SAT Math - SAT Subject Test in Math I

x varies inversely with y. When x=10, y=6. When x=3, what is y?

Explanation

Inverse variation takes the form:

$y=\frac{k}{x}$

Plugging in:

$6=\frac{k}{10}$

Then solve when x=3:

If $\sin \beta = \frac{3}{5}$ and $0 < \beta < \frac{\pi}{2}$ , evaluate $\cos 2\beta$ .

$\frac{7}{25}$

$\frac{9}{25}$

$\frac{16}{25}$

$\frac{4}{5}$

$\frac{8}{5}$

Explanation

The easiest identity to use here is:

$\cos 2\beta = 1 - 2 \sin^2 \beta$

Substituting in the given values we get:

$= 1 - 2 \left ( \frac{3}{5} \right )^2 = 1 - \frac{18}{25} = \frac{7}{25}$

A convex polyhedron has twenty faces and thirty-six vertices. How many edges does it have?

Explanation

The number of vertices , edges , and faces of any convex polyhedron are related by By Euler's Formula:

Setting and solving for :

The polyhedron has 54 edges.

Triangle

Note: Figure NOT drawn to scale.

Refer to the figure above, which shows a square inscribed inside a large triangle. What percent of the entire triangle has been shaded blue?

$44\frac{4}{9} %$

$33 \frac{1}{3} %$

Insufficient information is given to answer the question.

Explanation

The shaded portion of the entire triangle is similar to the entire large triangle by the Angle-Angle postulate, so sides are in proportion. The short leg of the blue triangle has length 20; that of the large triangle, 30. Therefore, the similarity ratio is . The ratio of the areas is the square of this, or $3^{2}:2^{2}$ , or .

The blue triangle is therefore $\frac{4}{9}$ of the entire triangle, or $\frac{4}{9} \times 100 = 44 \frac{4}{9} %$ of it.

Based on the figure below, which line depicts a quadratic function?

Red line

Blue line

Green line

Purple line

None of them

Explanation

A parabola is one example of a quadratic function, regardless of whether it points upwards or downwards.

The red line represents a quadratic function and will have a formula similar to $\small {f(x)=ax^2+bx+c}$ .

The blue line represents a linear function and will have a formula similar to $\small {f(x)=ax+b$ .

The green line represents an exponential function and will have a formula similar to $\small {f(x)=ax^b}$ .

The purple line represents an absolute value function and will have a formula similar to $\small {f(x)=\left |ax+b \right |}.$ .

In a triangle, , what is the measure of angle A if the side opposite of $\angleA$ angle A is 3 and the adjacent side to angle A is 4?

(Round answer to the nearest tenth of a degree.)

$36.9^{\circ}$

$40^{\circ}$

$32^{\circ}$

$34.7^{\circ}$

Explanation

To find the measure of angle of A we will use tangent to solve for A. We know that

$tan A=\frac{opposite}{adjacent}$

In our case opposite = 3 and adjacent = 4, we substitute these values in and get:

$tan A= \frac{3}{4}$

Now we take the inverse tangent of each side to find the degree value of A.

$A= tan^{^{-1}}\left(\frac{3}{4}\right)$

What is the vertex of ? Is it a max or min?

$-\frac{5}{6}, \textup{Max}$

$-\frac{5}{6}, \textup{Min}$

$-\frac{5}{3}, \textup{Max}$

$-\frac{5}{3}, \textup{Min}$

$\frac{5}{6}, \textup{Min}$

Explanation

The polynomial is in standard form of a parabola.

To determine the vertex, first write the formula.

$x=-\frac{b}{2a}$

Substitute the coefficients.

$x=-\frac{-5}{2(-3)} = -\frac{5}{6}$

Since the is negative is negative, the parabola opens down, and we will have a maximum.

The answer is: $-\frac{5}{6}, \textup{Max}$

A regular seven sided polygon has a side length of 14”. What is the measurement of one of the interior angles of the polygon?

128.57 degrees

257.14 degrees

180 degrees

154.28 degrees

252 degrees

Explanation

The formula for of interior angles based on a polygon with a number of side n is:

Each Interior Angle = (n-2)*180/n

= (7-2)*180/7 = 128.57 degrees

Find the area of a kite with diagonal lengths of and .

Explanation

Write the formula for the area of a kite.

$A= \frac{d1\cdot d2}{2}$

Plug in the given diagonals.

$A= \frac{(a+b)\cdot (2a-2b)}{2}$

Pull out a common factor of two in and simplify.

$A= \frac{(a+b)\cdot2(a-b)}{2}$

Use the FOIL method to simplify.

What is the domain of the following function? Please use interval notation.

$y=\left | -x\right |$

$(-\infty ,\infty )$

$(0,\infty )$

$(-\infty ,0)$

Explanation

A basic knowledge of absolute value and its functions is valuable for this problem. However, if you do not know what the typical shape of an absoluate value function looks like, one can always plug in values and plot points.

Upon doing so, we learn that the -values (domain) are not restricted on either end of the function, creating a domain of negative infinity to postive infinity.

If we plug in -100000 for , we get 100000 for .

If we plug in 100000 for , we get 100000 for .

Additionally, if we plug in any value for , we will see that we always get a real, defined value for .

**Extra Note: Due to the absolute value notation, the negative (-) next to the is not important, in that it will always be made positive by the absolute value, making this function the same as $y=\left | x\right |$ . If the negative (-) was outside of the absolute value, this would flip the function, making all corresponding -values negative. However, this knowledge is most important for range, rather than domain.

SAT Subject Test in Math I

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