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SAT Math : SAT Mathematics

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Example Questions

Example Question #2891 : Sat Mathematics

Use substitution to solve to calculate $\frac{3d}{c}$ given $\frac{c}{d}=6$ .

Possible Answers:

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{3}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

To solve this problem first manipulate the given equation to solve for .

$\frac{c}{d}=6$

Multiply by on both sides. The 's on the left hand side of the equation will cancel out.

$d\cdot\frac{c}{d}=6\cdot d$

c=6d

Now to calculate $\frac{3d}{c}$ , substitute the value for that was just found, into the denominator and simplify by canceling out common factors.

$\frac{3d}{c}=\frac{3d}{6d}=\frac{3}{6}=\frac{1\cdot 3}{2\cdot 3}=\frac{1}{2}$

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Example Question #2892 : Sat Mathematics

Write the following quadratic equation into vertex form.

y=x^2-5x+6

Possible Answers:

y=(x-2.5)^2-0.25

y=(x-2.5)^2

y=(x+2.5)^2

y=(x-2)^2

y=(x-2.5)^2+0.25

Correct answer:

y=(x-2.5)^2-0.25

Explanation:

y=x^2-5x+6

First we group terms

y=x^2-5x+6=(x^2-5x)+6

Now we want to have a perfect square, so we add $\left(\frac{b}{2}\right)^2$ , and we subtract $\left(\frac{b}{2}\right)^2$ , so now it looks like

$\left(x^2-5x+\left(\frac{-5}{2}\right)^2\right)-\left(\frac{-5}{2}\right)^2+6$

(x^2-5x+6.25)-6.25+6

Simplify to get

y=(x-2.5)^2-0.25

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Example Question #3 : Algebraic Functions

f(x) = x^2 + 32x -12

What is f(4) ?

Possible Answers:

130

128

156

144

132

Correct answer:

132

Explanation:

f(x) = x^2 + 32x -12

f(4) = 4^2 + 32(4) -12

= 16 + 128 -12

= 132

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Example Question #2893 : Sat Mathematics

$\begin{tabular}{c c c} x & \vline& y\\ \hline 0 & \vline& -3 \\ 1 & \vline & 0\\ 2 & \vline & 3\\ 3 & \vline & 6 \end{tabular}$

Using the table above, find the equation of a line.

Possible Answers:

y=-x-3

y=-2x-3

y=x-3

y=2x-3

y=3x-3

Correct answer:

y=3x-3

Explanation:

We can use point slope form to determine the equation of a line that fits the data.

Point slope form is y-y_0=m(x-x_0) , where (x_0, y_0) , and is the slope, where $m=\frac{y_2-y_1}{x_2-x_1}$ .

Let y_2=6 , y_1=3 , x_2=3 , and x_1=2 .

$m=\frac{6-3}{3-2}=3$

If we do this for every other point, we will see that they have the same slope of .

y-y_0=3(x-x_0)

Now let x_0=0 , and y_0=-3 .

y-(-3)=3(x-0)

y+3=3x

y=3x-3

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Example Question #2894 : Sat Mathematics

$\begin{tabular}{cccc} x & \vline & y\\ \hline 0 & \vline & 2\\ 1& \vline &7 \\ 2 & \vline & 12\\ 3 & \vline & 17\\ 15 &\vline & ? \end{tabular}$

What is the value of at x=15 ?

Possible Answers:

y=100

y=-77

y=80

y=77

y=75

Correct answer:

y=77

Explanation:

If we use the equation that solved for previously, y=5x+2 , we just plug in for .

y=5(15)+2=75+2=77

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Example Question #2895 : Sat Mathematics

The average number of college graduates per year is modeled by the equation y=0.6x+250.3 . Which of the following answers best describes 0.6 in the equation?

Possible Answers:

The estimated decrease in the average number of college graduates each year

The estimated increase in the average number of college graduates each year

The number of college graduates each year

The average number of college graduates each year

Correct answer:

The estimated increase in the average number of college graduates each year

Explanation:

The answer is, "The estimated increase in the average number of college graduates each year" because the equation is a model, which is an estimation.

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Example Question #2896 : Sat Mathematics

Solve for .

$3r+5t=\frac{-4Q+5z}{2}$

Possible Answers:

$Q=\frac{6r+10t-5z}{-4}$

$Q=\frac{6r+10t+5z}{4}$

$Q=\frac{6r+10t-z}{-4}$

$Q=\frac{6r+10t+5z}{-4}$

Correct answer:

$Q=\frac{6r+10t-5z}{-4}$

Explanation:

$3r+5t=\frac{-4Q+5z}{2}$

Multiply by on each side

2(3r+5t)=-4Q+5z

Expand right side

6r+10t=-4Q+5z

Subtract on each side

-4Q=6r+10t-5z

Divide by on each side

$Q=\frac{6r+10t-5z}{-4}$

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Example Question #2897 : Sat Mathematics

If a rocket is shot from the ground, and it takes $5 \sec$ to reach a height of $500\:\text{m}$ . Determine the equation of its trajectory.

Possible Answers:

y=10x

y=50x

y=100x

y=-100x

y=500x

Correct answer:

y=100x

Explanation:

To figure out what the equation is, we need to use the point-slope form.

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

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

In this example, y_2=500, y_1=0, x_2=5, x_1=0

$\text{Slope}=\frac{500-0}{5-0}=100$

y-0=100(x-0)

y=100x

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Example Question #2898 : Sat Mathematics

Screen shot 2016 02 18 at 1.42.15 pm

Determine the x-intercepts in the graph above.

Possible Answers:

Not enough information

Correct answer:

Explanation:

The x-intercepts are the points on the graph where the y=0 line touches or intersects the x axis. By looking at the graph, there are two points. One at x=2 , and then another one at x=3 . So there are two x intercepts.

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Example Question #1124 : Algebra

Stuff animals were a strange craze of the 90's. A Cat stuff animal with white paws sold for $6 in 1997. In 2015, the Cat will sell for $1015. What has been the approximate rate of growth for these stuff animal felines?

Possible Answers:

$33 \%$

$16.8 \%$

$13.29 \%$

$3.2 \%$

$168 \%$

Correct answer:

$33 \%$

Explanation:

Use the formula for exponential growth y = A*(1+r)^t where y is the current value, A is the initial value, r is the rate of growth, and t is time. Between 1997 and 2015, 18 years passed, so use t=18 . The stuffed animal was originally worth $6, so A=6 . It is now worth $1,015, so y=1015 .

Our equation is now:

$1015 = 6*(1+r)^{18}$ divide by 6:

$169.1\overline{6}=(1+r)^{18}$ take both sides to the power of $\frac{1}{18}=0.0\overline{5}$ :

$1.329 \approx 1+r$ subtract 1

0.329 = r

As a percent, r is about 33%.

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #2891 : Sat Mathematics

Example Question #2892 : Sat Mathematics

Example Question #3 : Algebraic Functions

Example Question #2893 : Sat Mathematics

Example Question #2894 : Sat Mathematics

Example Question #2895 : Sat Mathematics

Example Question #2896 : Sat Mathematics

Example Question #2897 : Sat Mathematics

Example Question #2898 : Sat Mathematics

Example Question #1124 : Algebra

All SAT Math Resources

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