ACT Math Subject Test
Level 2

Algebra II Topics

  1. Model relationships from a context as equations and inequalities.

  2. Solve compound linear inequalities with implied or explicit “and” and “or” connectors.

  3. Solve linear inequalities containing absolute value.

  4. Solve systems of equations in three variables.

  5. Identify solutions to systems of equations and inequalities from a graph

  6. Find maximum and minimum values of a linear function over a region defined by linear inequalities.

  7. Solve quadratic equations and equalities; understand different methods.

  8. Interpret the discriminant.

  9. Solve quadratic equations with complex number solutions.

  10. Perform operations with complex numbers.

  11. Solve quadratic systems.

  12. Recognize functions as composition of other functions, in particular for translation and reflection, and connect to graphs.

  13. Classify conic sections from their equations in standard form.

  14. For circles and parabolas, translate between equations, graphs, and descriptions in terms of the characteristics.

  15. For a polynomial function, determine or approximate zeros, local minima and maxima, domain, and range.

  16. Related factors, solutions, zeros, and intercepts.

  17. Determine the number and multiplicity of rational zeros for a polynomial function.

  18. Find all rational zeros of a polynomial function.

  19. Manipulate rational expressions and solve rational equations.

  20. Manipulate expressions with Russian exponents and radicals.

  21. Solve equations expressed in terms of rational exponents and radicals.

  22. Identify graphs of exponential and logarithmic functions.

  23. Convert equations between exponential and logarithmic forms apply the law of science and law of cosines.

  24. Find the measure of angles in standard position in degrees or radians.

  25. Find values of sine and cosine functions for general angles and relate to coordinates of the unit circle .

  26. Model relationships with sine and cosine functions and their transformations.

  27. Find and interpret domain, range, and amplitude for sine and cosine functions and their transformations.

  28. Determine the number of ways and event can happen using counting techniques such as the fundamental counting principle, permutation, and combinations.

  29. Find probabilities using properties of events including independence and mutually exclusivity.

  30. Solve problems involving conditional probability.

  31. Represent sample spaces and events in terms of unions, intersections, and complements and use these relationships to find probabilities of compound events.

  32. Find terms and term positions in arithmetic and geometric sequences.

  33. Interpret segment notation and find sums of finite arithmetic and geometric sequences.

  34. Add, subtract, and multiply matrices.

  35. Calculate the determinants of 2 * 2 and 3 * 3 matrices.

  36. Find the inverse of 2 * 2 matrices.

  37. Use inverse matrices to solve systems of linear equations.

Practice Tests

  1. Test 1

  2. Test 2

  3. Test 3

  4. Test 4

  5. Test 5

  6. Test 6

  7. Test 7

  8. Test 8

  9. Test 9

  10. Test 10

  11. Test 11

  12. Test 12 

  13. Test 13 

  14. Test 14 

  15. Test 15 

  16. Test 16

  17. Test 17

Pre-Calculus Topics

  1. Identify and graph piecewise defined functions including greatest integer, step, and absolute value functions.

  2. Find inverse (or partial inverses) and transformation of variable functions including polynomial, rational, radical, absolute value, and trigonometric

  3. For ellipses and hyperbolas, translate between equations, graphs, and descriptions in terms of the characteristics.

  4. Solve systems of conics

  5. Solve polynomial equations exactly or approximately to find rational, real, and complex solutions; understand different methods.

  6. Identify polynomial functions and graphs given characteristics such as degree, sign of lead coefficient, zeros, and multiplicities.

  7. Classify functions as even, odd, or neither; identify symmetry.

  8. Expand polynomials or find terms using the binomial theorem and pascals triangle

  9. Use limits to approximate the slope of a curve at a point.

  10. Use numbers to approximate the area under A curve

  11. Identify rational functions and graphs given characteristics such as intercepts, symmetry, asymptotes, and removal discontinuities

  12. Find characteristics of rational and radical functions such as intercepts, symmetry, asymptotes, removal discontinuities, domain, and range

  13. Evaluate exponential functions and use properties of exponents to rewrite in different forms

  14. Evaluate logarithmic functions, including those with base E, and use properties of logarithms to rewrite in different forms

  15. Solve exponential and logarithmic equations and real world problems such as compound interest and exponential growth/decay.

  16. Identify graphs of trigonometric functions and characteristics such as., amplitude, amount of stretch, phase shift, vertical translation, and midline

  17. Use and interpret the cometric identities including double angle and half angle, some and differences, and sin^2 (x) + cos^2(x)=1

  18. Identify and graph inverse sign, cosine, and tangent functions and use them to solve trigonometric equations.

  19. Determine quartiles and interquartile range of a set of data.

  20. Understand and apply the concepts of standard deviation and these course to data sets.

  21. Understand and apply the concept of standard deviation and Z scores to data sets.

  22. Estimate population characteristics based on samples.

  23. Recognize different types of sampling procedures and identify strengths and limitations .

  24. Use properties of the normal distribution to approximate percent of data within a given interval.

  25. Find the sum of an infinite geometric series.

  26. Determine or approximate the limit of an infinite sequence or determine that it does not exist.

  27. Interpret arguments that use mathematical induction.

  28. Use matrices as transformation of the plane.

  29. Find the reduced row echelon form of an augmented matrix to solve systems of equations.

  30. Graph polar functions and points in the polar coordinate plane.

  31. Convert points and functions between rectangular and polar forms.

  32. Find powers and roots of complex numbers in polar form using DeMoivre’s theorem.

  33. Find the magnitude and direction of vector.

  34. Identify the results of vector addition, subtraction, and scalar multiplication with coordinate and graphically.

  35. Resolve A vector into horizontal and vertical components.

  36. Find the angle between vectors using the dot product.

  37. Solve real world problems involving vector displacements such as path of airplane in wind.

  38. Identify parametric equations of lines and graphs of parametric equations.