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1 | HEART OF ALGEBRA: LINEAR EQUATIONS AND FUNCTIONS: 19 Questions (11 Calc & 8 NonCalc); 33% of Test | Standard | Standard | Standard | Problems from Released SAT Exams | Oct 2019 Form E - SAT: Items | Oct 2019 Form E:Solution with Explanation | March 2019 Form J | March 2019 Form J Solutions | May 2019 Form E | May 2019 Form E Solutions | Oct 2018 Form E | Oct 2018 Form E Solutions | |||||||||||||
2 | Linear equations in one variable | 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 | Practice Test 8-Calculator-Problem 1 Practice Test 6-No Calculator-Problem 2 Practice Test 6-Calculator-Problem 4 Practice Test 7-Calculator-Problem 3 | Calc Q21 | Q21 Soln | |||||||||||||||||||
3 | No Calc Q2 | Q2 Soln | ||||||||||||||||||||||||
4 | 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 | 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 | ||||||||||||||||||||||
5 | 3. Solve a linear equation in one variable, making strategic use of algebraic structure. | A.REI.B.3 | 8.EE.C.7.B | A.SSE.A.2 | Practice Test 6-Calculator-Problem 32 Practice Test 7-No Calculator-Problem 16 | Math Calc Q22 | Q22 Soln | Calc Q30 | Q30 Soln | Calc Q6 | Q6 Soln | Calc Q27 | Q27 Soln | |||||||||||||
6 | Calc Q4 | Q4 Soln | ||||||||||||||||||||||||
7 | 4. For a linear equation in one variable, | |||||||||||||||||||||||||
8 | a. interpret a constant, variable, factor, or term in a context; | Math Calc Q9 | Q9 Soln | |||||||||||||||||||||||
9 | b. determine the conditions under which the equation has no solution, a unique solution, or infinitely many solutions. | 8.EE.C.7.A | Math Calc Q30 | Q30 Soln | Calc Q27 | Q27 Soln | No Calc Q1 | Q1 Soln | Calc Q35 | Q35 Soln | ||||||||||||||||
10 | 5. Fluently solve a linear equation in one variable. | 8.EE.C.7.B | 7.EE.B.4.A | Practice 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 17 | Q1 No Calc | Q1 Soln | Calc Q3 | Q3 Soln | No Calc Q1 | Q1 Soln | ||||||||||||||||
11 | Q4 No Calc | Q4 Soln | Calc Q2 | Q2 Soln | ||||||||||||||||||||||
12 | Q16 No Calc | Q16 Soln | No Calc Q2 | Q2 Soln | ||||||||||||||||||||||
13 | Linear functions | 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. | ||||||||||||||||||||||||
14 | 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.2 | Practice 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 17 | Math Calc 35 | Q35 Soln | |||||||||||||||||||
15 | 2. Create a linear function to model a relationship between two quantities. | 8.F.B.4 | 8.F.B.5 | Practice Test 3-Calculator-Problem 3 Practice Test 3-Calculator-Problem 26 Practice Test 5-Calculator-Problem 7 Practice Test 6-Calculator-Problem 14 | Math Calc Q23 | Q23 Soln | ||||||||||||||||||||
16 | 3. For a linear function that represents a context, | |||||||||||||||||||||||||
17 | 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.4 | Practice Test 1-Calculator-Problem 22 Practice Test 6-Calculator-Problem 13 Practice Test 7-No Calculator-Problem 19 Practice Test 7-Calculator-Problem 32 | Calc Q10 | Q10 Soln | Calc Q8 | Q8 Soln | |||||||||||||||||
18 | b. given an input value, find and/or interpret the output value using the given representation; | 8.F.A.1 | F.IF.A.2 | Practice Test 1-Calculator-Problem 2 Practice Test 7-No Calculator-Problem 3 | Calc Q28 | Q28 Soln | Calc Q5 | Q5 Soln | ||||||||||||||||||
19 | No Calc Q4 | Q4 Soln | ||||||||||||||||||||||||
20 | c. given an output value, find and/or interpret the input value using the given representation, if it exists. | F.IF.A.2 | Practice Test 6-No Calculator-Problem 8 | Calc Q11 | Q11 Soln | |||||||||||||||||||||
21 | 4. Make connections between verbal, tabular, algebraic, and graphical representations of a linear function by | |||||||||||||||||||||||||
22 | a. deriving one representation from the other; | 8.F.A.2 | F.IF.C.9 | Practice Test 1-Calculator-Problem 16 Practice Test 5-No Calculator Problem 1 | Q12 No Calc | Q12 Soln | Calc Q19 | Q19 Soln | No Calc Q3 | Q3 Soln | ||||||||||||||||
23 | Calc Q12 | Q12 Soln | No Calc Q3 | Q3 Soln | ||||||||||||||||||||||
24 | b. identifying features of one representation given another representation; | 8.F.A.2 | F.IF.C.9 | Practice Test 1-Calculator-Problem 15 | ||||||||||||||||||||||
25 | c. determining how a graph is affected by a change to its equation. | F.BF.B.3 | ||||||||||||||||||||||||
26 | 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 25 | Q9 No Calc Math Calc Q26 | Q26 Soln | |||||||||||||||||||||
27 | Linear equations in two variables | 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. | ||||||||||||||||||||||||
28 | 1. Create and use a linear equation in two variables to solve problems in a variety of contexts. | A.CED.A.2 | 7.RP.A.2c | 8.EE.B.5 | Practice Test 8-No Calculator-Problem 2 Practice Test 8-Calculator-Problem 7 | Q16 No Calc | Q16 Soln | Calc Q37 | Q37 Soln | Calc Q1 | Q1 Soln | Calc Q23 | Q23 Soln | |||||||||||||
29 | Q1 No Calc | Q1 Soln | No Calc Q17 | Q17 Soln | ||||||||||||||||||||||
30 | No Calc Q19 | Q19 Soln | Calc Q1 | Q1 Soln | ||||||||||||||||||||||
31 | 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.c | Practice Test 7-Calculator-Problem 33 | Math Calc Q7 | Q7 Soln | Calc Q23 | Q23 Soln | |||||||||||||||||
32 | 3. For a linear equation in two variables that represents a context, | |||||||||||||||||||||||||
33 | 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.7 | Practice 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 6 | Math Calc Q33 | Q33 Soln | Calc Q29 | Q29 Soln | |||||||||||||||||
34 | No Calc Q10 | Q10 Soln | ||||||||||||||||||||||||
35 | b. given a value of one quantity in the relationship, find a value of the other, if it exists. | 8.SP.A.3 | Practice Test 8-No Calculator-Problem 19 Practice Test 6-Calculator-Problem 35 | Q2 No Calc | Q2 Soln | no Calc Q16 | Q16 Soln | |||||||||||||||||||
36 | 4. Make connections between tabular, algebraic, and graphical representations of a linear equation in two variables by | |||||||||||||||||||||||||
37 | a. deriving one representation from the other; | Q8 No Calc | Q8 Soln | Q15 No Calc | Q15 Soln | No Calc Q9 | Q9 Soln | |||||||||||||||||||
38 | b. identifying features of one representation given the other representation; | 8.F.B.4 | Practice Test 6-No Calculator-Problem 5 | |||||||||||||||||||||||
39 | c. determining how a graph is affected by a change to its equation. | F.BF.B.3 | ||||||||||||||||||||||||
40 | 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.5 | Practice Test 3-No Calculator-Problem 8 Practice Test 8-Calculator-Problem 27 Practice Test 5-Calculator-Problem 11 | Calc Q8 | Q8 Soln | Calc Q21 | Q21 Soln | |||||||||||||||||||
41 | Calc Q24 | Q24 Soln | No Calc Q10 | Q10 Soln | ||||||||||||||||||||||
42 | Calc Q36 | Q36 Soln | ||||||||||||||||||||||||
43 | Systems of two linear equations in two variables | 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 | Practice Test 3-No Calculator-Problems 6 & 9 | |||||||||||||||||||||
44 | 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.c | Practice 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 11 | Q4 No Calc | Q4 Soln | |||||||||||||||||||
45 | 3. Make connections between tabular, algebraic, and graphical representations of the system by deriving one representation from the other. | Calc Q14 | Q14 Soln | |||||||||||||||||||||||
46 | 4. Solve a system of two linear equations in two variables, making strategic use of algebraic structure. | A-REI.C.5 | Practice 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 16 | Math Calc Q24 | Q24 Soln | Q18 No Calc | Q18 Soln | |||||||||||||||||||
47 | 5. For a system of linear equations in two variables, | |||||||||||||||||||||||||
48 | 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 | 8.EE.C | A.SSE.A.1 | Practice Test 1-No Calculator-Problem 11 Practice Test 6-Calculator-Problem 11 Practice Test 7-Calculator-Problem 35 | No Calc Q19 | Q19 Soln | |||||||||||||||||||
49 | 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 | Practice Test 3-No Calculator-Problems 6 Practice Test 3-No Calculator-Problems 9 Practice Test 5-Calculator-Problem 12 | Q20 No Calc | Q20 Soln | Calc Q5 | Q5 Soln | Calc Q29 | Q29 Soln | No Calc Q15 | Q15 Soln | ||||||||||||||
50 | 6. Fluently solve a system of linear equations in two variables. | 8.EE.C.8.B | A.REI.C.6 | Practice Test 1-No Calculator-Problem 9 Practice Test 5-Calculator-Problem 12 Practice Test 7-No Calculator-Problem 3 | Q19 No Calc | Q19 Soln | No Calc Q16 | Q16 Soln | Calc Q25 | Q25 Soln | ||||||||||||||||
51 | Math Calc Q11 | Q11 Soln | ||||||||||||||||||||||||
52 | Linear inequalities in one or two variables | 1. Create and use linear inequalities in one or two variables to solve problems in a variety of contexts. | A.CED.A.1 | 6.EE.B | 7.EE.B | Practice 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 5 | Q3 No Calc | Q3 Soln | Calc Q34 | Q34 Soln | ||||||||||||||||
53 | No Calc Q4 | Q4 Soln | ||||||||||||||||||||||||
54 | 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 | Practice 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 9 | Math Calc Q21 | Q21 Soln | Calc Q35 | Q35 Soln | Calc Q31 | Q31 Soln | ||||||||||||||||
55 | 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 | ||||||||||||||||||||||||
56 | 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 | ||||||||||||||||||||||||
57 | 5. Given a linear inequality or system of linear inequalities, interpret a point in the solution set. | A.REI.D.12 | A.CED.A.3 | Practice 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 | ||||||||||||||||||||||