Math Alignment Document SAT-PSAT-NMSQT-PSAT10, & PSAT 8/9 (all items are property of the College Board, available for public, non-commercial use)
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HEART OF ALGEBRA: LINEAR EQUATIONS AND FUNCTIONSColor Key
StandardStandardStandardOctober 2019 PSAT/NMSQT QuestionsOctober 2019 PSAT/NMSQT Answer KeyFall 2019 PSAT 8/9 Form E QuestionsFall 2019 PSAT 8/9 Form E Answer Key2019 PSAT/NMSQT Form H Questions2019 PSAT/NMSQT Form H Answer Key2018 PSAT/NMSQT Form A Questions2018 PSAT/NMSQT Form A Answer Key2018 PSAT/NMSQT Form G Questions2018 PSAT/NMSQT Form G Answer Key2017 PSAT/NMSQT Form D2017 PSAT/NMSQT Form D Answer Key2019 Spring Form H PSAT 8/92019 Spring Form H PSAT 8/9 Answer Key2019 Spring Form F PSAT 8/92019 Spring Form F PSAT 8/9 Answer Key
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In both the SAT & PSAT 10, but not PSAT 8/9 or slightly different as noted in red fontSAT OnlyExactly the same in all three Assessments
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Content DimensionSAT Description
PSAT/NMSQT and PSAT 10 Description
PSAT 8/9 Description
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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.1. Create and use linear equations in one variable to solve problems in a variety of contexts.1. Create and use linear equations in one variable to solve problems in a variety of contexts.A.CED.A.1
7.EE.B.4
Q3 CalcQ3 Soln
Q17 No CalcQ17 SolnQ14 No CalcQ14 SolnQ3 CalcQ3 Soln
5
2. Create a linear equation in one variable, and when in context interpret solutions in terms of the context.2. Create a linear equation in one variable, and when in context interpret solutions in terms of the context.2. Create a linear equation in one variable, and when in context interpret solutions in terms of the context.7.EE.B.4.A
6.EE.B.7
Q1 No CalcQ1 SolnQ28 CalcQ28 SolnQ1 No CalcQ1 Soln
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3. Solve a linear equation in one variable, making strategic use of algebraic structure.3. Solve a linear equation in one variable, making strategic use of algebraic structure.3. Solve a linear equation in one variable, making strategic use of algebraic structure.A.REI.B.38.EE.C.7.BA.SSE.A.2Q16 CalcQ16 SolnQ7 CalcQ7 SolnQ15 Calc Q15 SolnQ15 No CalcQ15 SolnQ28 CalcQ28 SolnQ22 CalcQ22 Soln
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Q5 (No Calc)Q5 SolnQ16 CalcQ16 Soln
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4. For a linear equation in one variable,4. For a linear equation in one variable,4/4a. For a linear equation in one variable, interpret a constant, variable, factor, or term in a context.
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a. interpret a constant, variable, factor, or term in a context; a. interpret a constant, variable, factor, or term in a context;Q15 No CalcQ15 Soln
10
b. determine the conditions under which the equation has no solution, a unique solution, or infinitely many solutions. b. determine the conditions under which the equation has no solution, a unique solution, or infinitely many solutions.8.EE.C.7.AQ29 CalcQ29 SolnQ9 No CalcQ9 Soln
Q27 CalcQ27 SolnQ17 CalcQ17 SolnQ23 CalcQ23 Soln
11
Q14 No CalcQ14 Soln
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5. Fluently solve a linear equation in one variable.5. Fluently solve a linear equation in one variable.5. Fluently solve a linear equation in one variable.8.EE.C.7.B7.EE.B.4.AQ15 (No Calc)Q15 SolnQ12 No CalcQ12 SolnQ1 No CalcQ1 SolnQ7 No CalcQ7 SolnQ3 CalcQ3 SolnQ1 No CalcQ1 SolnQ2 No CalcQ2 Soln
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Q3 Calc Q3 Soln Q1 No CalcQ1 SolnQ11 No CalcQ11 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.Algebraically, 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.Algebraically, 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.1. Create and use linear functions to solve problems in a variety of contexts.1. Create and use linear functions to solve problems in a variety of contexts.F-BF.A.1
8.SP.A.3
F-IF.A.2Q14 CalcQ14 Soln
Q19 CalcQ19 Soln
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2. Create a linear function to model a relationship between two quantities.2. Create a linear function to model a relationship between two quantities.2. Create a linear function to model a relationship between two quantities.8.F.B.48.F.B.5Q14 CalcQ14 SolnQ9 No CalcQ9 SolnQ4 No CalcQ4 SolnQ4 Calc
Q4 Soln
17
Q13 No CalcQ13 Soln
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3. For a linear function that represents a context,3. For a linear function that represents a context,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. 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. 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.A
F.LE.B.5
F.IF.B.4Q12 CalcQ12 SolnQ14 CalcQ14 SolnQ4 No CalcQ4 SolnQ18 CalcQ18 Soln
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b. given an input value, find and/or interpret the output value using the given representation; b. given an input value, find and/or interpret the output value using the given representation; b. given an input value, find and/or interpret the output value using the given representation;8.F.A.1
F.IF.A.2
Q14 (No Calc)Q14 SolnQ3 No CalcQ3 SolnQ3 No CalcQ3 SolnQ3 No CalcQ3 SolnQ11 No CalcQ11 Soln
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c. given an output value, find and/or interpret the input value using the given representation, if it exists. c. given an output value, find and/or interpret the input value using the given representation, if it exists. c. given an output value, find and/or interpret the input value using the given representation, if it exists.F.IF.A.2Q13 CalcQ13 SolnQ11 CalcQ11 Soln
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4. Make connections between verbal, tabular, algebraic, and graphical representations of a linear function by4. Make connections between verbal, tabular, algebraic, and graphical representations of a linear function by4. 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; a. deriving one representation from the other; a. deriving one representation from the other;8.F.A.2F.IF.C.9Q4 Calc Q4 SolnQ2 No CalcQ2 Soln
24
Q2 (No Calc)Q2 Soln
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b. identifying features of one representation given another representation; b. identifying features of one representation given another representation; b. identifying features of one representation given another representation;8.F.A.2
F.IF.C.9
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c. determining how a graph is affected by a change to its equation. c. determining how a graph is affected by a change to its equation. 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.5. Write the rule for a linear function given two input/output pairs or one input/output pair and the rate of change.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
Q14 No CalcQ14 SolnQ6 No CalcQ6 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.A 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.A 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.1. Create and use a linear equation in two variables to solve problems in a variety of contexts.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.5Q21 CalcQ21 SolnQ2 No CalcQ2 SolnQ16 CalcQ16 SolnQ2 CalcQ2 Soln
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Q25 CalcQ25 Soln
31
2. Create a linear equation in two variables to model a constraint or condition on two quantities.2. Create a linear equation in two variables to model a constraint or condition on two quantities.2. Create a linear equation in two variables to model a constraint or condition on two quantities.A.CED.A.2
A.CED.A.3
8.EE.C.8.cQ3 (No Calc)Q3 SolnQ4 No CalcQ4 SolnQ29 CalcQ29 SolnQ16 No CalcQ16 SolnQ16 No CalcQ16 SolnQ9 CalcQ9 Soln
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3. For a linear equation in two variables that represents a context,3. For a linear equation in two variables that represents a context,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. interpret a solution, constant, variable, factor, or term based on the context, including situations where seeing structure provides an advantage; 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.7Q1 (No Calc)Q1 SolnQ4 No CalcQ4 SolnQ15 CalcQ15 SolnQ5 No CalcQ5 SolnQ17 Calc
Q17 Soln
Q3 No CalcQ3 Soln
34
Q4 CalcQ4 Soln
Q10 No Calc
Q10 Soln
35
b. given a value of one quantity in the relationship, find a value of the other, if it exists. b. given a value of one quantity in the relationship, find a value of the other, if it exists. b. given a value of one quantity in the relationship, find a value of the other, if it exists.8.SP.A.3Q23 CalcQ23 SolnQ17 No CalcQ17 Soln
36
Q 2 No CalcQ2 Soln
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4. Make connections between tabular, algebraic, and graphical representations of a linear equation in two variables by4. Make connections between tabular, algebraic, and graphical representations of a linear equation in two variables by4. 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; a. deriving one representation from the other; a. deriving one representation from the other;8.F.A.2
F.IF.C.9
Q9 CalcQ9 SolnQ23 CalcQ23 SolnQ8 No CalcQ8 SolnQ18 CalcQ18 Soln
39
b. identifying features of one representation given the other representation; b. identifying features of one representation given the other representation; b. identifying features of one representation given the other representation;8.F.B.4Q22 CalcQ22 SolnQ1 No CalcQ1 SolnQ6 No CalcQ6 SolnQ4 CalcQ4 SolnQ9 No CalcQ9 Soln
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c. determining how a graph is affected by a change to its equation. c. determining how a graph is affected by a change to its equation. 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.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.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.5Q11 No CalcQ11 SolnQ26 CalcQ26 SolnQ16 CalcQ16 SolnQ27 CalcQ27 SolnQ23 CalcQ23 SolnQ6 No CalcQ6 Soln
42
Q24 CalcQ24 SolnQ5 No CalcQ5 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.1. Create and use a system of two linear equations in two variables to solve problems in a variety of contexts.1. Create and use a system of two linear equations in two variables to solve problems in a variety of contexts.A.REI.C.6
8.EE.C.8.B
Q16 No CalcQ16 SolnQ13 No CalcQ13 Soln
44
2. Create a system of linear equations in two variables, and when in context interpret solutions in terms of the context.2. Create a system of linear equations in two variables, and when in context interpret solutions in terms of the context.2. Create a system of linear equations in two variables, and when in context interpret solutions in terms of the context.A.CED.A.3
A.REI.C.6
8.EE.C.8.cQ9 CalcQ9 Soln
45
3. Make connections between tabular, algebraic, and graphical representations of the system by deriving one representation from the other.3. Make connections between tabular, algebraic, and graphical representations of the system by deriving one representation from the other.3. Make connections between tabular, algebraic, and graphical representations of the system by deriving one representation from the other.Q8 No CalcQ8 SolnQ12 No CalcQ12 Soln
46
4. Solve a system of two linear equations in two variables, making strategic use of algebraic structure.4. Solve a system of two linear equations in two variables, making strategic use of algebraic structure.4. Solve a system of two linear equations in two variables, making strategic use of algebraic structure.A-REI.C.5Q27 CalcQ27 SolnQ 10 CalcQ10 SolnQ22 CalcQ22 SolnQ4 No Calc
Q4 Soln
Q16 CalcQ16 SolnQ8 CalcQ8 SolnQ19 CalcQ19 Soln
47
5. For a system of linear equations in two variables,5. For a system of linear equations in two variables,5/5a. For a system of linear equations in two variables, interpret a solution, constant, variable, factor, or term based on the context, including situations where seeing structure provides an advantage.Q9 No CalcQ9 SolnQ6 No CalcQ6 SolnQ18 CalcQ18 SolnQ20 CalcQ20 Soln
48
a. interpret a solution, constant, variable, factor, or term based on the context, including situations where seeing structure provides an advantage; a. interpret a solution, constant, variable, factor, or term based on the context, including situations where seeing structure provides an advantage;A.CED.A.3
A.SSE.A.1
S.ID.C.7Q19 CalcQ19 Soln
Q12 No Calc
Q12 SolnQ22 CalcQ22 Soln
49
b. determine the conditions under which the system has no solution, a unique solution, or infinitely many solutions. b. determine the conditions under which the system has no solution, a unique solution, or infinitely many solutions.8.EE.C.8.A
8.EE.C.8.B
Q16 (No Calc)Q16 SolnQ25 CalcQ25 SolnQ11 CalcQ11 Soln
50
6. Fluently solve a system of linear equations in two variables.6. Fluently solve a system of linear equations in two variables.6. Fluently solve a system of linear equations in two variables.8.EE.C.8.B
A.REI.C.6
Q7 No Calc
Q7 No Calc
Q3 No CalcQ3 SolnQ1 CalcQ1 SolnQ2 No CalcQ2 SolnQ7 No CalcQ7 SolnQ7 No CalcQ7 Soln
51
Linear inequal- ities in one or two variables1. Create and use linear inequalities in one or two variables to solve problems in a variety of contexts.1. Create and use linear inequalities in one or two variables to solve problems in a variety of contexts.1. 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.BQ17 CalcQ17 SolnQ6 CalcQ6 Soln
52
Q9 CalcQ9 Soln
53
2. Create linear inequalities in one or two variables, and when in context interpret the solutions in terms of the context.2. Create linear inequalities in one or two variables, and when in context interpret the solutions in terms of the context.2. Create linear inequalities in one or two variables, and when in context interpret the solutions in terms of the context.A.CED.A.3
A.REI.B.3
Q15 CalcQ15 SolnQ23 CalcQ23 SolnQ4 CalcQ4 Soln
54
3. For linear inequalities in one or two variables, interpret a constant, variable, factor, or term, including situations where seeing structure provides an advantage.3. For linear inequalities in one or two variables, interpret a constant, variable, factor, or term, including situations where seeing structure provides an advantage.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
55
4. Make connections between tabular, algebraic, and graphical representations of linear inequalities in one or two variables by deriving one from the other.4. Make connections between tabular, algebraic, and graphical representations of linear inequalities in one or two variables by deriving one from the other.Q11 No CalcQ11 Soln
56
5. Given a linear inequality or system of linear inequalities, interpret a point in the solution set.5. Given a linear inequality or system of linear inequalities, interpret a point in the solution set.4. Given a linear inequality, interpret a point in the solution set. (NOTE: No Systems of linear inequalities as in SAT & PSAT/NMSQT & PSAT 10)A.REI.D.12A.CED.A.3Q24 Calc Q24 Soln
57
Q4 (No Calc)Q4 Soln