Prep for LA Geometry EOC Assessment

Transcription

1 Prep for LA Geometry EOC Assessment This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs. Curriculum (262 topics + 48 additional topics) Arithmetic Readiness (40 topics) Whole Numbers, Fractions, and Decimals (20 topics) Introduction to exponents Order of operations with whole numbers Order of operations with whole numbers and grouping symbols Order of operations with whole numbers and exponents: Basic Evaluating an algebraic expression: Whole numbers with two operations Factors Least common multiple of 2 numbers Equivalent fractions Simplifying a fraction Finding the LCD of two fractions Addition or subtraction of fractions with different denominators Product of a fraction and a whole number: Problem type 1 Fraction multiplication The reciprocal of a number Fraction division Writing an improper fraction as a mixed number Decimal place value: Tenths and hundredths Rounding decimals Writing a ratio as a percentage without a calculator Finding a percentage of a whole number without a calculator: Basic Signed Numbers (16 topics) Plotting integers on a number line Ordering integers Integer addition: Problem type 1 Integer addition: Problem type 2 Integer subtraction: Problem type 1 Integer subtraction: Problem type 2 Integer subtraction: Problem type 3 Signed fraction addition or subtraction: Basic Signed decimal addition and subtraction Integer multiplication and division Multiplication of 3 or 4 integers Signed fraction multiplication: Basic Exponents and integers: Problem type 1 Evaluating a linear expression: Integer multiplication with addition or subtraction Evaluating a quadratic expression: Integers Absolute value of a number Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 1/8

2 Radicals (4 topics) Square root of a perfect square Square root of a rational perfect square Simplifying the square root of a whole number less than 100 Rationalizing the denominator of a radical expression Equations and Inequalities (26 topics) Properties of Real Numbers (3 topics) Distributive property: Whole number coefficients Combining like terms: Whole number coefficients Combining like terms: Integer coefficients Linear Equations (13 topics) Translating a sentence into a one step equation Additive property of equality with integers Additive property of equality with a negative coefficient Multiplicative property of equality with integers Multiplicative property of equality with fractions Multiplicative property of equality with signed fractions Using two steps to solve an equation with whole numbers Solving a two step equation with integers Solving a two step equation with signed fractions Solving a linear equation with several occurrences of the variable: Variables on the same side and distribution Solving a linear equation with several occurrences of the variable: Variables on both sides and distribution Introduction to algebraic symbol manipulation Algebraic symbol manipulation: Problem type 1 Proportions (7 topics) Solving a proportion of the form x/a = b/c Solving a proportion of the form a/(x+b) = c/x Solving a rational equation that simplifies to linear: Denominator x Writing ratios for real world situations Word problem on proportions: Problem type 1 Word problem on proportions: Problem type 2 Converting between metric and U.S. Customary unit systems Linear Inequalities (3 topics) Graphing a linear inequality on the number line Graphing a compound inequality on the number line Solving a linear inequality: Problem type 1 Linear Equations in Two Variables (24 topics) Ordered Pairs (4 topics) Reading a point in the coordinate plane Plotting a point in the coordinate plane Table for a linear equation Finding a solution to a linear equation in two variables Graphing Lines (5 topics) Graphing a line given its x and y intercepts Graphing a line given its equation in slope intercept form Graphing a line given its equation in standard form Graphing a line through a given point with a given slope Graphing a vertical or horizontal line Equations of Lines (15 topics) Finding the y intercept of a line given its equation Finding x and y intercepts of a line given the equation: Advanced Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 2/8

3 Finding slope given the graph of a line on a grid Finding slope given two points on the line Finding the slope of a line given its equation Writing a function rule given a table of ordered pairs: One step rules Writing a function rule given a table of ordered pairs: Two step rules Writing an equation of a line given the y intercept and another point Writing the equation of a line given the slope and a point on the line Writing the equation of the line through two given points Finding slopes of lines parallel and perpendicular to a line given in the form Ax + By = C Writing equations of lines parallel and perpendicular to a given line through a point Choosing a graph to fit a narrative: Advanced Sketching the line of best fit Scatter plots and correlation Reasoning, Lines, and Angles (30 topics) Reasoning and Logic (8 topics) Finding the next terms of a sequence with whole numbers Finding a specified term of an arithmetic sequence given the common difference and first term Finding patterns in shapes Interpreting a Venn diagram of 2 sets Interpreting a Venn diagram of 3 sets Conditional statements and negations The converse, inverse, and contrapositive of a conditional statement Conditional statements and deductive reasoning Segments (6 topics) Naming segments, rays, and lines Computing distances between decimals on the number line Midpoint of a number line segment Segment addition and midpoints Introduction to proofs: Justifying statements Proofs involving segment congruence Distance and Midpoint in the Plane (2 topics) Distance between two points in the plane: Exact answers Midpoint of a line segment in the plane Lines (3 topics) Identifying parallel and perpendicular lines Introduction to proofs involving parallel lines Proofs involving parallel lines Angles (11 topics) Measuring an angle with the protractor Drawing an angle with the protractor Acute, obtuse, and right angles Finding supplementary and complementary angles Identifying corresponding and alternate angles Identifying supplementary and vertical angles Solving equations involving vertical angles Solving equations involving angles and a pair of parallel lines Angle addition with relationships between angles Angle addition and angle bisectors Proofs involving angle congruence Triangles (25 topics) Properties of Triangles (14 topics) Acute, obtuse, and right triangles Classifying scalene, isosceles, and equilateral triangles by side lengths or angles Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 3/8

4 Area of a triangle Finding an angle measure of a triangle given two angles Finding angle measures of a right or isosceles triangle given angles with variables Finding an angle measure for a triangle with an extended side Finding an angle measure for a triangle sharing a side with another triangle Finding an angle measure given extended triangles Finding an angle measure given a triangle and parallel lines Using triangle inequality to determine if side lengths form a triangle Using triangle inequality to determine possible lengths of a third side Relationship between angle measures and side lengths in a triangle Relationship between angle measures and side lengths in two triangles Indirect proof (proof by contradiction) Congruent Triangles (7 topics) Identifying congruent shapes on a grid Identifying and naming congruent triangles Proofs involving congruent triangles and vertical angles or the reflexive property Proofs involving congruent triangles and segment or angle bisectors Proofs involving congruent triangles that overlap: Basic Proofs involving congruent triangles, parallel or perpendicular segments, and CPCTC Proofs involving congruent triangles that overlap: Advanced Right Triangles (4 topics) Pythagorean Theorem Computing an area using the Pythagorean Theorem Using the Pythagorean Theorem repeatedly Special right triangles: Exact answers Polygons (32 topics) Polygons and Quadrilaterals (13 topics) Properties of quadrilaterals Conditions for quadrilaterals Classifying parallelograms Finding coordinates of vertices of polygons Finding the coordinates of a point to make a parallelogram Congruence in the coordinate plane Sum of the angle measures of a quadrilateral Finding measures involving diagonals of parallelograms Conditions for parallelograms Finding measures involving diagonals of rectangles Finding measures involving diagonals of rhombi The sum of interior angle measures in a convex polygon Interior and exterior angle measures in a regular polygon Perimeters and Areas of Polygons (19 topics) Perimeter of a square or a rectangle Perimeter of a polygon Finding the missing length in a figure Perimeter of a piecewise rectangular figure Finding a side length given the perimeter and side lengths with variables Sides of polygons having the same perimeter Area of a square or a rectangle Distinguishing between the area and perimeter of a rectangle Areas of rectangles with the same perimeter Area of a piecewise rectangular figure Word problem involving the area between two rectangles Finding the side length of a rectangle given its perimeter or area Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 4/8

5 Finding the perimeter or area of a rectangle given one of these values Area of a parallelogram Area of a trapezoid Area involving rectangles and triangles Area of a regular polygon Area of quadrilaterals in the coordinate plane Finding an area in terms of variables Similarity, Trigonometry, and Transformations (22 topics) Similar Polygons (6 topics) Identifying similar or congruent shapes on a grid Similar polygons Similar right triangles Indirect measurement Triangles and parallel lines Right triangles and geometric mean Trigonometric Ratios (6 topics) Sine, cosine, and tangent ratios: Variables for side lengths Using the Pythagorean Theorem to find a trigonometric ratio Using a trigonometric ratio to find a side length in a right triangle Using trigonometry to find a length in a word problem with one right triangle Using a trigonometric ratio to find an angle measure in a right triangle Using trigonometry to find angles of elevation or depression in a word problem Transformations (10 topics) Identifying transformations Translating a polygon Using a translated point to find coordinates of other translated points Reflecting a polygon over a vertical or horizontal line Finding the coordinates of three points reflected over an axis Drawing lines of symmetry Rotating a figure about the origin Finding an angle of rotation Rotational and point symmetries Dilating a figure Circles (21 topics) Circles (8 topics) Introduction to a circle: Diameter, radius, and chord Identifying central angles, inscribed angles, arcs, chords, and tangents of a circle Tangents of a circle: Problem type 1 Tangents of a circle: Problem type 2 Lengths of chords, secants, and tangents Inscribed angles of a circle Central angles and inscribed angles of a circle Angles of intersecting secants and tangents Circumferences and Areas of Circles (10 topics) Circumference of a circle Finding the radius or the diameter of a circle given its circumference Perimeter involving rectangles and circles Circumference ratios Circumference and area of a circle Arc length and area of a sector of a circle Area involving rectangles and circles Word problem involving the area between two concentric circles Area involving inscribed figures Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 5/8

6 Circles inscribed in and circumscribed about regular polygons Equations of Circles (3 topics) Graphing a circle given its equation in standard form Writing an equation of a circle given its center and a point on the circle Writing an equation of a circle given the endpoints of a diameter Volumes and Surface Areas (22 topics) Volumes (10 topics) Counting the cubes in a solid made of cubes Volume of a rectangular prism made of unit cubes Volume of a rectangular prism Volume of a piecewise rectangular prism Volume of a triangular prism Volume of a pyramid Volume of a cylinder Word problem involving the rate of filling or emptying a cylinder Volume of a cone: Exact answers in terms of pi Volume of a sphere Surface Areas (10 topics) Vertices, edges, and faces of a solid Nets of solids Nets of solids: Advanced Side views of a solid made of cubes Surface area of a cube or a rectangular prism Surface area of a piecewise rectangular prism made of unit cubes Surface area of a triangular prism Surface area of a cylinder: Exact answers in terms of pi Surface area involving prisms or cylinders Surface area of a sphere Similar Solids (2 topics) Computing ratios of side lengths, surface areas, and volumes for similar solids Similar solids: Problem type 2 Statistics and Probability (20 topics) Graphical Displays (7 topics) Interpreting a bar graph Interpreting a double bar graph Interpreting a line graph Computing a percentage from a table of values Interpreting a circle graph or pie chart Computations from a circle graph Angle measure in a circle graph Counting (5 topics) Interpreting a tree diagram Introduction to the counting principle Counting principle Word problem involving permutations Word problem involving combinations Probability (8 topics) Introduction to the probability of an event Probability of an event Outcomes and event probability Probabilities involving two dice Area as probability Introduction to expectation Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 6/8

7 Probability of independent events Probability of dependent events Other Topics Available(*) (48 additional topics) Arithmetic Readiness (11 topics) Word problem with addition or subtraction of integers Signed decimal addition and subtraction with 3 numbers Order of operations with integers Exponents and integers: Problem type 2 Exponents and signed fractions Order of operations with integers and exponents Operations with absolute value: Problem type 2 Estimating a square root Cube root of an integer Square root addition or subtraction Square root multiplication: Advanced Equations and Inequalities (14 topics) Identifying numbers as integers or non integers Identifying numbers as rational or irrational Distributive property: Integer coefficients Combining like terms: Advanced Combining like terms in a quadratic expression Properties of addition Properties of real numbers Translating a phrase into a two step expression Algebraic symbol manipulation: Problem type 2 Translating a sentence by using an inequality symbol Writing an inequality given a graph on the number line Solving a linear inequality: Problem type 2 Solving a linear inequality: Problem type 3 Solving a compound linear inequality: Graph solution, basic Linear Equations in Two Variables (2 topics) Determining whether given points lie on one, both, or neither of 2 lines given equations Writing the equations of vertical and horizontal lines through a given point Reasoning, Lines, and Angles (5 topics) Constructing the perpendicular bisector of a line segment Constructing a pair of perpendicular lines Constructing a pair of parallel lines Constructing an angle bisector Constructing congruent angles Similarity, Trigonometry, and Transformations (11 topics) Solving a triangle with the law of sines: Problem type 1 Solving a triangle with the law of sines: Problem type 2 Solving a triangle with the law of cosines Magnitude of a vector given in component form Translation of a vector Scalar multiplication of a vector: Geometric Approach Vector addition: Geometric approach Vector addition and scalar multiplication: Component form Linear combination of vectors: Component form Finding the magnitude and direction of a vector given its graph Finding the components of a vector given its graph Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 7/8

8 Statistics and Probability (5 topics) Constructing a bar graph for non numerical data Permutations, combinations, and the multiplication principle for counting Odds of an event Experimental and theoretical probability Probability of the union of two events Other Topics AvailableBy default, these topics are NOT included in the course, but can be added using the content editor in the Teacher Module. Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 8/8