SAT Practice Questions

Rectangle \(ABCD\) is similar to rectangle \(EFGH\). The area of rectangle \(ABCD\) is \(648\) square inches, and the area of rectangle \(E…

For each real number \(r\), which of the following points lies on the graph of each equation in the \(xy\)-plane for the given system? \(2x…

In the given expression \(34z^{14}+bz^{7}+70\), \(b\) is a positive integer. If \(qz^{7}+r\) is a factor of the expression, where \(q\) and…

If \(\frac{x-4}{5} = \frac{x-4}{7}\), the value of \(x-4\) is between which of the following pairs of values?

A computer repair specialist charges \$160 for the first two hours of repair plus \$40 for each additional hour. The total cost for \(x\) h…

The graph of the function \(f\) is shown, where \(y=f(x)\). What is the value of \(f(0)\)?

In the figure, two lines intersect at a point. If \(r=61\), what is the value of \(s\)?

The function \(f\) is defined by \(f(x)=5x^2\). What is the value of \(f(7)\)?

\[x+5y=5 \\ x-5y=7\] The solution to the given system of equations is \((x,y)\). What is the value of \(x\)?

Which expression is equivalent to \(6x(x+3)\)?

The function \(f\) is defined by \(f(x)=3x^5\). In the \(xy\)-plane, the graph of \(y = g(x)\) is the result of shifting the graph of \(y=f…

For the linear function \(f\), the graph of \(y=f(x)\) in the \(xy\)-plane has a slope of 69 and \(f(0)=3\). Which equation defines \(f\)?

5% of \(w\) is 741.41. What is the value of \(w\)?

The graph of a system of a linear and a quadratic equation is shown. What system is represented by the graph?

The function \(W\) gives the total time, in minutes, it takes for a gardener to water \(x\) plants and mow the grass. \(W(x)=4x+80\). Accor…

\[19=x+y \\ x-y=9\] The solution to the given system of equations is \((x,y)\). What is the value of \(x\)?

\(x^2-16x+y^2-10y-55=0\) In the \(xy\)-plane, the graph of the given equation is a circle. If this circle is inscribed in a square, what is…

If \(5(3x+6)=3(3x+6)+78\), what is the value of \(3x+6\)?

If \(f(x)=x^2+5\) and \(g(x)=5x\), what is the value of \(7f(4)-g(4)\)?

The function \(C\) gives the estimated number of cephalopods in a certain area, where \(t\) is the number of months since a study began. \(…

An object moves at a speed of \(\frac{3}{17}\) feet per second. What is this speed in yards per second? (\(3 \text{ feet} = 1 \text{ yard}\…

For the linear function \(g\), the table shows four values of \(x\) and their corresponding values of \(g(x)\). The function can be written…

The current value of a house is $174,000, and this value increases by 2.4% each year from the value of the previous year. Which function \(…

What is the value of \(\sin(18\pi)\)?

In triangle \(QRS\) shown, \(QR = 17 \text{ and } QR \perp RS\). Which expression represents the length of \(QS\)?

\(\frac{1}{9}x + \frac{3r}{7}y = 34\) One of the equations in a system of two linear equations is given, where \(r\) is a nonzero constant.…

A machine makes 8-inch, 9-inch, and 3-inch parts. During a certain day, the number of 8-inch parts that the machine makes is 4 times the nu…

The ratio of the base to the height of a triangle is 1 to 8. The base of the triangle is 104 centimeters. What is the height, in centimeter…

\(q(x)=15(3^x)\) Which table gives three values of \(x\) and their corresponding values of \(q(x)\) for function \(q\)?

A plant nursery classifies a perennial flower species as tall if its typical height when fully grown is more than 100 centimeters. Which in…

A linear function \(f\) gives a company's profit, in dollars, for selling \(x\) items. The company's profit is \$170 when it sells 4 items,…

Each year, the value of an investment increases by 0.69% of its value the previous year. Which of the following functions best models how t…

Line \(p\) in the \(xy\)-plane is defined by \(y=x+8/3\) and passes through the points \((a, 0)\) and \((0, b)\). What is the value of \(a\…

\[\frac{25x}{x^2-25}=\frac{x}{x-5}+\frac{20}{x+5}\] What is the positive solution to the given equation?

How many solutions does the equation \(7(x+12)+5x=12(x+7)\) have?

If a gym manager repeats a survey with a random sample of 284 members (larger than the original 142) and calculates results the same way, w…

The function \(f\) is defined by \(f(x)=-9x+9\). What is the \(y\)-coordinate of the \(y\)-intercept of the graph of \(y=f(x)\)?

If an additional weight of 68 pounds is added to the original data set of 14 salmon, which measures must be greater for the new data set?

The table shows three values of \(x\) and their corresponding values of \(y\). There is a linear relationship between \(x\) and \(y\), and …

\((x+k)^2+37=37\) In the given equation, \(k\) is a constant. How many distinct real solutions does this equation have?

\(\frac{CV^3}{P}=\sqrt{PR}\) When \(R=18\), which equation correctly expresses \(P\) in terms of \(C\) and \(V\)?

\(y \lt -5x - 21\) \(y \gt -3x - 8\) For which of the following tables are all the values of \(x\) and \(y\) solutions?

A circle is inscribed in a square so that the circle is tangent to all four sides of the square. The length of the diagonal of the square i…

The expression \(k-12\) represents the result of decreasing a positive force, \(k\), measured in newtons, acting on an object, by 12 newton…

A polygon has exactly 87 sides. If the measure of each of the 87 interior angles of this polygon is \((180p)^{\circ}\), what is the value o…

The number of bacteria in a liquid medium doubles every hour. There are 66,000 bacteria at the start. Which represents the number of bacter…

The function \(f\) is defined by \(f(n)=7(20.44)^{n/4}\), where \(f(n)\) gives the value of the term in position \(n\) of a sequence. The v…

A right square pyramid has a total surface area of 28,160 sq in, and the combined surface area of the four lateral faces is 16,060 sq in. W…

The expression \(6x^4+17x^2+7\) can be rewritten as \((3x^2+a)(2x^2+b)\), where \(a\) and \(b\) are integers, or as \((3x^2+c)(2x^2+d)\), w…

The system of two equations, \(y=\frac{16}{x}\) and \(y=16x\), is graphed in the \(xy\)-plane as shown. Which ordered pair is a solution to…

The function \(h\) is defined by \(h(x)=5x-9\). What is the value of \(h(-3)\)?

If \(8x + 7 = 79\), what is the value of \(80x + 70\)?

Casey is raising \(h\) horses and \(g\) goats. Each horse requires 2 acres of land, and each goat requires 1 acre of land. The \(h\) horses…

The function gives a toy car's height above the ground \(f(x)\) in inches, \(x\) seconds after it started moving on an elevated track, wher…

Which expression is equivalent to \((w+7)(3w-10)\)?

Two numbers have a product \(y\), such that one number is \(x\) and the other number is 99 less than \(x\). Which of the following equation…

A bank account was opened with an initial deposit. Over the next several months, regular deposits were made into this account, and there we…

The function \(F(m)=7m\) models the force, in newtons, acting on each object in a certain field as a function of the object's mass \(m\), i…

In the figure shown, lines \(j\) and \(k\) are parallel and line \(t\) intersects both lines. If \(x \gt 154\), which of the following must…

The graph of a polynomial function \(y=f(x)\) in the \(xy\)-plane passes through the point \((5, 7)\). What is the value of \(f(5)\)?

The solution to the given system of equations is \((x, y)\). What is the value of \(x\)? \[y = -\frac{1}{7}x \\ y = \frac{1}{5}x\]

In the right triangle shown, \(c\) is a constant. The value of \(\sin x^{\circ} = \dfrac{k}{39}\), where \(k\) is a constant. What is the v…

The functions \(g\) and \(h\) are defined by the given equations. \[g(x)=\sqrt{(x-11)^{2}+45} \\ h(x)=\sqrt[3]{64}+\frac{x^{2}}{2}\] If \(g…

If \((\frac{1}{2}x - \frac{33}{2})^2 - 64 = 0\), what is the value of \((x - 33)^2\)?

A circle has center \(O\), and points \(A\) and \(B\) lie on the circle. The measure of arc \(AB\) is \(20^{\circ}\), and the length of thi…

For \(x > 0\), the function \(f\) is defined as follows: \(f(x)\) equals \(111\%\) of \(x\). Which of the following could describe this fun…

In the given system of equations, \(w\) is a constant. The system has infinitely many solutions. What is the value of \(w\)? \[45x + 33y - …

The functions \(f\) and \(g\) are defined as \(f(x)=\frac{1}{5}x-9\) and \(g(x)=\frac{4}{5}x+27\). If the function \(h\) is defined as \(h(…

A beaker containing a liquid is placed on a table. The function \(g(t)=294+(363-294)(2.72)^{-0.103t}\) gives the approximate temperature, i…

A researcher surveyed undergraduate students, graduate students, and postdoctoral students. The number of undergraduate students surveyed w…

What is the minimum value of the given function? \[f(x)=(2x-20)(2x+8)\]

A line in the \(xy\)-plane has a slope of \(-\frac{1}{4}\) and passes through the point \((0, 19)\). Which equation represents this line?

Cristina was elected to the city council. Each city council person is required to attend at least 21 of the 27 scheduled council meetings i…

The function \(f(x)=-40x+280\) gives the predicted height above the ground, in feet, of a model airplane \(x\) minutes after it begins to d…

The given equation relates the distinct positive numbers \(v, w,\) and \(x\). Which equation correctly expresses \(w\) in terms of \(v\) an…

Which expression is equivalent to \((x+8)^{2}+14(x+8)+49\)?

If \(8(x+7)=7(x+7)+68,\) what is the value of \(x+7?\)

Which of the following best represents the line of best fit shown?

In triangle \(ABC\), angle \(B\) is a right angle. The length of side \(AB\) is \(10\sqrt{39}\) and the length of side \(BC\) is \(24\sqrt{…

To cut a lawn, Antwan charges a fee of \$10.00 for his equipment and \$8.50 per hour spent cutting a lawn. Taylor charges a fee of \$7.00 f…

In the \(xy\)-plane, line \(p\) has a slope of \(\frac{3}{4}\) and an \(x\)-intercept of \((16, 0)\). What is the \(y\)-coordinate of the \…

The given table shows the number of even and odd integers contained in list A and list B. No integer is contained in both lists. What fract…

In a certain state, the population of pheasants, a type of bird, is estimated each year from 2005 to 2015 the number of pheasants counted p…

The function \(g\) is defined by \(g(x)=3x\). For what value of \(x\) is \(g(x)=12\)?

One solution to the given equation can be written as \(x=h+\sqrt{k}\), where \(h\) and \(k\) are integer constants. What is the value of \(…

Data set F consists of 55 integers, where the value of each integer is between 150 and 260. Data set G consists of the same 55 integers in …

A gallery had \(x\) artifacts in a collection. When more artifacts were added to the collection, the number of artifacts increased by \(149…

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…

One gallon of sealant costs $23 and will cover 250 square feet of a surface. A deck has a total surface area of \(d\) square feet. Which eq…

A right square pyramid has a height of 11 centimeters (cm). A second right square pyramid has a height of 22 centimeters. The area of the b…

An object's speed is increasing at a rate of 5.70 meters per second squared. What is this rate, in miles per minute squared, rounded to the…

For triangle \(ABC\), the length of \(AB\) is 11 less than the length of \(AC\). Point \(D\) (not shown) lies on \(AC\) such that \(BD\) (n…

In the given equation, \(c\) is a constant. If the equation has exactly one solution, what is the value of \(c\)? \[\frac{1}{cx}=\frac{x}{1…

The graph of the function \(f\) is shown, where \(y=f(x)\). What is the value of \(f(0)\)?

In the figure, two lines intersect at a point. If \(r=61\), what is the value of \(s\)?

The function \(f\) is defined by \(f(x)=5x^{2}\). What is the value of \(f(7)\)?

Which expression is equivalent to \(6x(x+3)\)?

The function \(f\) is defined by \(f(x)=3x^{5}\). In the \(xy\)-plane, the graph of \(y=g(x)\) is the result of shifting the graph of \(y=f…

For the linear function \(f\), the graph of \(y=f(x)\) in the \(xy\)-plane has a slope of 69 and \(f(0)=3\). Which equation defines \(f\)?

5% of \(w\) is 741.41. What is the value of \(w\)?