SAT Math Practice Test

The table shows the distribution of two types of flowers at two different sites.

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If a flower represented in the table is selected at random, what is the probability of selecting a flower from site A, given that the flower is a tulip?

Circle A in the $xy$-plane has the equation

$$
(x+5)^2+(y-5)^2=25.
$$

Circle B has the same center as circle A. The radius of circle B is two times the radius of circle A. The equation defining circle B in the $xy$-plane is

$$
(x+5)^2+(y-5)^2=k,
$$

where $k$ is a constant. What is the value of $k$?

In the $xy$-plane, line $k$ intersects the $y$-axis at the point $(0,-6)$ and passes through the point $(2,2)$.
If the point $(20,w)$ lies on line $k$, what is the value of $w$?

In 2008, Zinah earned 14\% more than in 2007, and in 2009 Zinah earned 4\% more than in 2008. If Zinah earned \(y\) times as much in 2009 as in 2007, what is the value of \(y\)?

Which of the following expressions is equivalent to
\[
(\sin24^\circ)(\cos66^\circ)+(\cos24^\circ)(\sin66^\circ)?
\]

Alan drives an average of $100$ miles each week. His car can travel an average of $25$ miles per gallon of gasoline.
Alan would like to reduce his weekly expenditure on gasoline by \$5.
Assuming gasoline costs \$4 per gallon, which equation can Alan use to determine how many fewer average miles, $m$, he should drive each week?

In August, a car dealer completed $15$ more than $3$ times the number of sales the car dealer completed in September.
In August and September, the car dealer completed $363$ sales.
How many sales did the car dealer complete in September?

The expression $6x^4+31x^2+35$ can be rewritten as $(3x^2+a)(2x^2+b)$, where $a$ and $b$ are positive integers, or as $(3x^2+c)(2x^2+d)$, where $c$ and $d$ are positive nonintegers.

What is the value of $a+c$?

The table shows the distribution of rooms in a certain facility by seating capacity.

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If a room in this facility is selected at random, which of the following is closest to the probability of selecting a room that has a seating capacity greater than $65$ seats, given that the room has a seating capacity of at least $18$ seats?

\[
\begin{cases}
y = 18\\
y = -3(x - 18)^2 + 15
\end{cases}
\]
If the given equations are graphed in the $xy$-plane, at how many points do the graphs of the equations intersect?

A number $x$ is at most $2$ less than $3$ times the value of $y$.
If the value of $y$ is $-4$, what is the greatest possible value of $x$?

Line $k$ is shown in the $xy$-plane. Line $j$ (not shown) is perpendicular to line $k$. What is the slope of line $j$?

\[
\begin{cases}
2(8x)+4(7y)=12\\
-2(8x)+4(7y)=12
\end{cases}
\]
The solution to the given system of equations is $(x,y)$.
What is the value of $8x+7y$?

Data set A consists of the heights of 75 buildings and has a mean of 32 meters.
Data set B consists of the heights of 50 buildings and has a mean of 62 meters.
Data set C consists of the heights of the 125 buildings from data sets A and B.
What is the mean, in meters, of data set C?

If \(4^{8c} = \sqrt[4]{4^7}\), what is the value of \(c?\)

Data set A and data set B each consist of 27 values.
The table shows the frequencies of the values for each data set.
Which of the following statements best compares the means of the two data sets?

The function $f$ is defined by $f(x)=56(0.19)^x$. For any positive integer $n$, the value of $f(n)$ is $p\%$ less than the value of $f(n-1)$. What is the value of $p$?

\yourlist
{19}
{44}
{56}
{81}

$(x-6)^{2}+(y+5)^{2}=16$

In the $xy$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{PQ}$ is a diameter of the circle, what are the coordinates of point $Q$?

The graph shows a linear relationship between $x$ and $y$.
Which equation represents this relationship, where $R$ is a positive constant?

A train traveled $173$ miles in the first $3$ hours of a trip and traveled at an average speed of $53$ miles per hour for the remainder of the trip. Which equation gives the total number of miles, $y$, the train traveled if the trip was $x$ hours long and $x>3$?

The function \(f\) is defined by \(f(x) = a^x + b\), where \(a\) and \(b\) are constants and \(a > 0.\)
In the \(xy\)-plane, the graph of \(y = f(x)\) has a \(y\)-intercept at \((0, -25)\) and passes through the point \((2, 23)\).
What is the value of \(a + b?\)

Rectangle $ABCD$ is similar to rectangle $EFGH$. The area of rectangle $ABCD$ is $648$ square inches, and the area of rectangle $EFGH$ is $72$ square inches. The length of the longest side of rectangle $ABCD$ is $36$ inches. What is the length, in inches, of the longest side of rectangle $EFGH$?

\yourlist
{4}
{9}
{12}
{36}

The length of a rectangle’s diagonal is $3\sqrt{17}$, and the length of the rectangle’s shorter side is $3$. What is the length of the rectangle’s longer side?