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Example Questions

Example Question #2431 : Sat Mathematics

A truck was bought for $\$ 20,000$ in 2008, and it depreciates at a rate of $13\%$ per year. What is the value of the truck in 2016? Round to the nearest cent.

Possible Answers:

y= 6764.23

y= 16564

y= 6664.23

y= 6564.23

y= 5664.23

Correct answer:

y= 6564.23

Explanation:

The first step is to convert the depreciation rate into a decimal. $13\%=0.13$ . Now lets recall the exponential decay model. y=C(1-r)^t , where is the starting amount of money, is the annual rate of decay, and is time (in years). After substituting, we get

y=20000(1-0.13)^8

y=20000(0.87)^8

$y=20000\cdot 0.3282117$

y= 6564.23

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Example Question #332 : Plane Geometry

What is $320^{\circ}$ in radians?

Possible Answers:

$\frac{16\pi}{9}$

$\frac{\pi}{9}$

$-\frac{13\pi}{9}$

$\frac{9\pi}{16}$

$\frac{16}{9}$

Correct answer:

$\frac{16\pi}{9}$

Explanation:

To convert degrees to radians, we need to remember the following formula.

$\mbox{degrees}\cdot \frac{\pi}{180}$ .

Now lets substitute for degrees.

$320\cdot \frac{\pi}{180}=\frac{16\pi}{9}$

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Example Question #81 : Lines

Trans

Lines P and Q are parallel. Find the value of .

Possible Answers:

$x=\pm \sqrt{ 205}$

$x=5 + \sqrt{ 205}$

$x=-5+ \sqrt{ 205}$

$x=-5- \sqrt{ 205}$

$x= \sqrt{ 205}$

Correct answer:

$x=-5+ \sqrt{ 205}$

Explanation:

Since these are complementary angles, we can set up the following equation.

x^2+4+10x-4=180

x^2+10x=180

x^2+10x-180=0

Now we will use the quadratic formula to solve for .

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-10\pm \sqrt{10^2-4(1)(-180)}}{2(1)}$

$x=\frac{-10\pm \sqrt{100+720}}{2}$

$x=\frac{-10\pm \sqrt{820}}{2}$

$x=\frac{-10\pm \sqrt{4\cdot 205}}{2}$

$x=\frac{-10\pm 2\sqrt{ 205}}{2}$

$x=-5\pm \sqrt{ 205}$

Note, however, that the measure of an angle cannot be negative, so $x=-5- \sqrt{ 205}$ is not a viable answer. The correct answer, then, is $x=-5+ \sqrt{ 205}$

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Example Question #21 : How To Find The Equation Of A Line

Find the equation of a line that goes through the points (0,3) , and (-10,4) .

Possible Answers:

$y=-\frac{1}{10}x+3$

y=-10x+3

y=-10x

y=-13x

$y=-\frac{1}{10}x$

Correct answer:

$y=-\frac{1}{10}x+3$

Explanation:

For finding the equation of a line, we will be using point-slope form, which is

y-y_0=m(x-x_0) , where is the slope, and (x_0, y_0) is a point.

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-3}{-10-0}=\frac{1}{-10}=-\frac{1}{10}$

We will pick the point (0,3)

$y-3=-\frac{1}{10}(x-0)$

$y=-\frac{1}{10}x+3$

If we picked the point (-10,4)

$y-4=-\frac{1}{10}(x+10)$

$y=-\frac{1}{10}x-1+4$

$y=-\frac{1}{10}x+3$

We get the same result

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Example Question #151 : Coordinate Geometry

Find the equation of a line that passes through the point (-2,5) , and is parallel to the line y=-3x+4 .

Possible Answers:

y=-3x+1

y=-3x-10

y=-3x-1

y=-3x

y=-3x-3

Correct answer:

y=-3x-1

Explanation:

Since we want a line that is parallel, we will have the same slope as the line (-3) . We can use point slope form to create an equation.

y-y_0=m(x-x_0) , where is the slope and (x_0, y_0) is a point.

y-5=-3(x-(-2))

y-5=-3(x+2)

y-5=-3x-6

y=-3x-1

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Example Question #8 : How To Find The Perimeter Of A Figure

A rectangular garden has an area of $80\: \mbox{m^2}$ . Its length is meters longer than its width. How much fencing is needed to enclose the garden?

Possible Answers:

$18\: \mbox{meters}$

$24\: \mbox{meters}$

$40\: \mbox{meters}$

$54\: \mbox{meters}$

$36\: \mbox{meters}$

Correct answer:

$36\: \mbox{meters}$

Explanation:

We define the variables as $w = \mbox{width}$ and $l = \mbox{length} = w + 2$ .

We substitute these values into the equation for the area of a rectangle and get $A_{\mbox{rectangle} }= wl = w(w + 2) = 80$ .

w^2 +2w-80=0

(w - 8)(w + 10) = 0

w = 8 or w = -10

Lengths cannot be negative, so the only correct answer is w = 8 . If w = 8 , then l = 10 .

Therefore, $\mbox{perimeter }= 2w + 2l = 16 + 20 = 36\:\mbox{m}$ .

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Example Question #2061 : Sat Mathematics

If 3x + 72 = 9x + 120 , what does equal?

Possible Answers:

Correct answer:

Explanation:

Subtract and from the both sides to get -6x = 48 .

Divide both sides by , to get

$x=\frac{48}{-6}=-8$

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Example Question #672 : Sat Mathematics

Screen shot 2016 02 10 at 1.10.30 pm

What is the equation of the graph?

Possible Answers:

y=2x^2-4x+4

y=x^2-4x-4

y=2x^2-4x-4

y=2x^2 +4x+4

y=ax^2-4x+4

Correct answer:

y=2x^2-4x+4

Explanation:

In order to figure out what the equation of the image is, we need to find the vertex. From the graph we can determine that the vertex is at (1,2) . We can use vertex form to solve for the equation of this graph.

Recall vertex form,

y=a(x-h)^2+k , where is the coordinate of the vertex, and is the coordinate of the vertex.

Plugging in our values, we get

y=a(x-1)^2+2

To solve for , we need to pick a point on the graph and plug it into our equation.

I will pick (-1,10) .

10=a(-1-1)^2+2

10=a(-2)^2+2

10=4a+2

8=4a

$a=\frac{8}{4}=2$

Now our equation is

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

Let's expand this,

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

y=2x^2-4x+2+2

y=2x^2-4x+4

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Example Question #61 : How To Find Order Of Operations

Which expression is equivalent to the following quotient? For b>0, c>0 .

$\frac{10a^2b^{-3}c^3}{5bc^2}$

Possible Answers:

$\frac{2ac}{b^2}$

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

$\frac{2a^2c}{b^4}$

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

$\frac{2a^2c^0}{b^4}$

Correct answer:

$\frac{2a^2c}{b^4}$

Explanation:

All we need to do is remember the quotient rule for exponents.

$\frac{a^n}{a^m}=a^{n-m}$

We apply this to each term and we get the following.

$\frac{10a^2b^{-3}c^3}{5bc^2}=2a^2b^{-3-1}c^{3-2}=2a^2b^{-4}c^1=\frac{2a^2c}{b^4}$

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Example Question #101 : Linear / Rational / Variable Equations

Solve for x:

$\frac{x+3}{7}=3$

Possible Answers:

x=18

x=42

x=0

x=24

x=6

Correct answer:

x=18

Explanation:

The first step is to cancel out the denominator by multiplying both sides by 7:

$7\cdot \frac{x+3}{7}=3\cdot7$

x+3=21

Subtract 3 from both sides to get by itself:

x+3-3=21-3

x=18

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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 #2431 : Sat Mathematics

Example Question #332 : Plane Geometry

Example Question #81 : Lines

Example Question #21 : How To Find The Equation Of A Line

Example Question #151 : Coordinate Geometry

Example Question #8 : How To Find The Perimeter Of A Figure

Example Question #2061 : Sat Mathematics

Example Question #672 : Sat Mathematics

Example Question #61 : How To Find Order Of Operations

Example Question #101 : Linear / Rational / Variable Equations

All New SAT Math - No Calculator Resources

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