SAT II Math I : Single-Variable Algebra

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

Example Question #33 : Solving Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Divide  on both sides. When dividing with a negative number, our answer is negative.

Example Question #34 : Solving Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Divide  on both sides. When dividing with another negative number, our answer is positive.

Example Question #35 : Solving Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Multiply both sides by . When multiplying with a positive number, our answer is negative.

Example Question #36 : Solving Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Multiply both sides by . When multiplying with a negative number, our answer is negative.

 Divide both sides by . When dividing with another negative number, our answer is positive.

Example Question #37 : Solving Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Square both sides to get rid of the radical.

 Subtract  on both sides.

Example Question #38 : Solving Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Square both sides to get rid of the radical.

 Multiply  on both sides.

Example Question #47 : Single Variable Algebra

Solve for .

Possible Answers:

Correct answer:

Explanation:

 We take the square root on both sides. We also need to consider the negative answer since two negatives multiplied together is positive.

Example Question #39 : Solving Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

 This is a quadratic equation. We can solve by factoring. We need to find teo terms that add to the b term but also multiply to get the c term.

 Solve individually.

 Add  to both sides. 

 Add  to both sides. 

Example Question #41 : Solving Equations

Solve for .

Possible Answers:



Correct answer:

Explanation:

 Take the square root on both sides. Remember to account for a negative square root.

 We will treat as two different equations.

 Subtract  on both sides. When adding another negative number, we treat as a sum and add a minus sign in the end. 

 Subtract  on both sides. Since  is greater than  and is negative, our answer is negative. We treat as a subtraction problem. 

 

Example Question #49 : Single Variable Algebra

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Let's subtract  on both sides. It will be easier to square both sides to get rid of the radical.

 This is recognition of a quadratic equation.

 We need to find two terms that multiply to the c term but add up to the b term.

 Solve individually for zero.

 Add  on both sides. 

 Add  on both sides. 

We need to check our answers.

If , then 

If , then 

Clearly,  doesn't work so our final answer is .

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