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SAT Math : Simplifying Expressions

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Example Questions

Example Question #1001 : Algebra

$a=\frac{x^2-y^2}{x-y}$

If both and are positive, what is the simplest form of ?

Possible Answers:

$x-y$

$1$

$x+y$

$xy$

$x^2-y^2-1$

Correct answer:

$x+y$

Explanation:

$x^2-y^2$ can also be expressed as $(x-y)(x+y))$

$a=\frac{(x-y)(x+y)}{x-y}=x+y$

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Example Question #1002 : Algebra

Which of the following does not simplify to ?

Possible Answers:

All of these simplify to

5x-(6x-2x)

(3-3)x

(x - 1)(x + 2) - x^2 + 2

$\frac{x(4x)}{4x}$

Correct answer:

(3-3)x

Explanation:

5x – (6x – 2x) = 5x – (4x) = x

(x – 1)(x + 2) - x² + 2 = x² + x – 2 – x² + 2 = x

x(4x)/(4x) = x

(3 – 3)x = 0x = 0

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Example Question #31 : Simplifying Expressions

Edward is years old. He is 5 years younger than his sister Francine. In terms of , how old will Francine be in 2 years?

Possible Answers:

e+3

e-7

e+7

e+4

e-3

Correct answer:

e+7

Explanation:

Let f = Francine's age now.

e = f – 5

f = e + 5

In 2 years, Francine will be f + 2. Use our previous calculation to substitute.

f + 2 = (e + 5) + 2 = e + 7

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Example Question #1 : Simplifying Expressions

a # b = (a * b) + a

What is 3 # (4 # 1)?

Possible Answers:

Correct answer:

Explanation:

Work from the "inside" outward. Therefore, first solve 4 # 1 by replacing a with 4 and b with 1:

4 # 1 = (4 * 1) + 4 = 4 + 4 = 8

That means: 3 # (4 # 1) = 3 # 8. Solve this now:

3 # 8 = (3 * 8) + 3 = 24 + 3 = 27

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Example Question #1 : How To Simplify An Expression

Simplify the result of the following steps, to be completed in order:

1. Add 7x to 3y

2. Multiply the sum by 4

3. Add x to the product

4. Subtract x – y from the sum

Possible Answers:

28x + 12y

28x + 11y

29x + 13y

28x – 13y

28x + 13y

Correct answer:

28x + 13y

Explanation:

Step 1: 7x + 3y

Step 2: 4 * (7x + 3y) = 28x + 12y

Step 3: 28x + 12y + x = 29x + 12y

Step 4: 29x + 12y – (x – y) = 29x + 12y – x + y = 28x + 13y

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Example Question #797 : Algebra

Which is the greater quantity: the median of 5 positive sequential integers or the mean of 5 positive sequential integers?

Possible Answers:

The quantities are equal

The relationship cannot be determined

The median is greater

The mean is greater

Correct answer:

The quantities are equal

Explanation:

If the first integer is $\dpi{100} \small n$ , then $\dpi{100} \small n+(n+1)+(n+2)+(n+3)+(n+4)=5n+10$

$\dpi{100} \small \frac{5n+10}{5}=n+2$

This is the same as the median.

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Example Question #798 : Algebra

You are told that $\dpi{100} \small x$ can be determined from the expression:

Capture7

Determine whether the absolute value of $\dpi{100} \small x$ is greater than or less than 2.

Possible Answers:

$\dpi{100} \small |x|>2$

$\dpi{100} \small |x|<2$

The relationship cannot be determined from the information given.

The quantities are equal

Correct answer:

$\dpi{100} \small |x|>2$

Explanation:

The expression is simplified as follows:

Capture8

Since $\dpi{100} \small 2^{4}=16$ the value of $\dpi{100} \small x$ must be slightly greater for it to be 17 when raised to the 4th power.

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Example Question #32 : Simplifying Expressions

Which best describes the relationship between (x+y)^3 and x^3+y^3 if $x,y\neq 0$ ?

Possible Answers:

$\small (x+y)^{3}=x^{3}+y^{3}$

(x+y)^3< x^3 + y^3

$\small (x+y)^{3}>x^{3}+y^{3}$

The relationship cannot be determined from the information given.

Correct answer:

The relationship cannot be determined from the information given.

Explanation:

Use substitution to determine the relationship.

For example, we could plug in x=2 and y=3 .

(x+y)^3=(2+3)^3=5^3=125

x^3+y^3=2^3+3^3=4+9=13

So far it looks like the first expression is greater, but it's a good idea to try other values of x and y to be sure. This time, we'll try some negative values, say, x=-4 and y=-3 .

(x+y)^3=(-4+-3)^3=-7^3=-343

x^3+y^3=-4^3+-3^3=-64+-27=-91

This time the first quantity is smaller. Therefore the relationship cannot be determined from the information given.

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Example Question #5 : Simplifying Expressions

If x + y = 5 and 3x - y + z = 3 , then 12x + 3z = ?

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

We have three variables and only two equations, so we will not be able to solve for each independent variable. We need to think of another solution.

Notice what happens if we line up the two equations and add them together.

(x + y) + (3x – y + z) = 4x + z

and 5 + 3 = 8

Lets take this equation and multiply the whole thing by 3:

3(4x + z = 8)

Thus, 12x + 3z = 24.

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Example Question #38 : How To Simplify An Expression

$x^{2} = y$

m + 3 = x

3n = m

Express in terms of . You may assume to be positive.

Possible Answers:

$n = \frac{ \sqrt{y}+3}{3}$

$n = \frac{ \sqrt{y}-3}{3}$

$n = 3 \sqrt{y} + 9$

$n = 3 \sqrt{y} - 1$

$n = 3 \sqrt{y} - 9$

Correct answer:

$n = \frac{ \sqrt{y}-3}{3}$

Explanation:

3n = m

$3n \div 3 = m \div 3$

$n = \frac{m}{3}$

m + 3 = x

m + 3 - 3= x - 3

m = x-3

$x^{2} = y$

$x = \sqrt{y}$ - we throw out the other possible value, $x = -\sqrt{y}$ , since we assume positive.

By substituting:

$n = \frac{m}{3}$

$n = \frac{x-3}{3}$

$n = \frac{ \sqrt{y}-3}{3}$

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SAT Math : Simplifying Expressions

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1001 : Algebra

Example Question #1002 : Algebra

Example Question #31 : Simplifying Expressions

Example Question #1 : Simplifying Expressions

Example Question #1 : How To Simplify An Expression

Example Question #797 : Algebra

Example Question #798 : Algebra

Example Question #32 : Simplifying Expressions

Example Question #5 : Simplifying Expressions

Example Question #38 : How To Simplify An Expression

All SAT Math Resources

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