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SAT II Math II : SAT Subject Test in Math II

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

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All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Simplifying Expressions

Simplify the expression: $\displaystyle 6(2x-3)-2(-x-3)$

Possible Answers:

10x-9 $\displaystyle 10x-9$

14x-12 $\displaystyle 14x-12$

14x-24 $\displaystyle 14x-24$

10x+9 $\displaystyle 10x+9$

12x-12 $\displaystyle 12x-12$

Correct answer:

14x-12 $\displaystyle 14x-12$

Explanation:

Distribute the integers through the binomials.

$\displaystyle 12x-18 +2x+6$

Combine like-terms.

The answer is: 14x-12 $\displaystyle 14x-12$

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Example Question #3 : Simplifying Expressions

Simplify $\displaystyle x - 5 - (2 - x)$ .

Possible Answers:

$\displaystyle -3$

$\displaystyle 0$

2x - 7 $\displaystyle 2x - 7$

x^2 - 7 $\displaystyle x^2 - 7$

x+3 $\displaystyle x+3$

Correct answer:

2x - 7 $\displaystyle 2x - 7$

Explanation:

We can start by distributing the negative sign in the parentheses term:

$\displaystyle x - 5 - 2 + x$

Now we can combine like terms. The constants go together, and the variables go together:

2x - 7 $\displaystyle 2x - 7$

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Example Question #3 : Simplifying Expressions

Simplify $\displaystyle -(x + y) + 4x + 2y$ .

Possible Answers:

3x + y $\displaystyle 3x + y$

3x-y $\displaystyle 3x-y$

3xy $\displaystyle 3xy$

3(x+y) $\displaystyle 3(x+y)$

5x+3y $\displaystyle 5x+3y$

Correct answer:

3x + y $\displaystyle 3x + y$

Explanation:

First, we can distribute the negative sign through the parentheses term:

$\displaystyle -x - y + 4x + 2y$

Now we gather like terms. Remember, you can't gather different variables together. The $\displaystyle x$ 's and $\displaystyle y$ 's will still be separate terms:

3x + y $\displaystyle 3x + y$

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Example Question #4 : Simplifying Expressions

Simplify $\displaystyle -(x + 2y + 3) - 3x + y$ .

Possible Answers:

$\displaystyle 4x +y +3$

$\displaystyle 2x +3y +3$

$\displaystyle -3x^2 -2y^2 - 3$

$\displaystyle 2x +3y -3$

$\displaystyle -4x - y - 3$

Correct answer:

$\displaystyle -4x - y - 3$

Explanation:

Start by distributing the negative sign through the parentheses term:

$\displaystyle -x - 2y - 3 - 3x + y$

Now combine like terms. Each variable can't be combined with different variables:

$\displaystyle -4x - y - 3$

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Example Question #5 : Simplifying Expressions

Simplify $(\sqrt{x^2})^2$ $\displaystyle (\sqrt{x^2})^2$

Possible Answers:

$\sqrt{x^3}$ $\displaystyle \sqrt{x^3}$

$x^{\frac{1}{4}}$ $\displaystyle x^{\frac{1}{4}}$

$\sqrt{x^4}$ $\displaystyle \sqrt{x^4}$

$\displaystyle x$

x^2 $\displaystyle x^2$

Correct answer:

x^2 $\displaystyle x^2$

Explanation:

A square root is the inverse of squaring a term, so they cancel each other out:

$(\sqrt{x^2})^2=x^2$ $\displaystyle (\sqrt{x^2})^2=x^2$

From there, there's nothing left to simplify.

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Example Question #11 : Simplifying Expressions

Simplify $\sqrt{x^{11}}$ $\displaystyle \sqrt{x^{11}}$ .

Possible Answers:

$(\sqrt{x})^5$ $\displaystyle (\sqrt{x})^5$

$x^5 \cdot \sqrt{x}$ $\displaystyle x^5 \cdot \sqrt{x}$

$\sqrt[5]{x}$ $\displaystyle \sqrt[5]{x}$

$x^{11}$ $\displaystyle x^{11}$

$5\sqrt{x}$ $\displaystyle 5\sqrt{x}$

Correct answer:

$x^5 \cdot \sqrt{x}$ $\displaystyle x^5 \cdot \sqrt{x}$

Explanation:

To begin, let's rewrite the equation so the square root is a fraction in the exponent:

$x^{\frac{11}{2}}$ $\displaystyle x^{\frac{11}{2}}$

From here, we can simplify the exponent:

$x^5 \cdot x^{\frac{1}{2}}$ $\displaystyle x^5 \cdot x^{\frac{1}{2}}$

Now we change the exponent fraction back into a square root:

$x^5 \cdot \sqrt{x}$ $\displaystyle x^5 \cdot \sqrt{x}$

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Example Question #201 : Sat Subject Test In Math Ii

Simplify $(\sqrt{4x^2})\cdot (\sqrt{25x})^2$ $\displaystyle (\sqrt{4x^2})\cdot (\sqrt{25x})^2$ .

Possible Answers:

$5 \sqrt{2x}$ $\displaystyle 5 \sqrt{2x}$

50x^2 $\displaystyle 50x^2$

50x^3 $\displaystyle 50x^3$

25x +2x $\displaystyle 25x +2x$

100x^2 $\displaystyle 100x^2$

Correct answer:

50x^2 $\displaystyle 50x^2$

Explanation:

For the first square root, each term inside has a natural solution. We can take the square root of each term individually because they are multiplied, and then combine them again:

$2x \cdot (\sqrt{25x})^2$ $\displaystyle 2x \cdot (\sqrt{25x})^2$

For the second square root, we remember that the square root and a square cancel each other out, and we're left with just the term inside:

$2x \cdot 25x$ $\displaystyle 2x \cdot 25x$

We finish by multiplying the terms together:

50x^2 $\displaystyle 50x^2$

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Example Question #202 : Sat Subject Test In Math Ii

Simplify $\displaystyle 2x^2 -5x(1 - 8x)$ .

Possible Answers:

-11x^2 $\displaystyle -11x^2$

$\displaystyle -38x^2 -5x$

$\displaystyle 42x^2 -5x$

$\displaystyle 2x^2-13x-1$

$\displaystyle 2x^2-13x$

Correct answer:

$\displaystyle 42x^2 -5x$

Explanation:

We start by distributing the -5x $\displaystyle -5x$ term through the parentheses:

$\displaystyle 2x^2 -5x + 40x^2$

Now we combine like terms. Remember, we can't add variables if they have different exponent terms:

$\displaystyle 42x^2 -5x$

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Example Question #203 : Sat Subject Test In Math Ii

Simplify $\displaystyle 2x^2+7x(-8x- 10)$ .

Possible Answers:

$\displaystyle 2x^2 -14x$

-124x^3 $\displaystyle -124x^3$

$\displaystyle 2x^2 -x-10$

$\displaystyle -54x^2- 70x$

$\displaystyle 56x^2 - 70x$

Correct answer:

$\displaystyle -54x^2- 70x$

Explanation:

Start by distributing the $\displaystyle 7x$ term:

$\displaystyle 2x^2-56x^2- 70x$

Now combine like terms. Remember, if a variable has a different exponent, you can't add them:

$\displaystyle -54x^2- 70x$

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Example Question #204 : Sat Subject Test In Math Ii

Simplify $\displaystyle -10x(9x+ 4) - 5x^2$ .

Possible Answers:

$\displaystyle 85x^2 +40x$

-135x^3 $\displaystyle -135x^3$

$\displaystyle 95x^2+40x$

$\displaystyle -95x^2- 40x$

$\displaystyle -90x^2 -45x$

Correct answer:

$\displaystyle -95x^2- 40x$

Explanation:

Start by distributing the -10x $\displaystyle -10x$ term:

$\displaystyle -90x^2- 40x - 5x^2$

Now collect like terms. Remember, you can't add or subtract variables that have different exponents:

$\displaystyle -95x^2- 40x$

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All SAT II Math II Resources

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SAT II Math II : SAT Subject Test in Math II

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

All SAT II Math II Resources

Example Questions

Example Question #2 : Simplifying Expressions

Example Question #3 : Simplifying Expressions

Example Question #3 : Simplifying Expressions

Example Question #4 : Simplifying Expressions

Example Question #5 : Simplifying Expressions

Example Question #11 : Simplifying Expressions

Example Question #201 : Sat Subject Test In Math Ii

Example Question #202 : Sat Subject Test In Math Ii

Example Question #203 : Sat Subject Test In Math Ii

Example Question #204 : Sat Subject Test In Math Ii

All SAT II Math II Resources

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