ACT I

ACT Subject Test
Math Level 1

Algebra I Topics

  1. Solve equations and inequalities in 1 variable and graph solutions on the number line 

  2. Solve Absolute-value equations

  3. Solve a formula for a specific variable

  4. Write linear equations and inequalities to capture relationships from real-world situations and graph in the coordinate plane

  5. Find an equation of a line that goes through 2 given points, or through a given point with a given slope.

  6. Translate between different representations of a line, including graph, table, verbale description, and different forms of equation

  7. Represent direct and inverse variation

  8. Solve systems of 2 equations in 2 variables; understand solution methods

  9. Apply function concepts and determine if a relationship is a function

  10. Find domain and range

  11. Evaluate functions at a given values

  12. Find rate of change in a function and connect this to slope for linear functions

  13. Translate between different representations of a function, including graph, table, set of ordered pairs, verbal description, and equations

  14. Factor trinomials; recognize perfect-square trinomials

  15. Recognize and factor difference of squares

  16. Solve quadratics equations using different methods

  17. Identify graphs of quadratic equations and functions

  18. Relate factors, solutions, zeros, and intercepts

  19. Use properties of exponents

  20. Manipulate radical and rational expressions

  21. Interpret data representations

  22. Identify arithmetic sequences

  23. Find the probability of simple events

  24. Distinguish between independent and dependent events

  25. Identify an approximate line of best fit to model data and use a model to make predictions

Geometry I Topics

  1. Use inductive and deductive reasoning to make valid conclusions.

  2. Apply theorems, definitions, and axioms to solve problems and draw conclusions

  3. Interpret a mathematical proof in different forms.

  4. Use properties of quadrilaterals to solve problems and identify valid reasoning.

  5. Use coordinate methods and geometric relationships to deduce whether two lines are about quadrilaterals.

  6. Use various methods, including SSS, SAS, ASA, AAS and HL, to deduce that triangles are congruent and corresponding parts are congruent.

  7. Use various methods including AA, SAS, and SSS, to deduce that triangles are similar, corresponding sides are proportional, and corresponding angles are congruent.

  8. Understand and interpret geometric language.

  9. Use angle relationships to solve problems and draw conclusions use relationships when a transversal crosses 2 parallel lines to solve problems and draw conclusions.

  10. Interpret geometric constructions.

  11. Identify and make deductions about a locus brackets the set of possible positions] in a plane or in three-dimensional space.

  12. Use relationships involving medians, altitudes, perpendicular bisectors, and angle bisectors to solve problems and draw conclusions.

  13. Apply the triangle inequality theorem about the relative size of angles and the relative size of opposite sides.

  14. Recognize Pythagorean relationships in complex diagrams and real world contexts, and use this to solve problems and draw conclusions

  15. Relate interior and exterior angles and angle sums to the number of sides of a Polygon.

  16. Recognize isosceles triangles in complex contexts and use properties to solve problems and draw conclusions.

  17. Recognize relationships between lines and line segments associated with circles, central angles, inscribed angles, intercepted arcs, and inscribed polygons and use properties to solve problems and draw conclusions.

  18. Identify and classify two and three-dimensional shapes and use their properties to solve problems recognize cross sections of prisms, cylinders, pyramids, and cones and use relationships to solve problems and draw conclusions.

  19. Determine points or lines of symmetry and apply properties of symmetry to solve problems and draw conclusions about figures.

  20. Identify congruent figures and corresponding parts.

  21. Identify similar figures and use ratio and proportion reasoning to solve mathematical and real-world problems, including situations with a geometric mean relationship such as right triangle and its altitude

  22. Identify transformations and transformed figures.

  23. Understand relationships between corresponding events, areas, and volumes for similar figures in terms of scale factor.

  24. Use length, with, parameter, circumference, area, surface area, and volume relationships and formulas to solve problems and draw conclusions.

  25. Find geometric probability and draw conclusions.

  26. Use coordinates to solve problems about geometric figures, including the effect of reflections, rotations, translations, and dilations.

  27. Find distance and midpoint and use distance at midpoint relationships to solve problems and draw conclusions.

  28. Identify parallel and perpendicular lines on the basis of slope.

  29. Find trigonometric ratios for triangles, in particular for 45-45-90 and 30-60-90 triangles.

  30. Recognize right triangles in real world context and use the grammatic ratios to find side length and angle measures.

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