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List of Concepts for Algebra and Geometry Placement Tests

Algebra Competency Test:

Before taking the De La Salle “Incoming Frosh Math Placement Test” the student should be able to:

  • simplify expressions before solving linear equations in one variable
  • add, subtract, multiply and divide real numbers
  • use the concept of adding the opposite in order to subtract real numbers
  • use the concept of finding the reciprocal to divide real numbers
  • follow instructions to take a root and raise to a fractional power
  • use the rules of exponents
  • write an equation from a statement
  • solve multi-step equations, including word problems, with simplifying expressions, with variables on both sides.
  • solve literal equations for a variable
  • solve absolute value equations
  • solve one-step and multi-step inequalities and graph their solutions
  • solve compound inequalities and graph their solutions
  • write a compound inequality from a graph
  • solve absolute-value inequalities
  • Find the domain and range of a relation
  • Identify and evaluate functions
  • Graph a function by selecting points
  • Graph scatter plots from given data by hand and using technology
  • Graph linear Equations
  • Find the intercepts of a line
  • Find slope from a graph
  • Find slope by using the slope formula
  • Find slope from an equation
  • Write, solve, and graph direct variation equations
  • Write linear equations in slope-intercept form
  • Use slope-intercept, slope and a point form to graph
  • Write linear equations in slope-intercept form
  • Write equations of parallel and perpendicular lines
  • identify solutions of systems
  • solve a system of linear equations by graphing, substitution, and elimination methods
  • classify systems as consistent or inconsistent and/or dependent or independent
  • solve the special application problems of rate, mixture, and number-digit
  • identify solutions of linear inequalities
  • solve, write, and graph linear inequalities in two variables
  • identify solutions of systems of linear inequalities
  • solve and graph systems of inequalities
  • evaluate and simplify expressions with zero and negative exponents
  • find products and quotients of powers
  • find powers of powers
  • rewrite a base with a fractional power as a radical
  • simplify expressions with fractional exponents
  • use properties of exponents to simplify expressions
  • find the degree of a monomial
  • write polynomials in standard form, classify polynomials,
  • identify roots of polynomials
  • add, subtract, and multiply polynomials
  • write the prime factorization of whole numbers
  • find the GCF of numbers and monomials
  • factor a polynomial using GCF, grouping, special products
  • Solve equations by factoring
  • identify and graph an inverse variation
  • identify excluded values, asymptotes and graph rational functions
  • simplify rational expressions using multiplication, division, addition, and subtraction
  • solve rational equations
  • apply rational equations to real life situations
  • Algebra: 3/2/11

    Geometry Competency Test:

    • Please note that students taking the Geometry Competency Test must also take an Algebra Competency Test at DLS to determine appropriate placement (Date and Time for this test TBA).
    • Before taking the De La Salle “Incoming Frosh Geometry Competency Test” the student should be able to:
    • Sketch simple figures of the basic terms in geometry and their intersections
    • Recognize and analyze a conditional statement
    • Write or verbalize conditional statements to describe properties of points, lines, and planes
    • Recognize and use definitions and biconditional statements
    • Write the converse, inverse, and contrapositive of conditional statements;
    • Apply the properties of equality from algebra
    • Justify statements about congruent segments
    • Justify statements about congruent angles.
    • Supply reasons for statements in a proof
    • Prove properties about special pairs of angles\identify relationships between lines
    • Identify angles formed by transversals
    • Apply theorems about perpendicular lines
    • Prove and use properties of parallel lines;
    • Prove and use theorems to prove that lines are parallel
    • Use slopes of lines to identify parallel and perpendicular lines in the coordinate plane
    • Write equations of lines in the coordinate plane
    • Classify triangles by sides and by angles
    • Find angle measures in triangles
    • Identify congruent figures and corresponding parts
    • Prove triangles are congruent
    • Apply congruence postulates in real-life problems
    • Use congruent triangles to plan and write proofs
    • Use congruent triangles to prove constructions are valid
    • Apply properties of isosceles, equilateral, and right triangles
    • Place geometric figures in a coordinate plane
    • Write coordinate proofs
    • Apply properties of perpendicular bisectors of the sides of triangles
    • Apply properties of angle bisectors of triangles
    • Apply properties of medians of a triangle
    • Apply properties of altitudes of a triangle
    • Locate, by construction, the incenter, circumcenter, centroid, and orthocenter
    • Identify the midsegments of a triangle and use the midsegment theorem
    • Apply the properties of midsegments both logically and algebraically
    • Identify, name, and describe polygons
    • Find the measure of the interior angles of a polygon
    • Apply the definition and theorems about a parallelogram
    • Prove that quadrilaterals are or are not parallelograms
    • Apply the definitions and theorems about rectangles, rhombuses, and squares
    • Apply the definitions and theorems about trapezoids and kites
    • Prove and use the properties of the diagonals of parallelograms, trapezoids, and kites
    • Determine, by formal and/or coordinate proof, if a quadrilateral is a special type Derive and use formulas to find the area of quadrilaterals
    • Identify similar polygons
    • Apply properties of similar polygons to solve problems
    • Identify similar triangles
    • Prove triangles similar by using the AA Similarity Postulate, the SAS
    • Similarity Theorem, and the SSS Similarity Theorem
    • Use the similarity of triangles to deduce information about segments and angles
    • Use proportionality theorems to calculate segment lengths
    • Divide a segment into a given number of equal parts by construction
    • Identify dilations
    • Find the geometric mean between two numbers;
    • Apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle
    • Prove the Pythagorean theorem by formal proof and by algebraic methods;
    • Find lengths using the Pythagorean theorem
    • Determine if a triangle is a right, obtuse, or acute by using the converse of the Pythagorean theorem
    • Find the lengths of the sides of the special triangles when one length is given
    • Solve right triangles and real-life problems by using trigonometry;
    • Define: sphere, circle, radius, chord, diameter, tangent, secant, chord, concentric circles
    • Construct circumscribed and inscribed polygons and circles
    • Apply theorems that relate tangents and radii
    • Apply properties of arcs and central angles;
    • Apply theorems about chords, secants, and tangents of a circle
    • Write the equation of a circle
    • Use the equation of a circle and its graph to solve problems
    • Find the measure of interior and exterior angles of polygons
    • Derive and apply formulas for the area of an equilateral triangle and for regular; polygons
    • Draw a regular polygon and find its center, radius, apothem, and central angle
    • Derive formulas for area and circumference of a circle by relating them to the area and perimeter of a regular polygon;
    • Compute the areas and circumferences of circles
    • Compute arc lengths and areas of sectors of circles.
    • Apply the relationships between scale factors, perimeters and areas of similar figures
    • Use properties of polyhedra to find the number of faces, edges, sides, or to find the measure of angles
    • Calculate the lateral area and total area of right prisms, right cylinders, right pyramids, and right cones
    • Find the volume of prisms, cylinders, cones, and pyramids
    • Find the area and volume of a sphere
    • Apply the properties of similar solids
    • Locate images of figures by reflection, translation, glide reflection, and rotation
    • Identify and use reflections, rotations, translations, and glide reflections
    • Represent transformations as compositions of simpler transformations

    Geometry: 3/2/11

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