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Example Questions

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Example Question #292 : Equations / Inequalities

81x + 64y = 65

9x + 16y = 25

What is ?

Possible Answers:

$\frac{40}{57}$

Correct answer:

Explanation:

Solve for by merging the equations so that gets factored out. To do so, multiply the lower equation by (so that 81x at the top is subtracted by -81x )

(-9)9x + (-9)16y = (-9)25

(81x + 64y = 65) - (-81x - 144y = -225) =

0x + (64 - 144)y = 65 - 225

-80y = -160

$y =\frac{-160}{-80}=2$

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Example Question #281 : Algebra

If f(x) = 4x + 2(x+1) , then f(8x) =?

Possible Answers:

48x + 2

32x + 1

16x + 4

48x + 8

Correct answer:

48x + 2

Explanation:

f(x) = 4x + 2(x+1) ,

f(8x) = 4(8x) + 2(8x+1) = 32x + 16x + 2 = 48x + 2

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Example Question #32 : How To Use Foil In The Distributive Property

Expand the following expression found below:

(x^2+5x)(x^3+6)

Possible Answers:

x^5+5x^4+6x^2+30x

x^5+6x^4+5x^2+30

x^6+5x^4+6x^2+30x

x^6+5x^3+6x^2+30x

Correct answer:

x^5+5x^4+6x^2+30x

Explanation:

If a problem asks you to expand an expression, you must use the Distributive property. If you are using the FOIL method, you first multiply the first term in each parentheses by each other, followed by the outside terms, then the inside terms, and then the last terms. This is illustrated below.

Screen shot 2015 10 27 at 1.54.06 pm

First, you multiply $x^2\times x^3$ which equals x^5

Second, you multiply $x^2\times6=6x^2$

Third, you multiply $5x\times x^3=5x^4$

Last, you multiply $5x\times 6=30x$

Then you simply rearrange them in order of exponents to get x^5+5x^4+6x^2+30x

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Example Question #1 : Expressions

If $\frac{b+c}{c}=\frac{14}{15}$ , then which of the following must be also true?

Possible Answers:

$\frac{b}{c}=10$

$\frac{b}{c}=1$

$\frac{b}{c}=\frac{7}{10}$

$\frac{b}{c}=-\frac{1}{15}$

Correct answer:

$\frac{b}{c}=-\frac{1}{15}$

Explanation:

$\frac{b+c}{c}=\frac{14}{15}$

$\frac{b}{c}+\frac{c}{c}=\frac{14}{15}$

$\frac{b}{c}+1=\frac{14}{15}$

$\frac{b}{c}+1\ {\color{Red} -1}=\frac{14}{15}\ {\color{Red} -1}$

$\frac{b}{c}=\frac{14}{15}-\frac{15}{15}$

$\frac{b}{c}=-\frac{1}{15}$

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Example Question #23 : How To Find X Or Y Intercept

What is the value of the -intercept for the line given below?

2y=14x+98

Possible Answers:

3.5

Correct answer:

Explanation:

The x-intercept is where the line crosses the x-axis. In other words,

y=0

This gives:

0=14x+98

Subtracting 98 from both sides gives:

-98=14x

Dividing both sides by 14 gives the final answer:

x=-7

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Example Question #41 : Lines

Which of the following lines is parallel to:

4y-12x=2

Possible Answers:

x-3y=9

x+4y=10

$x-\frac{1}{3}y=7$

$y=\frac{1}{3}x+2$

Correct answer:

$x-\frac{1}{3}y=7$

Explanation:

First write the equation in slope intercept form. Add 12x to both sides to get 4y = 12x + 2 . Now divide both sides by to get y = 3x + 0.5 . The slope of this line is , so any line that also has a slope of would be parallel to it. The correct answer is $x - \frac{1}{3}y = 7$ .

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Example Question #2 : How To Find Excluded Values

Find the extraneous solution for

$\sqrt{x}=3x-4$

Possible Answers:

x=-1

x=1

$x=\frac{16}{9}$

There are no extraneous solutions

Correct answer:

x=1

Explanation:

$\sqrt{x}=3x-4$

$(\sqrt{x})^2=(3x-4)^2$

x=9x^2-24x+16

0=9x^2-25x+16

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

$x=\frac{25\pm\sqrt{(-25)^2-4\cdot9\cdot16}}{2\cdot9}$

$x=\frac{25\pm\sqrt{625-576}}{18}$

$x=\frac{25\pm\sqrt{49}}{18}$

$x=\frac{25+7}{18}=\frac{32}{18}=\frac{16}{9}$

$x=\frac{25-7}{18}=\frac{18}{18}=1$

Now lets plug these values into our original equation.

For $x=\frac{16}{9}$

$\sqrt{x}=3x-4$

$\sqrt{\frac{16}{9}}=3\left(\frac{16}{9}\right)-4$

$\frac{4}{3}=\frac{16}{3}-4$

$\frac{4}{3}=\frac{16}{3}-\frac{12}{3}=\frac{4}{3}$

So this isn't an extraneous solution.

For x=1

$\sqrt{x}=3x-4$

$\sqrt{1}=3(1)-4$

1=3-4=-1

Since $1\neq-1$ , x=1 is an extraneous solution.

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Example Question #101 : Algebra

Solve

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

Possible Answers:

$x=-\frac{22}{3}$

x=-3

x=-22

$x=\frac{22}{3}$

Correct answer:

$x=-\frac{22}{3}$

Explanation:

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

First multiply by the denominator on each side

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

4x-4=10(x+4)

Expand left side, and solve for

4x-4=10x+40

-44=6x

$x=\frac{-44}{6}=-\frac{22}{3}$

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Example Question #41 : New Sat Math No Calculator

Given:

$x+y-2=0$

$y=x^{2}-4$

How many solutions will there be for the system of equations?

Possible Answers:

Correct answer:

Explanation:

Use the substitution method to solve the system of equations. There are two ways to do this - either substitute the first equation into the second, or the second equation into the first. Since the second equation is already solved for one variable, we will choose the latter.

$x+\left ( x^{2}-4\right )-2=0$

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

Now factor the equation:

$\left ( x+3\right )\left ( x-2\right )=0$

x=-3 or x=2

For this particular question, you could stop right here, as you can only need to know the number of solutions not the ordered pair of the solutions. Here there are two solutions. The ordered pairs would be:

$\left ( -3,5\right )$ and $\left ( 2,0\right )$

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Example Question #18 : Fractions

Bob and Jill go eat dinner at a fancy restaurant. Bob gets lobster and Jill gets crab legs. The lobster cost $\$60.00$ , and the crab legs cost $\$ 50.00$ . If they leave $15\%$ tip, how much is the combined bill?

Possible Answers:

$\$126$

$\$126.50$

$\$110$

$\$110.50$

Correct answer:

$\$126.50$

Explanation:

To do this, we need to sum up each meal, and then convert the tip into a decimal.

$15\%=0.15$

$\text{Bill}=\$60+\$50+0.15(\$60+\$50)$

$\text{Bill}=\$110+0.15(\$110)$

$\text{Bill}=\$110+\$16.50$

$\text{Bill}=\$126.50$

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New SAT Math - No Calculator : New SAT Math - No Calculator

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

All New SAT Math - No Calculator Resources

Example Questions

Example Question #292 : Equations / Inequalities

Example Question #281 : Algebra

Example Question #32 : How To Use Foil In The Distributive Property

Example Question #1 : Expressions

Example Question #23 : How To Find X Or Y Intercept

Example Question #41 : Lines

Example Question #2 : How To Find Excluded Values

Example Question #101 : Algebra

Example Question #41 : New Sat Math No Calculator

Example Question #18 : Fractions

All New SAT Math - No Calculator Resources

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