SAT II Math I : Single-Variable Algebra

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

varsity tutors app store varsity tutors android store

Example Questions

Example Question #31 : Single Variable Algebra

Solve for \(\displaystyle x\).

\(\displaystyle \frac{x}{27}=-12\)

Possible Answers:

\(\displaystyle 246\)

\(\displaystyle -234\)

\(\displaystyle 324\)

\(\displaystyle -324\)

\(\displaystyle 345\)

Correct answer:

\(\displaystyle -324\)

Explanation:

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

\(\displaystyle x=-324\)

Example Question #32 : Single Variable Algebra

Solve for \(\displaystyle x\).

\(\displaystyle \frac{x}{-32}=-11\)

Possible Answers:

\(\displaystyle 352\)

\(\displaystyle 374\)

\(\displaystyle 242\)

\(\displaystyle 252\)

\(\displaystyle 364\)

Correct answer:

\(\displaystyle 352\)

Explanation:

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

\(\displaystyle x=352\)

Example Question #33 : Single Variable Algebra

Solve for \(\displaystyle x\).

\(\displaystyle \sqrt{x+12}=13\)

Possible Answers:

\(\displaystyle 157\)

\(\displaystyle 169\)

\(\displaystyle 144\)

\(\displaystyle 1\)

\(\displaystyle 181\)

Correct answer:

\(\displaystyle 157\)

Explanation:

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

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

\(\displaystyle x=157\)

Example Question #31 : Single Variable Algebra

Solve for \(\displaystyle x\).

\(\displaystyle \sqrt{x}=\frac{1}{7}\)

Possible Answers:

\(\displaystyle \pm \frac{1}{49}\)

\(\displaystyle -\frac{1}{49}\)

\(\displaystyle 49\)

\(\displaystyle \frac{1}{7}\)

\(\displaystyle \frac{1}{49}\)

Correct answer:

\(\displaystyle \frac{1}{49}\)

Explanation:

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

\(\displaystyle x=\frac{1}{49}\)

Example Question #35 : Single Variable Algebra

Solve for \(\displaystyle x\).

\(\displaystyle x^2=361\)

Possible Answers:

\(\displaystyle 19\)

\(\displaystyle 361\)

\(\displaystyle 19\sqrt{19}\)

\(\displaystyle -19\)

\(\displaystyle \pm19\)

Correct answer:

\(\displaystyle \pm19\)

Explanation:

\(\displaystyle x^2=361\) 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.

\(\displaystyle x=\pm19\)

Example Question #32 : Single Variable Algebra

Solve for \(\displaystyle x\).

\(\displaystyle x^2=6x-5\)

Possible Answers:

\(\displaystyle -1, -5\)

\(\displaystyle 1\)

\(\displaystyle \pm1\)

\(\displaystyle 1, 5\)

\(\displaystyle 5\)

Correct answer:

\(\displaystyle 1, 5\)

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.

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

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

\(\displaystyle x=1, 5\)

 

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.

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

\(\displaystyle x=-27\)

Example Question #192 : Sat Subject Test In Math I

Solve for \(\displaystyle x\).

\(\displaystyle 3x+306=444\)

Possible Answers:

\(\displaystyle 69\)

\(\displaystyle 64\)

\(\displaystyle 52\)

\(\displaystyle 138\)

\(\displaystyle 46\)

Correct answer:

\(\displaystyle 46\)

Explanation:

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

\(\displaystyle 3x=138\) Divide \(\displaystyle 3\) on both sides.

\(\displaystyle x=46\)

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.

\(\displaystyle x=-18\)

Example Question #35 : Single Variable Algebra

Solve for \(\displaystyle x\).

\(\displaystyle 2x-173=259\)

Possible Answers:

\(\displaystyle 86\)

\(\displaystyle 216\)

\(\displaystyle 43\)

\(\displaystyle 432\)

\(\displaystyle 368\)

Correct answer:

\(\displaystyle 216\)

Explanation:

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

\(\displaystyle 2x=432\) Divide \(\displaystyle 2\) on both sides.

\(\displaystyle x=216\)

Learning Tools by Varsity Tutors