Spring 2012 2014 Student Performance Analysis Algebra I

Spring 2012 -2014 Student Performance Analysis Algebra I Standards of Learning Presentation may be paused and resumed using the arrow keys or the mouse.

Representing and Evaluating Cube Roots and Square Roots 2012, 2013 SOL A. 1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables.

2012 Suggested Practice for SOL A. 1 Students need additional practice using replacement values to evaluate expressions with cube roots and square roots.

2013 Suggested Practice for SOL A. 1 Students need additional practice evaluating expressions that contain an absolute value. Evaluate the following expressions: a. b.

2013 Suggested Practice for SOL A. 1 Students need additional practice evaluating expressions with cube roots, square roots, and the square of a number, particularly when the replacement variable has a negative value. Evaluate the following expressions: a. b. c.

2012 Suggested Practice for SOL A. 1 Students need additional practice translating expressions with square and cube roots. Translate into an algebraic expression: a) The quotient of the square root of x and five b) The cube root of the product of x and y, less twelve c) The sum of the square root of sixteen and the product of four and the cube root of eight Translate into a verbal expression: d) Five times the cube root of the product of 4 and x less the square root of y e) A number y plus the cube root of a number x

2013 Suggested Practice for SOL A. 1 Students need additional practice translating expressions. Select each phrase that verbally translates this algebraic expression: One fourth times the cube root of x less five. One fourth times the cube root of x less than five. Five subtract one fourth times the cube root of x. Five less than one fourth times the cube root of x.

Express Square Roots and Cube Roots in Simplest Radical Form 2012, 2013, 2014 SOL A. 3 The student will express the square roots and cube roots of whole numbers and the square root of a monomial algebraic expression in simplest radical form.

2012 Suggested Practice for SOL A. 3 Students need additional practice simplifying square roots of monomial expressions and cube roots of whole numbers. Completely simplify: a) b) c) d)

2013 Suggested Practice for SOL A. 3 Students need additional practice simplifying the square root of a monomial algebraic expression. Write each expression in simplest radical form. a. b. c.

2014 Suggested Practice for SOL A. 3 Students need additional practice identifying expressions that are in simplest radical form. Identify each expression that is in simplest radical form.

Solving Linear and Quadratic Equations 2012, 2013, 2014 SOL A. 4 The student will solve multistep linear and quadratic equations in two variables, including a) solving literal equations (formulas) for a given variable; b) justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets; d) solving multistep linear equations algebraically and graphically; f) solving real-world problems involving equations and systems of equations. Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions.

2012 Suggested Practice for SOL A. 4 a Students need additional practice solving a literal equation for a given variable. Solve each equation: a) b)

2013 Suggested Practice for SOL A. 4 a Students need additional practice solving literal equations. The formula for the surface area (S) of a triangular prism is where h is the height of the prism, p is the perimeter of the base, and B is the area of the base. Solve the equation for the given variable: a. Solve for h: b. Solve for B:

2013 Suggested Practice for SOL A. 4 b Students need additional practice solving multi-step equations with the variable on both sides and with fractions. Students also need additional practice justifying steps in solving a linear equation. Solve for x: What property justifies the work between each step?

2014 Suggested Practice for SOL A. 4 b Students need additional practice justifying steps used to solve an equation using the axioms of equality. What property justifies the work between step 1 and step 2? a. b. c. d. Commutative property of addition Inverse property of addition Addition property of equality Associative property of addition

2013 Suggested Practice for SOL A. 4 d Students need additional practice describing solutions to equations that have the following solutions: x=0, an infinite number of real solutions, and no real solutions. Describe the solution to each equation. a. No real solutions b. x=0 c. An infinite number of real solutions

2014 Suggested Practice for SOL A. 4 d Students need additional practice determining solutions to equations that have the following solutions: x=0, an infinite number of real solutions, and no real solutions. 1. What is the solution to ? There an infinite number of real solutions. 2. What describes the solution to a. b. c. d. There is an infinite number of real solutions. There are no real solutions. The only solution is 0. The only solution is 5. ?

2014 Suggested Practice for SOL A. 4 d Students need additional practice finding solutions to equations that contain rational expressions. Find the solution to the equation shown: a. b. c. d.

2014 Suggested Practice for SOL A. 4 d Students need additional practice finding solutions to equations that require computation with positive and negative rational numbers. Find the solution to the equation shown.

2014 Suggested Practice for SOL A. 4 f Students need additional practice finding solutions to systems of equations presented in a real-world situation. James bought a total of 15 bottles of drinks for his team. • Each drink was either a bottle of water or a bottle of juice. • He spent $1. 50 on each bottle of water. • He spent $3. 00 on each bottle of juice. • James spent a total of $28. 50. How many bottles of juice did James buy?

Solving Multistep Inequalities 2012, 2013, 2014 SOL A. 5 The student will solve multistep linear inequalities in two variables, including a) solving multistep linear inequalities algebraically and graphically; b) justifying steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers and its subsets; c) solving real-world problems involving inequalities;

2012 Suggested Practice for SOL A. 5 a Students need additional practice solving multistep linear inequalities which require a sign change. Solve and graph on a number line:

2013 Suggested Practice for SOL A. 5 a Students need additional practice solving multistep inequalities. An inequality is solved as shown. Between which two steps is an error made? Explain the error. The -3 was not distributed properly to the second term.

2013 Suggested Practice for SOL A. 5 b Students need additional practice identifying properties of inequality. Given: Using the given inequality, select all that illustrate the application of the subtraction property of inequality.

Spring 2012 - 2014 Student Performance Analysis Algebra II Standards of Learning Presentation may be paused and resumed using the arrow keys or the mouse. 26

Identify Field Properties 2012, 2013 SOL AII. 3 The student will perform operations on complex numbers, express the results in simplest form using patterns of the powers of i, and identify field properties that are valid for the complex numbers.

2012 Suggested Practice for SOL AII. 3 Students need additional practice identifying the field properties that are valid for complex numbers. Identify the property used in each of the following: a) Identity Property of Multiplication b) Distributive Property c) Associative Property of Addition d) Symmetric Property e) Transitive Property

2013 Suggested Practice for SOL AII. 3 Students need additional practice identifying the field properties that are valid for complex numbers. Identify the property represented in each example. a. b. Inverse Property of Multiplication Commutative Property of Addition c. d. e. Transitive Property Distributive Property Symmetric Property

2013 Suggested Practice for SOL AII. 3 Identify the property used between each step: Step 1: Given Step 2: Distributive Property Step 3: Commutative Property of Addition Step 4: Substitution Property Step 5: Substitution Property

2014 Suggested Practice for SOL AII. 3 Students need additional practice performing operations on complex numbers involving radicals. What number is equivalent to. A B C D

2014 Suggested Practice for SOL AII. 3 Students need additional practice performing operations on complex numbers involving radicals. A B

2014 Suggested Practice for SOL AII. 3 Students need additional practice identifying the field properties that are valid for complex numbers. Identify the property that justifies each step of the simplification shown. STEPS JUSTIFICATIONS Given Expression Commutative Property of Addition Distributive Property Substitution Property Associative Property of Addition Substitution Property

2014 Suggested Practice for SOL AII. 1 b Students need additional practice simplifying and performing operations on radical expressions. Simplify the expression for positive x and y values. a) b)

2014 Suggested Practice for SOL AII. 1 c Students need additional practice writing radical expressions as expressions containing rational exponents and vice versa. a. Write an expression in radical form equivalent to b. Write an expression containing rational exponents equivalent to. .

2014 Absolute Value Equations Suggested Practice for SOL AII. 4 a Students need additional practice solving absolute value equations and inequalities algebraically and graphically. a. Find the solution to: b. Determine an ordered pair that is a solution to:

2014 Suggested Practice for SOL AII. 4 a How many values of x will satisfy the absolute value equation? a. one b. two c. zero Extension: What value(s) of x would be the solutions to the equations?

2014 Suggested Practice for SOL AII. 4 a Graph the solutions to the problems shown. a. b.

Shapes of Functions SOL AII. 6 The student will recognize the general shape of function (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and will convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions.

Analyzing Functions SOL AII. 7 The student will investigate and analyze functions algebraically and graphically. Key concepts include a) domain and range, including limited and discontinuous domains and ranges; b) zeros; c) x- and y-intercepts; d) intervals in which a function is increasing or decreasing; e) asymptotes; f)end behavior; g) inverse of a function; and h) composition of multiple functions. Graphing calculators will be used as a tool to assist in investigation of functions.