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SAT II Math I : Single-Variable Algebra

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All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : Single Variable Algebra

Solve for $\displaystyle x$.

$\frac{x}{27}=-12$ $\displaystyle \frac{x}{27}=-12$

Possible Answers:

246 $\displaystyle 246$

$\displaystyle -234$

324 $\displaystyle 324$

$\displaystyle -324$

345 $\displaystyle 345$

Correct answer:

$\displaystyle -324$

Explanation:

$\frac{x}{27}=-12$ $\displaystyle \frac{x}{27}=-12$ Multiply $\displaystyle 27$ on both sides. When multiplying with a negative number, our answer is negative.

x=-324 $\displaystyle x=-324$

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Example Question #32 : Single Variable Algebra

Solve for $\displaystyle x$.

$\frac{x}{-32}=-11$ $\displaystyle \frac{x}{-32}=-11$

Possible Answers:

352 $\displaystyle 352$

374 $\displaystyle 374$

242 $\displaystyle 242$

252 $\displaystyle 252$

364 $\displaystyle 364$

Correct answer:

352 $\displaystyle 352$

Explanation:

$\frac{x}{-32}=-11$ $\displaystyle \frac{x}{-32}=-11$ Multiply $\displaystyle -32$ on both sides. When multiplying with another negative number, our answer is positive.

x=352 $\displaystyle x=352$

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Example Question #33 : Single Variable Algebra

Solve for $\displaystyle x$.

$\sqrt{x+12}=13$ $\displaystyle \sqrt{x+12}=13$

Possible Answers:

157 $\displaystyle 157$

169 $\displaystyle 169$

144 $\displaystyle 144$

$\displaystyle 1$

181 $\displaystyle 181$

Correct answer:

157 $\displaystyle 157$

Explanation:

$\sqrt{x+12}=13$ $\displaystyle \sqrt{x+12}=13$ Square both sides to get rid of the radical.

$\displaystyle x+12=169$ Subtract $\displaystyle 12$ on both sides.

x=157 $\displaystyle x=157$

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Example Question #21 : Solving Equations

Solve for $\displaystyle x$.

$\sqrt{x}=\frac{1}{7}$ $\displaystyle \sqrt{x}=\frac{1}{7}$

Possible Answers:

$\frac{1}{49}$ $\displaystyle \frac{1}{49}$

$-\frac{1}{49}$ $\displaystyle -\frac{1}{49}$

$\pm \frac{1}{49}$ $\displaystyle \pm \frac{1}{49}$

$\frac{1}{7}$ $\displaystyle \frac{1}{7}$

$\displaystyle 49$

Correct answer:

$\frac{1}{49}$ $\displaystyle \frac{1}{49}$

Explanation:

$\sqrt{x}=\frac{1}{7}$ $\displaystyle \sqrt{x}=\frac{1}{7}$ Square both sides to get rid of the radical.

$x=\frac{1}{49}$ $\displaystyle x=\frac{1}{49}$

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Example Question #35 : Single Variable Algebra

Solve for $\displaystyle x$.

x^2=361 $\displaystyle x^2=361$

Possible Answers:

$\displaystyle 19$

361 $\displaystyle 361$

$19\sqrt{19}$ $\displaystyle 19\sqrt{19}$

$\displaystyle -19$

$\pm19$ $\displaystyle \pm19$

Correct answer:

$\pm19$ $\displaystyle \pm19$

Explanation:

x^2=361 $\displaystyle x^2=361$ To get rid of the exponent, take the square root of both sides. Remember, the answer can be both positive and negative as two negative signs when multiplied gives you a positive answer.

$x=\pm19$ $\displaystyle x=\pm19$

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Example Question #32 : Single Variable Algebra

Solve for $\displaystyle x$.

$\displaystyle x^2=6x-5$

Possible Answers:

-1, -5 $\displaystyle -1, -5$

$\displaystyle 1$

$\pm1$ $\displaystyle \pm1$

1, 5 $\displaystyle 1, 5$

$\displaystyle 5$

Correct answer:

1, 5 $\displaystyle 1, 5$

Explanation:

$\displaystyle x^2=6x-5$ By inspection, we can see it's a quadratic equation since we have an exponent of $\displaystyle 2$. So let's move everything to the left so the equation equals zero.

$\displaystyle x^2-6x+5=0$ So we need to find two numbers when multiplied is $\displaystyle 5$ but at the same time having a sum of $\displaystyle -6$.

$\displaystyle (x-1)(x-5)=0$ Solve each equation individually.

x-1=0 $\displaystyle x-1=0$ Add $\displaystyle 1$ to both sides. x=1 $\displaystyle x=1$

x-5=0 $\displaystyle x-5=0$ Add $\displaystyle 5$ to both sides. x=5 $\displaystyle x=5$

x=1, 5 $\displaystyle x=1, 5$

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Example Question #37 : Single Variable Algebra

Solve for $\displaystyle x$.

$\displaystyle 2x+78=24$

Possible Answers:

$\displaystyle -27$

$\displaystyle -63$

$\displaystyle -51$

$\displaystyle 54$

$\displaystyle -102$

Correct answer:

$\displaystyle -27$

Explanation:

$\displaystyle 2x+78=24$ Subtract $\displaystyle 78$ on both sides. Since $\displaystyle 78$ is greater than $\displaystyle 24$ and is negative, our answer is negative. We treat as a subtraction problem.

2x=-54 $\displaystyle 2x=-54$ Divide $\displaystyle 2$ on both sides. When dividing with a negative number, our answer is negative.

x=-27 $\displaystyle x=-27$

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Example Question #192 : Sat Subject Test In Math I

Solve for $\displaystyle x$.

$\displaystyle 3x+306=444$

Possible Answers:

$\displaystyle 69$

$\displaystyle 64$

$\displaystyle 52$

138 $\displaystyle 138$

$\displaystyle 46$

Correct answer:

$\displaystyle 46$

Explanation:

$\displaystyle 3x+306=444$ Subtract 306 $\displaystyle 306$ on both sides.

3x=138 $\displaystyle 3x=138$ Divide $\displaystyle 3$ on both sides.

x=46 $\displaystyle x=46$

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Example Question #34 : Single Variable Algebra

Solve for $\displaystyle x$.

$\displaystyle x-36=-54$

Possible Answers:

$\displaystyle -18$

$\displaystyle -90$

$\displaystyle 18$

$\displaystyle 90$

$\displaystyle 48$

Correct answer:

$\displaystyle -18$

Explanation:

$\displaystyle x-36=-54$ Add $\displaystyle 36$ on both sides. Since $\displaystyle 54$ is greater than $\displaystyle 36$ and is negative, our answer is negative. We treat as a subtraction problem.

x=-18 $\displaystyle x=-18$

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Example Question #35 : Single Variable Algebra

Solve for $\displaystyle x$.

$\displaystyle 2x-173=259$

Possible Answers:

$\displaystyle 86$

216 $\displaystyle 216$

$\displaystyle 43$

432 $\displaystyle 432$

368 $\displaystyle 368$

Correct answer:

216 $\displaystyle 216$

Explanation:

$\displaystyle 2x-173=259$ Add 173 $\displaystyle 173$ on both sides.

2x=432 $\displaystyle 2x=432$ Divide $\displaystyle 2$ on both sides.

x=216 $\displaystyle x=216$

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All SAT II Math I Resources

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SAT II Math I : Single-Variable Algebra

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

All SAT II Math I Resources

Example Questions

Example Question #31 : Single Variable Algebra

Example Question #32 : Single Variable Algebra

Example Question #33 : Single Variable Algebra

Example Question #21 : Solving Equations

Example Question #35 : Single Variable Algebra

Example Question #32 : Single Variable Algebra

Example Question #37 : Single Variable Algebra

Example Question #192 : Sat Subject Test In Math I

Example Question #34 : Single Variable Algebra

Example Question #35 : Single Variable Algebra

All SAT II Math I Resources

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