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New SAT Writing and Language : New SAT

Study concepts, example questions & explanations for New SAT Writing and Language

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3 Diagnostic Tests 39 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : How To Factor A Common Factor Out Of Squares

Simplify the radical expression.

$\sqrt[3]{-64x^{6}y^{12}}$

Possible Answers:

$-4x^{2}y^{4}$

4ix^2y^4

-2x^3y^4

2ix^3y^4

Correct answer:

$-4x^{2}y^{4}$

Explanation:

$\sqrt[3]{-64x^{6}y^{12}}$

Look for perfect cubes within each term. This will allow us to factor out of the radical.

$\sqrt[3]{-64}*\sqrt[3]{x^6}*\sqrt[3]{y^{12}}$

$\sqrt[3]{-4*-4*-4}*\sqrt[3]{x^2*x^2*x^2}*\sqrt[3]{y^4*y^4*y^4}$

Simplify.

$-4x^{2}y^4$

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Example Question #133 : Exponential Operations

Simplify:

$\frac{\left ( 5 st^{2} \right )^{3}}{s^{4} \cdot 50 t}$

Possible Answers:

$\frac{ 5 t^{4} }{2s }$

$\frac{ 3 t^{5} }{10s }$

None of the other responses gives a correct answer.

$\frac{ 5 t^{5} }{2s }$

$\frac{ 3 t^{4} }{10s }$

Correct answer:

$\frac{ 5 t^{5} }{2s }$

Explanation:

$\frac{\left ( 5 st^{2} \right )^{3}}{s^{4} \cdot 50 t}$

$=\frac{5^{3} s^{3}\left ( t^{2} \right )^{3}}{50 s^{4} t}$

$=\frac{125 s^{3}\cdot t^{2 \cdot 3} }{50 s^{4} t}$

$=\frac{125 s^{3} t^{6} }{50 s^{4} t}$

$=\frac{125 }{50 } \cdot \frac{s^{3} t^{6} }{s^{4} t}$

$=\frac{5 }{2 } \cdot \frac{ t^{6-1} }{s^{4-3} }$

$=\frac{5 }{2 } \cdot \frac{ t^{5} }{s^{1} }$

$= \frac{ 5 t^{5} }{2s }$

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Example Question #2 : How To Find The Solution To A Quadratic Equation

What is the sum of all the values of that satisfy:

3x^2-5x=2x+6

Possible Answers:

$\frac{14}{15}$

$\frac{2}{3}$

$\frac{7}{3}$

Correct answer:

$\frac{7}{3}$

Explanation:

With quadratic equations, always begin by getting it into standard form:

Ax^2+Bx+C=0

Therefore, take our equation:

3x^2-5x=2x+6

And rewrite it as:

3x^2-7x-6=0

You could use the quadratic formula to solve this problem. However, it is possible to factor this if you are careful. Factored, the equation can be rewritten as:

(3x+2)(x-3)=0

Now, either one of the groups on the left could be and the whole equation would be . Therefore, you set up each as a separate equation and solve for :

3x+2=0

3x=-2

$x=\frac{-2}{3}$

x-3=0

x=3

The sum of these values is:

$3+(-\frac{2}{3})=3-\frac{2}{3}=\frac{9}{3}-\frac{2}{3}=\frac{7}{3}$

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Example Question #1 : New Sat Math No Calculator

Solve the system of equations.

4x+6y=2

y=2x

Possible Answers:

$(\frac{1}{8}, \frac{1}{4})$

$(4,\frac{1}{4})$

$(\frac{2}{9}, \frac{1}{9})$

$(\frac{1}{8}, 4)$

Correct answer:

$(\frac{1}{8}, \frac{1}{4})$

Explanation:

4x+6y=2

y=2x

For this system, it will be easiest to solve by substitution. The variable is already isolated in the second equation. We can replace in the first equation with , since these two values are equal.

4x+6y=2

4x+6(2x)=2

Now we can solve for .

4x+12x=2

16x=2

$x=\frac{2}{16}=\frac{1}{8}$

Now that we know the value of , we can solve for by using our original second equation.

$y=2x\ \text{and}\ x=\frac{1}{8}$

$y=2(\frac{1}{8})$

$y=\frac{2}{8}=\frac{1}{4}$

The final answer will be the ordered pair $(\frac{1}{8}, \frac{1}{4})$ .

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Example Question #1 : How To Multiply Polynomials

Find the product:

( x^4-5x+7)(x^4+2x+1)

Possible Answers:

x^8-3x^5+8x^4-10x^2+9x+7

x^8+7x^4-10x^2

x^4+8x^2+10x-9

x^7+9x^4-10x^2+8

x^6+5x^5+3x^4+x^2

Correct answer:

x^8-3x^5+8x^4-10x^2+9x+7

Explanation:

Find the product:

( x^4-5x+7)(x^4+2x+1)

Step 1: Use the distributive property.

x^4(x^4+2x+1)-5x(x^4+2x+1)+7(x^4+2x+1)

x^8+2x^5+x^4-5x^5-10x^2-5x+7x^4+14x+7

Step 2: Combine like terms.

x^8+2x^5-5x^5+x^4+7x^4-10x^2-5x+14x+7

x^8-3x^5+8x^4-10x^2+9x+7

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Example Question #1 : How To Add Complex Numbers

Add $5 + i \sqrt {5 }$ and its complex conjugate.

Possible Answers:

$2 i \sqrt{5}$

$-2 i \sqrt{5}$

Correct answer:

Explanation:

The complex conjugate of a complex number a+ bi is a - bi . Therefore, the complex conjugate of $5 + i \sqrt {5 }$ is $5 - i \sqrt {5 }$ ; add them by adding real parts and adding imaginary parts, as follows:

$(5 + i \sqrt {5 } )+( 5 - i \sqrt {5 })$

$= 5 + 5 + i \sqrt {5 } - i \sqrt {5 }$

= 10 ,

the correct response.

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Example Question #2 : New Sat Math No Calculator

The width of a rectangle is a+b . The length of the rectangle is . What must be the area?

Possible Answers:

ac+bc

ac+b

a+bc

abc

a+b+c

Correct answer:

ac+bc

Explanation:

The area of a rectangle is:

$A=\textup{Length}\times \textup{ Width}$

Substitute the variables into the formula.

A=(a+b)(c) = ac+bc

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Example Question #1 : How To Find The Area Of A Rectangle

George wants to paint the walls in his room blue. The ceilings are 10 ft tall and a carpet 12 ft by 15 ft covers the floor. One gallon of paint covers 400 $ft^{2}$ and costs $40. One quart of paint covers 100 $ft^{2}$ and costs $15. How much money will he spend on the blue paint?

Possible Answers:

$\$80$

$\$70$

$\$55$

$\$30$

$\$40$

Correct answer:

$\$70$

Explanation:

The area of the walls is given by $A = 2wh + 2lh = 2(12)(10) + 2(15)(10) = 540 ft^{2}$

One gallon of paint covers 400 $ft^{2}$ and the remaining 140 $ft^{2}$ would be covered by two quarts.

So one gallon and two quarts of paint would cost $\$40 + \$15 + \$15 = \$70$

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Example Question #1 : How To Use Foil

Find the product in terms of :

(3x-4)(9x+13)

Possible Answers:

27x^2-52x+3

27x^2-3x-52

27x^2+3x+52

3x^2+27x-52

27x^2+3x-52

Correct answer:

27x^2+3x-52

Explanation:

This question can be solved using the FOIL method. So the first terms are multiplied together:

(3x)(9x)

This gives:

27x^2

The x-squared is due to the x times x.

The outer terms are then multipled together and added to the value above.

(3x)13=39x

The inner two terms are multipled together to give the next term of the expression.

(-4)(9x)=-36x

Finally the last terms are multiplied together.

(-4)(13)=-52

All of the above terms are added together to give:

27x^2+39x-36x-52

Combining like terms gives

27x^2+3x-52 .

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Example Question #1 : How To Find An Angle In A Quadrilateral

If a polygon has 10 sides, what is the measure of each exterior angle?

Possible Answers:

$3.6^{\circ}$

$36^{\circ}$

$72^{\circ}$

$360^{\circ}$

$63^{\circ}$

Correct answer:

$36^{\circ}$

Explanation:

In order to figure this out, we need to remember the formula for finding exterior angles. $\frac{360^{\circ}}{n}$ , where is the number of sides of a polygon. Now we simply do the following calculation.

$\frac{360^{\circ}}{10}=36^{\circ}$

So the measure of each exterior angle is $36^{\circ}$ .

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New SAT Writing and Language : New SAT

Study concepts, example questions & explanations for New SAT Writing and Language

All New SAT Writing and Language Resources

Example Questions

Example Question #3 : How To Factor A Common Factor Out Of Squares

Example Question #133 : Exponential Operations

Example Question #2 : How To Find The Solution To A Quadratic Equation

Example Question #1 : New Sat Math No Calculator

Example Question #1 : How To Multiply Polynomials

Example Question #1 : How To Add Complex Numbers

Example Question #2 : New Sat Math No Calculator

Example Question #1 : How To Find The Area Of A Rectangle

Example Question #1 : How To Use Foil

Example Question #1 : How To Find An Angle In A Quadrilateral

All New SAT Writing and Language Resources

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