The ACT math section covers five areas of math. So, what kinds of math questions can you expect to see on this section? The content can be grouped as follows: number & quantity, algebra, functions, geometry, and statistics & probability.
The 5 Kinds of ACT Math Questions
Number & Quantity
Number and Quantity questions test your knowledge of real and complex number systems, like central tendency and distribution (mean, median, mode, range), manipulating expressions and equations, understanding factoring, greatest common factor, and least common multiple, and more.
For the Number & Quantity questions you may need to:
- Manipulate, order, and solve problems involving whole numbers, fractions, decimals, percents, and percentage change
- Compute values using proportional relationships and ratios
- Understand factoring, greatest common factor, and least common multiple
- Find distance on a number line, between points on a coordinate plane, or in terms of absolute value
- Manipulate exponents in powers of 10 and apply properties of rational exponents
- Demonstrate knowledge of the real number system – rational, irrational, and complex numbers
- Demonstrate knowledge of operations on matrices and vectors
Algebra questions test your ability to solve and graph expressions. You will need to find solutions to systems of equations, understand matrices, and apply your knowledge to word problems.
Algebra concepts may test your ability to:
- Use word to symbol translation to solve real-world problems
- Manipulate and evaluate variable expressions and equations (including absolute value)
- Solve linear and quadratic inequalities and match with appropriate graphs
- Find and interpret slope and intercepts from equations, word problems and graphs (also using properties of parallel and perpendicular lines
- Match, interpret, and analyze information from graphs in the coordinate plane
- Add, subtract, multiply, and divide polynomials
- Solve quadratic equations
- Manipulate exponents such as squares, cubes, roots, and scientific notation
- Solve and interpret systems of linear equations
- Solve multi-step problems using proportions, rate, percentages, and/or conversion of units of measure
Functions questions test your ability to manipulate and translate a variety of functions, including linear, polynomial, and logarithmic. You’ll also be asked to find and apply important features of graphs.
Functions questions may ask you to:
- Understand the concept of what makes a function (one input cannot have more than one output value)
- Interpret and evaluate functions and composite functions
- Find the domain and range of functions (and vertical asymptote of rational functions)
- Write functions that are directly or inversely proportional or exponential
- Extend patterns (constant increase or decrease or factor)
- Demonstrate knowledge of arithmetic and geometric sequences
- Understand the trigonometry of the unit circle, basic trigonometric graphs, and basic trig identities to solve problems
- Demonstrate knowledge of logarithms
- Identify a function when the graph of a given function is translated horizontally or vertically
Geometry questions test your knowledge of shapes and solids. You will need to know how to manipulate shapes, calculate equations of conic sections, and more (below).
Geometry questions will test your ability to:
- Calculate lengths and midpoints of line segments (overlapping segments and those in the coordinate plane)
- Compute perimeter and area of polygons and circumference and area of circles
- Use properties of parallel lines and other angle properties to find missing angle measures
- Use properties of isosceles and right triangles to compute unknown side lengths and angle measures (symmetry, Pythagorean theorem, etc…)
- Translate points horizontally, vertically, reflectively, or rotationally in a coordinate plane
- Demonstrate knowledge of right triangles (30o, 60o, 90o; 45o, 45o, 90o) and apply trigonometric ratios (sine, cosine, tangent) to solve for missing values
- Manipulate between area, volume, and surface area
- Understand special characteristics of conics (circle, ellipse, parabola, hyperbola) such as the center, radius, or vertex
- Compute angles (degrees and radians), arcs, and distances in a circle
Statistics and Probability
Statistics and probability questions will require you to calculate probability and apply and analyze data.
For Statistics and Probability concepts you will need to:
- Interpret data, charts, frequency tables, and graphs to get information for computations or for transformation into a different type of data display
- Demonstrate knowledge of measures of central tendency and distribution (mean, median, mode, range), how to compute each, and how to compute for missing data point given a measure of central tendency
- Compute probabilities of an event, its complement, and combinations (conditional and joint probability)
- Demonstrate knowledge of the fundamental counting principle and Venn Diagrams
- Understand the fundamentals of statistics (random sampling, distribution, deviation, confidence interval, and interpretation of results)
Now that you’ve learned about the kinds of ACT math questions you’ll see on the test, it’s time to get practicing. Olive Book’s ACT course contains hundreds of math practice questions with explanations that more than cover each area of math. The course is literally all you need to study successfully for the ACT. Enroll at www.olive-book.com.