Content Covered by the ACT Mathematics Test

1. Content Covered by the ACT Mathematics Test In the Mathematics Test, three subscores are based on six content areas: pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry.

2. Pre-Algebra Pre-Algebra (23%). Questions in this content area are based on basic operations using whole numbers, decimals, fractions, and integers; place value; square roots and approximations; the concept of exponents; scientific notation; factors; ratio, proportion, and percent; linear equations in one variable; absolute value and ordering numbers by value; elementary counting techniques and simple probability; data collection, representation, and interpretation; and understanding simple descriptive statistics.

3. Elementary Algebra Elementary Algebra (17%). Questions in this content area are based on properties of exponents and square roots, evaluation of algebraic expressions through substitution, using variables to express functional relationships, understanding algebraic operations, and the solution of quadratic equations by factoring.

4. Intermediate Algebra Intermediate Algebra (15%). Questions in this content area are based on an understanding of the quadratic formula, rational and radical expressions, absolute value equations and inequalities, sequences and patterns, systems of equations, quadratic inequalities, functions, modeling, matrices, roots of polynomials, and complex numbers.

5. Coordinate Geometry Coordinate Geometry (15%). Questions in this content area are based on graphing and the relations between equations and graphs, including points, lines, polynomials, circles, and other curves; graphing inequalities; slope; parallel and perpendicular lines; distance; midpoints; and conics.

6. Plane Geometry Plane Geometry (23%). Questions in this content area are based on the properties and relations of plane figures, including angles and relations among perpendicular and parallel lines; properties of circles, triangles, rectangles, parallelograms, and trapezoids; transformations; the concept of proof and proof techniques; volume; and applications of geometry to three dimensions.

7. Trigonometry Trigonometry (7%). Questions in this content area are based on understanding trigonometric relations in right triangles; values and properties of trigonometric functions; graphing trigonometric functions; modeling using trigonometric functions; use of trigonometric identities; and solving trigonometric equations.

8. Read each question carefully to make sure you understand the type of answer required. • If you use a calculator, be sure it is working on test day and has reliable batteries. • Solve the problem. • Locate your solution among the answer choices. • Make sure you answer the question asked. • Make sure your answer is reasonable. • Check your work.

9. Pre-Algebra 1. Number Problems 2. Multiples, Factors, & Primes 3. Divisibility and Remainders 4. Percentages 5. Ratios and Proportions 6. Mean, Median, & Mode 7. Probability 8. Absolute Value 9. Exponents and Roots 10. Series

10. Elementary Algebra 1. Substitution 2. Simplifying Algebraic Expressions 3. Writing Expressions & Equations 4. Solving Linear Equations 5. Multiplying Binomials 6. Inequalities

11. Intermediate Algebra 1. Solving & Factoring Quadratic Equations 2. Solving Systems of Equations 3. Relationship between Sides of an Equation 4. Functions 5. Matrices 6. Logarithms

12. Plane Geometry 1. Angles 2. Triangles 3. Polygons 4. Circles 5. Simple 3-D Geometry

13. Coordinate Geometry 1. Number Lines & Inequalities 2. The (x,y) Coordinate Plane 3. Distance and Midpoints 4. Slope 5. Parallel & Perpendicular Lines 6. Graphing Equations 7. Conic Sections

14. Trigonometry 1. SOHCAHTOA 2. Solving Triangles 3. Trigonometric Identities 4. Trigonometric Graphs

15. Whole Numbers

16. Terms and Operations • Basic Terms • sum (total) • difference • product • quotient • remainder

17. Terms and Operations 2. Symbols of inclusion • parentheses • brackets • braces (2 + 3) •4 = 20 2 + (3 • 4) = 14

18. Terms and Operations 3. Order of Operation • Parentheses • Exponents, radicals • Multiplication/division • Addition/subtraction

19. Terms and Operations • Factoring and Canceling • 5(2 + 3 + 4) = 5(9) = 45

20. Factors, Multiples, and Primes • Factor - A number that divides another number evenly. • Multiple - A number that is evenly divisible by another number. • Prime - A number that is only divisible by 1 and itself.

21. Odd and Even Numbers • Odd number - A number that is not evenly divisible by 2. • Even number - A number that is divisible by 2. 1. Even + Even = Even 5. Even • Even = Even 2. Even + Odd = Odd 6. Even • Odd = Even 3. Odd + Even = Odd 7. Odd • Even = Even 4. Odd + Odd = Even 8. Odd • Odd = Odd

22. Consecutive Integers Consecutive integers immediately follow one another 1st 2nd 3rd n n + 1 n + 2 Consecutive even integers and consecutive odd integers 1st 2nd 3rd n n + 2 n + 4

23. Fractions • Convert Mixed Numbers to Improper Fractions • Convert Improper Fractions to Mixed Numbers • Reducing Fractions to Lowest Terms • Common Denominators • Operations of Fractions • Comparing Fractions

24. Signed Numbers • Absolute Value • Adding Negative Numbers • Subtracting Negative Numbers • Multiplying Negative Numbers • Dividing Negative Numbers • Subtracting a negative is the same as adding a positive number. • Adding a negative number is the same as subtracting a positive number. • Multiplying or dividing an odd number of negative signs will always result in a negative number. • Multiplying or dividing an even number of negative signs will always result in a positive number.

25. Decimals • A decimal is a special way of writing fractions using a denominator that is a power of 10. 0 . 1 2 3 4 5 6 Millionths Hundred Thousandths Ten Thousandths Thousandths Hundredths Tenths

26. Decimals • Converting Fractions to Decimals • Converting Mixed Numbers to Decimals • Converting Improper Fractions to Decimals • Converting Decimals and Fractions to Mixed Numbers • Operations of Decimals

27. Percents • Converting to and from Percents • Operations of Percents • Percent Story Problems

28. Mean, Median, and Mode • Mean - The average of a set data values • Median • The median of an odd number of data values is the middle value • The median of an even number of data values is the average of the middle two • Mode - The value that occurs most often

29. Ratios and Proportions • Ratio - A relationship between two quantities • Proportion - An equation relating two proportions 1:2 = 2:4 1*4 = 2*2 The product of the means equals the product of the extremes.

30. Exponents Rules For Exponents If a > 0 and b > 0, the following hold true for all real numbers x and y.

31. Roots and Radicals • Square Root • Cube Root • Rational Exponents

32. Variables Coefficients Algebraic Operations • Elements of Algebra • Algebraic Terms • Term • Coefficient • Variable • Exponent Exponent

33. Operations of Algebraic Terms • Adding and Subtracting • Multiplying and Dividing • Algebraic Fractions • Factoring Algebraic Expressions • Absolute Value in Algebraic Expressions • Radicals in Algebraic Expressions

34. Algebraic Equations and Inequalities • Solving Algebraic Formulas • Solving Linear Equations • Solving Simultaneous Equations • Solving Quadratic Equations • Algebraic Inequalities • Exponents in Equations and Inequalities • Rational Equations and Inequalities • Radical Equations

35. P Q Geometry Notation Line Segment PQ B Angle BAC <BAC Vertex A C

36. Angle Properties 90° 180° 0° 270°

37. Angle Properties • Right Angle • Acute Angle • Obtuse Angle • Vertical Angle x = z w = y x y w z

38. 12 3 4 5 6 7 8 Angle Properties • Transversal - A line that intersects parallel line • Alternate Interior • Alternate Exterior • Vertical Angles • Same Side Interior Angles

39. Polygon Properties • Polygon - A closed figure created by three or more lines. • Triangle - A polygon with exactly three sides • Quadrilateral - A polygon with exactly four sides • Pentagon - A polygon with exactly five sides • Hexagon - A polygon with exactly six sides

40. Polygon Properties • Regular Polygon - A polygon with equal sides and equal angles. • The sum of the exterior angles of a polygon is 360° • The sum of the interior angles of a polygon is 180(n - 2) where n is the number of sides in the polygon

41. Triangle Properties • Scalene Triangle - A triangle with no equal sides • Isosceles Triangle - A triangle with exactly two sides equal, If the two sides are equal than the angles opposite the two sides are equal and vice versa. • Equilateral Triangle - A triangle with three sides equal, If the three sides are equal than each angle equal 60° and vice versa

44. Perimeter and Area

45. Area and Volume

46. Circle Properties chord diameter secant radius tangent

47. Circle Properties Central Angle - An angle with the vertex at the center and with sides that are radii. Inscribed Angle - An angle with a vertex on the circle and with sides that are chords. B A O D C E

48. Coordinate Geometry

49. Coordinate Geometry Equations of Lines Slope

50. Coordinate Geometry Parallel lines m1 = m2 Perpendicular linesm1 = -1/m2