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In theory, the ACT Math Test seems fairly straightforward: 60 questions in 60 minutes, calculator permitted. Every question is multiple-choice, and there’s also no guessing penalty, which means that wrong answers won’t deduct any points from your total score. For more information on scoring specifics, check out the Complete Guide to Your ACT Score Report .
Topics covered on ACT Math include middle and high school algebra, plane and coordinate geometry, statistics and probability, and trigonometry. Unlike on the SAT, however, the ACT doesn’t provide a formula sheet/box for reference during the test. As such, it’s crucial that you memorize the formulas you’ll need and practice using them ahead of test day. In this post, we’ll discuss why the ACT matters and which formulas are important for success on ACT Math.
Your GPA and standardized test scores are used to calculate your academic index , which determines whether you pass the first stage of the admissions process at most colleges. This is because colleges want students who will thrive academically and graduate on time, so they prefer applicants who have a demonstrated history of solid academic performance. Altogether, high school transcripts and test scores provide some projection of your likely future success in the classroom, and the academic index becomes an efficient method for screening out academically unqualified students.
As such, think of your ACT score as a prerequisite. It determines whether you’ll pass the academic cutoff and make it into the next stage, which is holistic review : essays, extracurriculars, and letters of recommendation. Excellent ACT scores can further qualify you for scholarships, honors programs, and other special opportunities.
This is why the ACT is important, but it generally won’t be the deciding factor in your acceptance. To better understand how ACT scores can affect your chances, check out our free Admissions Calculator ! Unlike other chancing engines, it also considers your high school coursework, extracurriculars, goals, and achievements in building your college list and assisting with your applications.
Now that we’ve established why the ACT matters, let’s discuss the math formulas you need to know.
This formula defines a sequence of numbers where the difference between each consecutive term is the same. The first term of the sequence is \(a_1\), the \(n^\) term of the sequence is \(a_n\), and the constant difference between consecutive terms is \(d\).
This formula defines a sequence of numbers where given the first term, each successive term is defined by multiplying the previous term by a fixed number, also known as the common ratio \((r)\). As with arithmetic sequences, the first term of the sequence is \(a_1\), and the \(n^\) term of the sequence is \(a_n\).
Logarithms are the inverse functions of exponents. In other words, the logarithm of a number, \(x\), is the exponent to which another number, the logarithmic base \(b\), must be raised to produce \(x\). You’ll likely need to rewrite logarithms on the ACT using the following formulas:
If \(log_b(x)=y\), then \(b^y=x\).
This is a common algebraic relationship where \(d\) is distance, \(r\) is rate, and \(t\) is time. You can rewrite this equation to isolate \(r\) or \(t\), and “distance” can be replaced with the more general concept of “quantity.” Just be sure to keep your units straight!
This is a composite function, where the output of \(g(x)\) is the input for \(f(x)\). Notice that \(f\:\circ\:g(x)\) is different from \(fg(x) = f(x)\:\times\:g(x)\).
This is a useful conversion to memorize for trigonometry problems, especially those involving the coordinate plane. To boost your speed, make sure to have the unit circle memorized!
Slope is a rate, specifically \(\frac\). The slope of any line, \(m\), can be determined given any two points on the line, \((x_1,y_1)\) and \((x_2,y_2)\).
This equation defines a line with slope \(m\) and a y-intercept of \((b,0)\) that passes through the point \((x,y)\).
This formula calculates the distance, \(d\), between two points \((x_1,y_1)\) and \((x_2,y_2)\).
This formula defines the midpoint of the line between two points, \((x_1,y_1)\) and \((x_2,y_2)\).
We use FOIL to multiply 2 binomials together. Below are some FOIL shortcuts to memorize, where \(y\) is a constant:
The quadratic formula provides values of \(x\), also known as solutions/roots/zeros, for a given quadratic function \(ax^2+bx+c=0\), where \(a\), \(b\), and \(c\) are constants. The expression underneath the square root, \(b^2-4ac\), is called the discriminant and determines the number of solutions. Specifically:
Image courtesy of ACT
This formula defines a quadratic function with the vertex at \((h,k)\) and a constant, \(a\), determining stretch and direction. The axis of symmetry is line \(x=h\), which crosses the vertex.
Note that FOIL will convert this equation to an expanded form. As such, you may be asked to factor back into vertex form in order to provide coordinates for the vertex.
Image courtesy of ACT
This equation defines a circle with center point \((h,k)\) and radius \(r\). As with the quadratic function above, FOIL will convert this equation to an expanded form, and you may be asked to factor in order to find the radius or central coordinates.
