ACT. It can be used to express a multitude of different situations, which means it can show up theoretically as a variable function or practically within a word problem. The formula looks like this: Final = Initial (1±growth/decay rate)time Key Takeaways…
Conjugates Conjugates are binomial pairs that have the same numbers/variables within them, but opposite signs. So for example (x-1) and (x+1) are conjugates. Conjugates have special properties that can be useful to know when they appear in questions or answers on the ACT. Simplifying and Rationalizing Denominators This particularly true when the original denominator contains either a radical…