# ACT I

## ACT Subject Test

Math Level 1

## Algebra I Topics

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

### Solve Absolute-value equations

### Solve a formula for a specific variable

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

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

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

### Represent direct and inverse variation

### Solve systems of 2 equations in 2 variables; understand solution methods

### Apply function concepts and determine if a relationship is a function

### Find domain and range

### Evaluate functions at a given values

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

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

### Factor trinomials; recognize perfect-square trinomials

### Recognize and factor difference of squares

### Solve quadratics equations using different methods

### Identify graphs of quadratic equations and functions

### Relate factors, solutions, zeros, and intercepts

### Use properties of exponents

### Manipulate radical and rational expressions

### Interpret data representations

### Identify arithmetic sequences

### Find the probability of simple events

### Distinguish between independent and dependent events

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

## Geometry I Topics

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

### Apply theorems, definitions, and axioms to solve problems and draw conclusions

### Interpret a mathematical proof in different forms.

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

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

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

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

### Understand and interpret geometric language.

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

### Interpret geometric constructions.

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

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

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

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

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

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

### 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.

### 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.

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

### Identify congruent figures and corresponding parts.

### 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

### Identify transformations and transformed figures.

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

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

### Find geometric probability and draw conclusions.

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

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

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

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

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

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