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New SAT Math - No Calculator : New SAT

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

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All New SAT Math - No Calculator Resources

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

Example Questions

Example Question #11 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

If a rectangle possesses a width of $4\textup{ inches}$ and has a perimeter of $20\textup{ inches}$ , then what is the length?

Possible Answers:

$7\textup{ inches}$

$8\textup{ inches}$

$6\textup{ inches}$

$9\textup{ inches}$

$5\textup{ inches}$

Correct answer:

$6\textup{ inches}$

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

P=2l+2w

We can substitute in our known values and solve for our unknown variable (i.e. length):

20=2l+2(4)

20=2l+8

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

$\frac{\begin{array}[b]{r}20=2l+8\\ -8\ \ \ \ \ \ -8\end{array}}{\\\\12=2l}$

Next, we can divide each side by

$\frac{\begin{array}[b]{r}\frac{12}{2}=\frac{2l}{2}\\\end{array}}{6=l}$

The length of the rectangle is $6\textup{ inches}$

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Example Question #501 : New Sat

If a rectangle possesses a width of $3\textup{ inches}$ and has a perimeter of $16\textup{ inches}$ , then what is the length?

Possible Answers:

$7\textup{ inches}$

$6\textup{ inches}$

$3\textup{ inches}$

$4\textup{ inches}$

$5\textup{ inches}$

Correct answer:

$5\textup{ inches}$

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

P=2l+2w

We can substitute in our known values and solve for our unknown variable (i.e. length):

16=2l+2(3)

16=2l+6

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

$\frac{\begin{array}[b]{r}16=2l+6\\ -6\ \ \ \ \ \ -6\end{array}}{\\\\10=2l}$

Next, we can divide each side by

$\frac{\begin{array}[b]{r}\frac{10}{2}=\frac{2l}{2}\\\end{array}}{5=l}$

The length of the rectangle is $5\textup{ inches}$

Report an Error

Example Question #71 : Expressions & Equations

If a rectangle possesses a width of $20\textup{ inches}$ and has a perimeter of $60\textup{ inches}$ , then what is the length?

Possible Answers:

$10\textup{ inches}$

$8\textup{ inches}$

$9\textup{ inches}$

$7\textup{ inches}$

$11\textup{ inches}$

Correct answer:

$10\textup{ inches}$

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

P=2l+2w

We can substitute in our known values and solve for our unknown variable (i.e. length):

60=2l+2(20)

60=2l+40

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

$\frac{\begin{array}[b]{r}60=2l+40\\ -40\ \ \ \ \ \ -40\end{array}}{\\\\20=2l}$

Next, we can divide each side by

$\frac{\begin{array}[b]{r}\frac{20}{2}=\frac{2l}{2}\\\end{array}}{10=l}$

The length of the rectangle is $10\textup{ inches}$

Report an Error

Example Question #504 : New Sat

If a rectangle possesses a width of $13\textup{ inches}$ and has a perimeter of $42\textup{ inches}$ , then what is the length?

Possible Answers:

$6\textup{ inches}$

$10\textup{ inches}$

$7\textup{ inches}$

$8\textup{ inches}$

$9\textup{ inches}$

Correct answer:

$8\textup{ inches}$

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

P=2l+2w

We can substitute in our known values and solve for our unknown variable (i.e. length):

42=2l+2(13)

42=2l+26

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

$\frac{\begin{array}[b]{r}42=2l+26\\ -26\ \ \ \ \ \ -26\end{array}}{\\\\16=2l}$

Next, we can divide each side by

$\frac{\begin{array}[b]{r}\frac{16}{2}=\frac{2l}{2}\\\end{array}}{8=l}$

The length of the rectangle is $8\textup{ inches}$

Report an Error

Example Question #111 : New Sat Math Calculator

If a rectangle possesses a width of $16\textup{ inches}$ and has a perimeter of $56\textup{ inches}$ , then what is the length?

Possible Answers:

$11\textup{ inches}$

$12\textup{ inches}$

$13\textup{ inches}$

$10\textup{ inches}$

$9\textup{ inches}$

Correct answer:

$12\textup{ inches}$

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

P=2l+2w

We can substitute in our known values and solve for our unknown variable (i.e. length):

56=2l+2(16)

56=2l+32

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

$\frac{\begin{array}[b]{r}56=2l+32\\ -32\ \ \ \ \ \ -32\end{array}}{\\\\24=2l}$

Next, we can divide each side by

$\frac{\begin{array}[b]{r}\frac{24}{2}=\frac{2l}{2}\\\end{array}}{12=l}$

The length of the rectangle is $12\textup{ inches}$

Report an Error

Example Question #71 : Expressions & Equations

If a rectangle possesses a width of $14\textup{ inches}$ and has a perimeter of $68\textup{ inches}$ , then what is the length?

Possible Answers:

$19\textup{ inches}$

$20\textup{ inches}$

$17\textup{ inches}$

$16\textup{ inches}$

$18\textup{ inches}$

Correct answer:

$20\textup{ inches}$

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

P=2l+2w

We can substitute in our known values and solve for our unknown variable (i.e. length):

68=2l+2(14)

68=2l+28

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

$\frac{\begin{array}[b]{r}68=2l+28\\ -28\ \ \ \ \ \ -28\end{array}}{\\\\40=2l}$

Next, we can divide each side by

$\frac{\begin{array}[b]{r}\frac{40}{2}=\frac{2l}{2}\\\end{array}}{20=l}$

The length of the rectangle is $20\textup{ inches}$

Report an Error

Example Question #1 : Systems Of Inequalities

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

$\sqrt{x + 7} > x + 1$

Possible Answers:

2.0 < x < -3.0

-3.0 < x < 2.0

$-3.0 \leq x$

2.0 < x

x = 2.0

Correct answer:

-3.0 < x < 2.0

Explanation:

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

$\left( \sqrt{x + 7} \right)^2> \left( x + 1 \right)^2$

Now simplify each side.

$x + 7 > x^{2} + 2 x + 1$

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

$x + 7 -\left( x + 7 \right)> x^{2} + 2 x + 1 -\left( x + 7 \right)$

$0 > x^{2} + x - 6$

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 = -6 .

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

x = 2.0

x = -3.0

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.

-3.0 < x < 2.0

Report an Error

Example Question #2 : Inequalities And Absolute Value

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

$\sqrt{x + 10} > x + 1$

Possible Answers:

-3.5 < x < 2.5

2.5 < x

$-3.5 \leq x$

2.5 < x < -3.5

x = 2.5

Correct answer:

-3.5 < x < 2.5

Explanation:

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

$\left( \sqrt{x + 10} \right)^2> \left( x + 1 \right)^2$

Now simplify each side.

$x + 10 > x^{2} + 2 x + 1$

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

$x + 10 -\left( x + 10 \right)> x^{2} + 2 x + 1 -\left( x + 10 \right)$

$0 > x^{2} + x - 9$

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 = -9 .

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

x = 2.5

x = -3.5

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.

-3.5 < x < 2.5

Report an Error

Example Question #1 : Systems Of Inequalities

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

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

Possible Answers:

0.0 < x

$-1.0 \leq x$

x = 0.0

-1.0 < x < 0.0

0.0 < x < -1.0

Correct answer:

-1.0 < x < 0.0

Explanation:

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

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

Now simplify each side.

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

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

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

$0 > x^{2} + x$

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 = 0 .

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

x = 0.0

x = -1.0

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.

-1.0 < x < 0.0

Report an Error

Example Question #3 : Inequalities And Absolute Value

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

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

Possible Answers:

$-1.0 \leq x$

0.0 < x < -1.0

0.0 < x

x = 0.0

-1.0 < x < 0.0

Correct answer:

-1.0 < x < 0.0

Explanation:

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

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

Now simplify each side.

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

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

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

$0 > x^{2} + x$

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 = 0 .

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

x = 0.0

x = -1.0

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.

-1.0 < x < 0.0

Report an Error

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All New SAT Math - No Calculator Resources

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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 #11 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

Example Question #501 : New Sat

Example Question #71 : Expressions & Equations

Example Question #504 : New Sat

Example Question #111 : New Sat Math Calculator

Example Question #71 : Expressions & Equations

Example Question #1 : Systems Of Inequalities

Example Question #2 : Inequalities And Absolute Value

Example Question #1 : Systems Of Inequalities

Example Question #3 : Inequalities And Absolute Value

All New SAT Math - No Calculator Resources

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