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New SAT Math - No Calculator : New SAT

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3 Diagnostic Tests 1 Practice Test Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #521 : New Sat

Solve the following inequality for $\uptext{x}$ , round your answer to the nearest tenth.

$\sqrt{x + 19} > x + 1$

Possible Answers:

3.8 < x

$-4.8 \leq x$

x = 3.8

-4.8 < x < 3.8

3.8 < x < -4.8

Correct answer:

-4.8 < x < 3.8

Explanation:

The first step is to square each side of the inequality.

$\left( \sqrt{x + 19} \right)^2> \left( x + 1 \right)^2$

Now simplify each side.

$x + 19 > x^{2} + 2 x + 1$

Now subtract the left side of the inequality to make it zero, so that we can use the quadratic formula.

$x + 19 -\left( x + 19 \right)> x^{2} + 2 x + 1 -\left( x + 19 \right)$

$0 > x^{2} + x - 18$

Now we can use the quadratic formula.

Recall the quadratic formula.

$\frac{ -b \pm \sqrt{ b ^2 -4 \cdot a \cdot c }}{ 2 \cdot a }$

Where $\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ , correspond to coefficients in the quadratic equation.

$a x^{2} + b x + c = 0$

In this case a = 1 , b = 1 , and c = -18 .

Now plug these values into the quadratic equation, and we get.

x = 3.8

x = -4.8

Now since we are dealing with an inequality, we put the least value on the left side, and the greatest value on the right. It will look like the following.

-4.8 < x < 3.8

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Example Question #1 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

Given and find A-B .

$\\A=x^2+2 \\B=4x^2-1$

Possible Answers:

-5x^2+3

-3x^2+3

-3x^2-3

3x^2-3

3x^2+3

Correct answer:

-3x^2+3

Explanation:

To find the difference of two polynomials first set up the operation and identify the like terms.

$\\A=x^2+2 \\B=4x^2-1$

A-B= (x^2+2)-(4x^2-1)

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign through to all terms in the second polynomial.

$A-B={\color{Red} x^2}{\color{Blue} +2}{\color{Red} -4x^2}{\color{Blue} --1}$

$\\x^2-4x^2=-3x^2 \\2-(-1)=3$

Therefore, the sum of these polynomials is,

-3x^2+3

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Example Question #2 : Arithmetic With Polynomials & Rational Expressions

Given and find A+B .

$\\A=x^2+2 \\B=4x^2-1$

Possible Answers:

5x^2+3

3x^2+1

3x^2-1

5x^2-1

5x^2+1

Correct answer:

5x^2+1

Explanation:

To find the sum of two polynomials first set up the operation and identify the like terms.

$\\A=x^2+2 \\B=4x^2-1$

A+B= (x^2+2)+(4x^2-1)

The like terms in these polynomials are the squared variable and the constant terms.

$A+B={\color{Red} x^2}{\color{Blue} +2}{\color{Red} +4x^2}{\color{Blue} -1}$

$\\x^2+4x^2=5x^2 \\2+(-1)=1$

Therefore, the sum of these polynomials is,

5x^2+1

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Example Question #2 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

Given and find B-A .

$\\A=x^2+2 \\B=4x^2-1$

Possible Answers:

3x^2+3

-3x^2-3

-3x^2+3

5x^2-3

3x^2-3

Correct answer:

3x^2-3

Explanation:

To find the difference of two polynomials first set up the operation and identify the like terms.

$\\A=x^2+2 \\B=4x^2-1$

B-A= (4x^2-1)-(x^2+2)

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign through to all terms in the second polynomial.

$B-A={\color{Red} 4x^2}{\color{Blue} -1}{\color{Red} -x^2}{\color{Blue} -2}$

$\\4x^2-x^2=3x^2 \\-1-2=-3$

Therefore, the sum of these polynomials is,

3x^2-3

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Example Question #3 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

Given and find A-B .

$\\A=3x^3+x+2 \\B=4x^3-2x-1$

Possible Answers:

-x^3-3x+3

x^3+3x+3

x^3+3x-3

-x^3+3x+3

-x^3-3x-3

Correct answer:

-x^3+3x+3

Explanation:

To find the difference of two polynomials first set up the operation and identify the like terms.

$\\A=3x^3+x+2 \\B=4x^3-2x-1$

A-B= (3x^3+x+2)-(4x^3-2x-1)

The like terms in these polynomials are the squared variable, the single variable, and the constant terms.

Remember to distribute the negative sign to all terms within the parentheses.

$A-B={\color{Red} 3x^3}{\color{Blue} +x}+2{\color{Red} -4x^3}{\color{Blue} +2x}+1$

$\\3x^3-4x^3=-x^3 \\x+2x=3x \\2+1=3$

Therefore, the sum of these polynomials is,

-x^3+3x+3

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Example Question #4 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

Given and find A+B .

$\\A=2x^2+2 \\B=4x^2-2$

Possible Answers:

6x^2+4

6x^2-4

6x^2

-6x^2

6x^2+2

Correct answer:

6x^2

Explanation:

To find the sum of two polynomials first set up the operation and identify the like terms.

$\\A=2x^2+2 \\B=4x^2-2$

A+B= (2x^2+2)+(4x^2-2)

The like terms in these polynomials are the squared variable and the constant terms.

$A+B={\color{Red} 2x^2}{\color{Blue} +2}{\color{Red} +4x^2}{\color{Blue} -2}$

$\\2x^2+4x^2=6x^2 \\2+(-2)=0$

Therefore, the sum of these polynomials is,

6x^2

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Example Question #5 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

Given and find A-B .

$\\A=2x^2+2 \\B=4x^2-2$

Possible Answers:

-2x^2+2

2x^2+4

-2x^2-4

-2x^2+4

2x^2-4

Correct answer:

-2x^2+4

Explanation:

To find the difference of two polynomials first set up the operation and identify the like terms.

$\\A=2x^2+2 \\B=4x^2-2$

A-B= (2x^2+2)-(4x^2-2)

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign to all terms in the second polynomial.

$A-B={\color{Red} 2x^2}{\color{Blue} +2}{\color{Red} -4x^2}{\color{Blue} +2}$

$\\2x^2-4x^2=-2x^2 \\2+2=4$

Therefore, the sum of these polynomials is,

-2x^2+4

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Example Question #7 : Arithmetic With Polynomials & Rational Expressions

Given and find B-A .

$\\A=2x^2+2 \\B=4x^2-2$

Possible Answers:

-2x^2+4

2x^2-4

2x^2+4

-2x^2-4

2x^2

Correct answer:

2x^2-4

Explanation:

To find the difference of two polynomials first set up the operation and identify the like terms.

$\\A=2x^2+2 \\B=4x^2-2$

B-A= (4x^2-2)-(2x^2+2)

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign to all terms in the second polynomial.

$B-A= {\color{Red} 4x^2}-2{\color{Red} -2x^2}-2$

$\\4x^2-2x^2=2x^2 \\-2-2=-4$

Therefore, the sum of these polynomials is,

2x^2-4

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Example Question #6 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

Given and find A+B .

$\\A=x^2 \\B=4x^2-1$

Possible Answers:

5x^2+1

-5x^2-1

-5x^2+1

5x^2

5x^2-1

Correct answer:

5x^2-1

Explanation:

To find the sum of two polynomials first set up the operation and identify the like terms.

$\\A=x^2 \\B=4x^2-1$

A+B= (x^2)+(4x^2-1)

The like terms in these polynomials are the squared variable.

$A+B={\color{Red} x^2}{\color{Red} +4x^2}-1$

$\\x^2+4x^2=5x^2 \\0+(-1)=-1$

Therefore, the sum of these polynomials is,

5x^2-1

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Example Question #7 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

Given and find .

$\\A=x^2+1 \\B=4x^2-1$

Possible Answers:

4x^4+3x^2+1

-4x^4+3x^2-1

4x^4+3x^2-1

4x^4-3x^2-1

-4x^4-3x^2-1

Correct answer:

4x^4+3x^2-1

Explanation:

To find the product of two polynomials first set up the operation.

$\\A=x^2+1 \\B=4x^2-1$

AB=(x^2+1)(4x^2-1)

Now, multiply each term from the first polynomial with each term in the second polynomial.

Remember the rules of exponents. When like base variables are multiplied together their exponents are added together.

$\\x^2\cdot 4x^2=4x^{2+2}=4x^4 \\x^2\cdot -1=-x^2 \\1\cdot 4x^2=4x^2 \\1\cdot -1=-1$

Therefore, the product of these polynomials is,

4x^4-x^2+4x^2-1

Combine like terms to arrive at the final answer.

4x^4+3x^2-1

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New SAT Math - No Calculator : New SAT

Study concepts, example questions & explanations for New SAT Math - No Calculator

All New SAT Math - No Calculator Resources

Example Questions

Example Question #521 : New Sat

Example Question #1 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

Example Question #2 : Arithmetic With Polynomials & Rational Expressions

Example Question #2 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

Example Question #3 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

Example Question #4 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

Example Question #5 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

Example Question #7 : Arithmetic With Polynomials & Rational Expressions

Example Question #6 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

Example Question #7 : Polynomials: Ccss.Math.Content.Hsa Apr.A.1

All New SAT Math - No Calculator Resources

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