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HEART OF ALGEBRA: LINEAR EQUATIONS AND FUNCTIONS: 19 Questions (11 Calc & 8 NonCalc); 33% of TestStandardStandardStandardProblems from Released SAT ExamsOct 2019 Form E - SAT: ItemsOct 2019 Form E:Solution with ExplanationMarch 2019 Form JMarch 2019 Form J SolutionsMay 2019 Form EMay 2019 Form E SolutionsOct 2018 Form EOct 2018 Form E Solutions
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Linear equations in one variable1. Create and use linear equations in one variable to solve problems in a variety of contexts.A.CED.A.17.EE.B.4Practice Test 8-Calculator-Problem 1 Practice Test 6-No Calculator-Problem 2 Practice Test 6-Calculator-Problem 4 Practice Test 7-Calculator-Problem 3Calc Q21Q21 Soln
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No Calc Q2Q2 Soln
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2. Create a linear equation in one variable, and when in context interpret solutions in terms of the context.7.EE.B.4.A6.EE.B.7
Practice Test 1-Calculator-Problem 4 Practice Test 8-No Calculator-Problem 5 Practice Test 5-No Calculator-Problem 15 Practice Test 5-Calculator-Problem 33 Practice Test 5-Calculator-Problem 37
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3. Solve a linear equation in one variable, making strategic use of algebraic structure.A.REI.B.38.EE.C.7.BA.SSE.A.2Practice Test 6-Calculator-Problem 32 Practice Test 7-No Calculator-Problem 16Math Calc Q22Q22 SolnCalc Q30Q30 Soln
Calc Q6Q6 SolnCalc Q27Q27 Soln
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Calc Q4Q4 Soln
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4. For a linear equation in one variable,
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a. interpret a constant, variable, factor, or term in a context;Math Calc Q9Q9 Soln
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b. determine the conditions under which the equation has no solution, a unique solution, or infinitely many solutions.8.EE.C.7.AMath Calc Q30Q30 SolnCalc Q27Q27 SolnNo Calc Q1Q1 SolnCalc Q35Q35 Soln
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5. Fluently solve a linear equation in one variable.8.EE.C.7.B7.EE.B.4.APractice Test 3-No Calculator-Problem 17 Practice Test 8 -No Calculator-Problem 1 PRactice Test 8-calculator-Problem 32 Practice Test 5-No Calculator-Problem 17Q1 No CalcQ1 SolnCalc Q3Q3 SolnNo Calc Q1Q1 Soln
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Q4 No CalcQ4 SolnCalc Q2Q2 Soln
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Q16 No CalcQ16 SolnNo Calc Q2Q2 Soln
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Linear functionsAlgebraically, a linear function can be defined by a linear expression in one variable or by a linear equation in two variables. In the first case, the variable is the input and the value of the expression is the output. In the second case, one of the variables is designated as the input and determines a unique value of the other variable, which is the output.
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1. Create and use linear functions to solve problems in a variety of contexts.F-BF.A.18.SP.A.3F-IF.A.2Practice Test 8-No Calculator-Problem 13 Practice Test 8-No Calculator-Problem 15 Practice Test 8-Calculator-Problem 4 Practice Test 7-No Calculator-Problem 6 Practice Test 7-Calculator-Problem 17Math Calc 35Q35 Soln
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2. Create a linear function to model a relationship between two quantities.8.F.B.48.F.B.5Practice Test 3-Calculator-Problem 3 Practice Test 3-Calculator-Problem 26 Practice Test 5-Calculator-Problem 7 Practice Test 6-Calculator-Problem 14Math Calc Q23Q23 Soln
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3. For a linear function that represents a context,
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a. interpret the meaning of an input/output pair, constant, variable, factor, or term based on the context, including situations where seeing structure provides an advantage;A.SSE.A.1.AF.LE.B.5F.IF.B.4Practice Test 1-Calculator-Problem 22 Practice Test 6-Calculator-Problem 13 Practice Test 7-No Calculator-Problem 19 Practice Test 7-Calculator-Problem 32Calc Q10Q10 SolnCalc Q8Q8 Soln
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b. given an input value, find and/or interpret the output value using the given representation;8.F.A.1F.IF.A.2Practice Test 1-Calculator-Problem 2 Practice Test 7-No Calculator-Problem 3Calc Q28Q28 SolnCalc Q5Q5 Soln
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No Calc Q4Q4 Soln
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c. given an output value, find and/or interpret the input value using the given representation, if it exists.F.IF.A.2Practice Test 6-No Calculator-Problem 8Calc Q11Q11 Soln
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4. Make connections between verbal, tabular, algebraic, and graphical representations of a linear function by
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a. deriving one representation from the other;8.F.A.2F.IF.C.9Practice Test 1-Calculator-Problem 16 Practice Test 5-No Calculator Problem 1Q12 No CalcQ12 Soln
Calc Q19Q19 SolnNo Calc Q3Q3 Soln
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Calc Q12Q12 SolnNo Calc Q3Q3 Soln
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b. identifying features of one representation given another representation;8.F.A.2F.IF.C.9Practice Test 1-Calculator-Problem 15
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c. determining how a graph is affected by a change to its equation.F.BF.B.3
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5. Write the rule for a linear function given two input/output pairs or one input/output pair and the rate of change.F.LE.A.2
Practice Test 1-No Calculator-Problem 12 Practice Test 8-Calculator-Problem 25 Practice Test 5-Calculator-Problem 2 Practice Test 5-Calculator-Problem 23 Practice Test 6-Calculator-Problem 15 Practice Test 6-Calculator-Problem 25Q9 No Calc
Math Calc Q26
Q26 Soln
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Linear equations in two variablesA linear equation in two variables can be used to represent a constraint or condition on two-variable quantities in situations where neither of the variables is regarded as an input or an output. A linear equation can also be used to represent a straight line in the coordinate plane.
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1. Create and use a linear equation in two variables to solve problems in a variety of contexts.A.CED.A.27.RP.A.2c8.EE.B.5Practice Test 8-No Calculator-Problem 2 Practice Test 8-Calculator-Problem 7Q16 No CalcQ16 SolnCalc Q37Q37 SolnCalc Q1Q1 SolnCalc Q23Q23 Soln
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Q1 No CalcQ1 SolnNo Calc Q17Q17 Soln
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No Calc Q19Q19 SolnCalc Q1Q1 Soln
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2. Create a linear equation in two variables to model a constraint or condition on two quantities.A.CED.A.2A.CED.A.38.EE.C.8.c Practice Test 7-Calculator-Problem 33Math Calc Q7Q7 SolnCalc Q23Q23 Soln
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3. For a linear equation in two variables that represents a context,
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a. interpret a solution, constant, variable, factor, or term based on the context, including situations where seeing structure provides an advantage;A.CED.A.3A.SSE.A.1S.ID.C.7Practice Test 3-Calculator-Problem 20 Practice Test 3-Calculator- Problem 8 Practice Test 1-No Calculator-Problem 6 Practice Test 7-Calculator-Problem 9 Practice Test 5-Calculator-Problem Practice Test 6-No Calculator-Problem 6Math Calc Q33Q33 SolnCalc Q29Q29 Soln
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No Calc Q10Q10 Soln
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b. given a value of one quantity in the relationship, find a value of the other, if it exists.8.SP.A.3Practice Test 8-No Calculator-Problem 19 Practice Test 6-Calculator-Problem 35Q2 No CalcQ2 Solnno Calc Q16Q16 Soln
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4. Make connections between tabular, algebraic, and graphical representations of a linear equation in two variables by
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a. deriving one representation from the other;Q8 No CalcQ8 SolnQ15 No CalcQ15 SolnNo Calc Q9Q9 Soln
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b. identifying features of one representation given the other representation;8.F.B.4Practice Test 6-No Calculator-Problem 5
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c. determining how a graph is affected by a change to its equation.F.BF.B.3
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5. Write an equation for a line given two points on the line, one point and the slope of the line, or one point and a parallel or perpendicular line.G.GPE.B.5Practice Test 3-No Calculator-Problem 8 Practice Test 8-Calculator-Problem 27 Practice Test 5-Calculator-Problem 11Calc Q8Q8 SolnCalc Q21Q21 Soln
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Calc Q24Q24 SolnNo Calc Q10Q10 Soln
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Calc Q36Q36 Soln
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Systems of two linear equations in two variables1. Create and use a system of two linear equations in two variables to solve problems in a variety of contexts.A.REI.C.68.EE.C.8.BPractice Test 3-No Calculator-Problems 6 & 9
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2. Create a system of linear equations in two variables, and when in context interpret solutions in terms of the context.A.CED.A.3A.REI.C.68.EE.C.8.cPractice Test 1-Calculator-Problem 19 Practice Test 8-No Calculator-Problem 10 Practice Test 8-Calculator-Problem 6 Practice Test 5-No Calculator-Problem 18 Practice Test 5-Calculator-Problem 6 Practice Test 7-Calculator-Problem 11Q4 No CalcQ4 Soln
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3. Make connections between tabular, algebraic, and graphical representations of the system by deriving one representation from the other.Calc Q14Q14 Soln
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4. Solve a system of two linear equations in two variables, making strategic use of algebraic structure.A-REI.C.5Practice Test 1-No Calculator-Problem 18 Practice Test 3- Calculator-Problem 30 Practice Test 8-No Calculator-Problem 18 Practice Test 8-Calculator_Problem 33 Practice Test 7-Calculator-Problem 16Math Calc Q24Q24 SolnQ18 No CalcQ18 Soln
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5. For a system of linear equations in two variables,
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a. interpret a solution, constant, variable, factor, or term based on the context, including situations where seeing structure provides an advantage;A.CED.A.38.EE.CA.SSE.A.1Practice Test 1-No Calculator-Problem 11 Practice Test 6-Calculator-Problem 11 Practice Test 7-Calculator-Problem 35No Calc Q19Q19 Soln
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b. determine the conditions under which the system has no solution, a unique solution, or infinitely many solutions.8.EE.C.8.A8.EE.C.8.BPractice Test 3-No Calculator-Problems 6 Practice Test 3-No Calculator-Problems 9 Practice Test 5-Calculator-Problem 12Q20 No CalcQ20 SolnCalc Q5Q5 Soln
Calc Q29Q29 SolnNo Calc Q15Q15 Soln
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6. Fluently solve a system of linear equations in two variables.8.EE.C.8.BA.REI.C.6Practice Test 1-No Calculator-Problem 9 Practice Test 5-Calculator-Problem 12 Practice Test 7-No Calculator-Problem 3Q19 No CalcQ19 SolnNo Calc Q16Q16 SolnCalc Q25Q25 Soln
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Math Calc Q11Q11 Soln
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Linear inequalities in one or two variables1. Create and use linear inequalities in one or two variables to solve problems in a variety of contexts.A.CED.A.16.EE.B7.EE.BPractice Test 3-Calculator-Problem 31 Practice Test 8-Calculator-Problem 20 Practice Test 6-No Calculator-Problem 10 Practice Test 7-No Calculator-Problem 8 Practice Test 7-No Calculator-Problem 14 Practice Test 7-Calculator-Problem 5Q3 No CalcQ3 SolnCalc Q34Q34 Soln
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No Calc Q4Q4 Soln
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2. Create linear inequalities in one or two variables, and when in context interpret the solutions in terms of the context.A.CED.A.3A.REI.B.3Practice Test 1-Calculator-Problem 11 Practice Test 5-No Calculator-Problem 7 Practice Test 5-No Calculator-Problem 16 Practice Test 6-Calculator-Problem 18 Practice Test 7-No Calculator-Problem 9Math Calc Q21Q21 SolnCalc Q35Q35 SolnCalc Q31Q31 Soln
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3. For linear inequalities in one or two variables, interpret a constant, variable, factor, or term, including situations where seeing structure provides an advantage.6.EE.B
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4. Make connections between tabular, algebraic, and graphical representations of linear inequalities in one or two variables by deriving one from the other.Practice Test 6-Calculator-Problem 5
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5. Given a linear inequality or system of linear inequalities, interpret a point in the solution set.A.REI.D.12A.CED.A.3Practice Test 3-Calculator-Problem 36 Practice Test 1-Calculator-Problem 18 Practice Test 1-Calculator-Problem 28 Practice Test 8-No Calculator-Problem 6 Practice Test 8-Calculator-Problem 12 Practice Test 5-Calculator-Problem 13 Practice Test 6-No Calculator-Problem 14