SAT Practice Questions

If \(x \ge -8\) represents all solutions to the inequality \(ax - 18 \le 14\), where \(a\) is a constant, what is the greatest possible val…

\(5(3x) + 4(8y) = 16\) \(-5(3x) + 4(8y) = 16\) The solution to the given system of equations is \((x, y)\). What is the value of \(3x + 8y\…

For the positive quantities \(h, j,\) and \(k, 35\)% of \(h\) is equivalent to \(49\)% of \(j,\) and \(j\) is equivalent to \(45\)% of \(k.…

\(4x^{2} + 19 = 32x + r\) In the given equation, \(r\) is a constant. The equation has exactly one real solution. What is the value of \(r\…

For the function \(f\), for every increase of \(2\) in the value of \(x\) the value of \(f(x)\) increases by a factor of \(c\), where \(c\)…

In the figure shown, \(AB = \sqrt{61}\) units, \(AC = 6\) units, and \(CE = 18\) units. What is the area, in square units, of triangle \(AD…

The graph of line \(g\) is shown in the \(xy\)-plane. Line \(k\) is defined by \(165x + py = w\), where \(p\) and \(w\) are constants. If l…

\(x^{2} - 4x + y^{2} - 8y - 80 = 0\) In the \(xy\)-plane, the graph of the given equation is a circle. If this circle is inscribed in a squ…

\(7x + 5y = 2\) The given equation is one equation in a system of two linear equations. If the system has at least one solution, which of t…

The function \(f\) is defined by \(f(x) = ax^{2} + bx + c\), where \(a\), \(b\), and \(c\) are constants. The graph of \(y = f(x)\) in the …

An object's speed is increasing at a rate of \(2.7\) meters per second squared. What is this rate, in miles per minute squared, rounded to …

The table summarizes members of a local organization by age and whether they live north or south of Center St. If a member of the organizat…

Which expression is equivalent to \(4(x^{2}+6)\)?

For the linear function \(f\), the graph of \(y=f(x)\) in the \(xy\)-plane has a slope of \(\frac{1}{4}\) and passes through the point \((0…

The function \(f\) is defined by \(f(x)=5+\sqrt{x}\). What is the value of \(f(144)\)?

\(7x-4y=-84\). For the given equation, which table gives three values of \(x\) and their corresponding values of \(y\)?

A geologist estimates that the volume of a boulder is greater than \(12.7\) cubic feet but less than \(15.7\) cubic feet. The geologist als…

If \(46=16+2(x-8)\), what is the value of \(2(x-8)\)?

\(y=x^{2}+1.7\), \(y=1.7-x\). Which graph represents the given system of equations?

In triangle \(ABC\), the measure of angle \(A\) is \(47^{\circ}\), the measure of angle \(B\) is \(90^{\circ}\), and the measure of angle \…

A clothing store buys shirts at a wholesale price of \(5.00\) dollars each and resells them each at a retail price that is \(270\%\) of the…

Which of the following is closest to the slope of this line of best fit?

The expression \(72y^{5}-48y^{4}\) is equivalent to \(ry^{4}(12y-8)\), where \(r\) is a constant. What is the value of \(r\)?

The equation \(y=0.25x^{2}-6.5x+64.25\) gives the estimated stock price \(y\), in dollars, for a certain company \(x\) days after the compa…

The total mass, in kilograms, of \(r\) identical objects is \(t\). Which expression represents the total mass, in kilograms, of \(146r\) of…

If \(\frac{42}{x}=7x\), what is the value of \(7x^{2}\)?

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

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

\(h=\frac{9(v-273.15)}{5}+32\). The equation gives the corresponding temperature \(h\), in degrees Fahrenheit, of any substance that has a …

A circle in the \(xy\)-plane has its center at \((16, 17)\) and has a radius of \(7k\). Which equation represents this circle?

In the triangle shown, \(RS=\sqrt{105}.\) What is the value of \(\sin R\)?

Parallelogram \(ABCD\) is similar to parallelogram \(PQRS\). The length of each side of parallelogram \(PQRS\) is \(2\) times the length of…

\(r(t)=55t-2t^{2}\). The function \(r\) is defined by the given equation. The function \(s\) is defined by \(s(t)=r(t)+1\). Which expressio…

The function \(f(x)=39-0.18x\) gives the estimated height, in centimeters (cm), of the water in the glass \(x\) days after the start of the…

The table shows the relationship between the area \(x\), in square feet, of a roof and the amount of water \(f(x)\), in gallons, drained fr…

In 2010, a skating team had a total of \(35\) skaters. From 2010 to 2020, the number of advanced skaters (\(a\)) increased by approximately…

\(b-72=\frac{x}{y}\). Which equation correctly expresses \(x\) in terms of \(b\) and \(y\)?

\(y=\frac{2}{7}x+3\). One of the two equations in a system of linear equations is given. The system has infinitely many solutions. If the s…

What is the solution \( (x, y) \) to the given system of equations? \( y=6x+16 \), \( -7x-y=36 \).

Which statement best compares the standard deviations of scores for these teams?

\(x^{2}-5x-24=0\). What is the sum of the solutions to the given equation?

The graph of \(y=f(x)\) is shown, where \(f(x)=ab^{x}+c\). For how many values of \(x\) does \(f(x)=0?\)

The length of the edge of a cube is \(3.000\) cm. This cube has a density of \(0.250\) g/cm\(^3\). What is the mass of this cube, in grams?

Function \(f\) is a quadratic function where \(f(-20)=0\) and \(f(-4)=0.\) The graph of \(y=f(x)\) has a vertex at \((r,-64).\) What is the…

The function \(f\) gives the product of a number, \(x\), and a number that is \(91\) more than \(x\). Which equation defines \(f\)?

\(-2x^{2}+20x+c=0\). In the given equation, \(c\) is a constant. The equation has exactly one solution. What is the value of \(c\)?

\(y=2x^{2}-15x+23\), \(y=x+a\). The graphs intersect at exactly one point \((x, y)\). What is the value of \(x\)?

The positive number \(a\) is \(2,352\%\) of the sum of \(b\) and \(c\), and \(b\) is \(84\%\) of \(c\). What percent of \(b\) is \(a\)?

Which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines, where \(x\ge0\)? I. …

\(\frac{12x+28}{4}-\frac{s}{13}=r(x-8)\). \(s\) and \(r\) are constants, and \(s>0\). If the equation has infinitely many solutions, what i…

The perimeter of an isosceles right triangle is \(18+18\sqrt{2}\) inches. What is the length, in inches, of the hypotenuse of this triangle?

A right triangular pyramid has exactly six edges. Each is \(96\) cm long. If the surface area is \(k\sqrt{3}\) cm\(^2\), what is \(k\)?

The cost of renting equipment for up to 5 days is \$270 for the first day and \$135 for each additional day. Which equation gives the cost …

A line intersects two parallel lines. One angle is \((7x-250)^\circ\). The sum of four angles is \(k^\circ\). Which could NOT be \(k\)?

\(7x+4y=3\), \(35x+20y=15\). For each real number \(r\), which point lies on the graph of each equation?

\(11x+50=160\) Which equation has the same solution as the given equation?

What is the y-intercept of the graph shown?

For a particular tree species, it is recommended to plant a maximum of 111 trees per acre. Based on this recommendation, what is the maximu…

Which expression is equivalent to \(14(x^{2}-100y^{2})\)?

Which expression is equivalent to \((3c+9)-(4c^{3}-5)\)?

In \(\triangle JKL\), the measures of both \(\angle J\) and \(\angle K\) are equal and the measure of \(\angle L\) is \(136^{\circ}\). What…

A student council group is selling car stickers for a fundraiser. They use the function \(p(x)=5x-190\) to determine their profit \(p(x)\),…

Line \(r\) is defined by the equation \(6x-5y=6\). Line \(s\) is parallel to line \(r\) in the xy-plane. What is the slope of line \(s\)?

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

At how many points do the graphs of the equations \(y=4x\) and \(y=x+13\) intersect in the xy-plane?

A quadratic model gives the predicted instantaneous rate of change, in bacteria per hour, of a bacteria population as a function of the pop…

The cost to rent a bus from Company X is \$950 for the first 2 hours and an additional \$50 per hour for each hour after the first 2 hours.…

A machine fills bags with approximately 11 ounces of sugar. To test the accuracy of the process, 132 bags of sugar were selected at random …

In the figure shown, \(\overline{JM}\) is the diameter and \(\overline{LM}\) is a radius of semicircle \(L\), and point \(K\) is the midpoi…

The kinetic energy \(K\), in joules, of an object is given by the formula \(K=\frac{1}{2}mv^{2}\), where \(m\) is the mass of the object, i…

The function \(f(x)=236(1.022)^{x}\) models the value, in dollars, of a certain bank account from 1958 through 1973, where \(x\) is the num…

\((3x-8)^{2}-11(3x-8)+28=0\) What is one possible value of \(x\)?

For the function \(f\), \(f(x)=-10x+b\), where \(b\) is a constant and \(f\left(\frac{2}{5}\right)=-53\). What is the value of \(b\)?

Which of the following equations is the most appropriate model for the data shown in the scatterplot?

The function \(f\) is defined by \(f(x)=(x-10)(x-8)(x-4)\). In the xy-plane, the graph of \(y=g(x)\) is the result of translating the graph…

\((x+3)^{2}+(y-18)^{2}=169\) The graph of the given equation is a circle in the xy-plane. The point \((a,b)\) lies on the circle. Which of …

Right triangle ABC is shown. What is the value of \(\sin A\)?

The function \(g\) is defined by \(g(x)=-8x+60\). What is the value of \(g(x)\) when \(x=-3\)?

A certain blue whale calf weighed 5,600 pounds when it was born, and its weight increased at an average rate of 250 pounds per day for the …

\(4x(x-3)(x+9)=0\) What is one of the solutions to the given equation?

\(y=\frac{x}{3}+4\) \(y=-\frac{x}{3}+40\) The solution to the given system of equations is \((x,y)\). What is the value of \(2y\)?

A hemisphere is half of a sphere. If a hemisphere has a radius of 69 inches, which of the following is closest to the volume, in cubic inch…

\(f(x)=18x^{2}-45x+13\) For what value of \(x\) does \(f(x)\) reach its minimum?

An exponential function \(f\) is defined by \(f(x)=c^{x}\) where \(c\) is a constant greater than 1. If \(f(7)=9 \cdot f(5)\), what is the …

How many solutions does the equation \(10(x+15)+5x=15(x+10)\) have?

A line in the xy-plane passes through the points \((7,1)\), \((0,4)\), and \((c,0)\). What is the value of \(c\)?

\(H=2.403L+23.31\) A group of biology students conducted an experiment to study the relationship between a person's femur length and the pe…

\(x(x+9)-15=0\) What are the solutions to the given equation?

The frequency histogram shows the distribution of the weights, in pounds, of 14 salmon in a data set. If an additional weight of 85 pounds …

In the figure shown, \(\overline{WZ}\) and \(\overline{XY}\) intersect at point \(Q\), \(YQ=36,\) \(WQ=90\), \(WX=70,\) and \(XQ=150.\) Wha…

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

The function \(T(x)=\frac{22,000-6.5x}{1,000}\) gives the estimated air temperature \(T(x)\) in degrees Celsius \((^{\circ}C)\), surroundin…

The function \(q\) is defined by \(q(x)=a|x-9|^{2}-87|x-9|+b\), where \(a\) and \(b\) are constants and \(a>b>87\). The graph of \(y=q(x)\)…

The graph of the linear function \(y=f(x)+13\) is shown. If \(c\) and \(d\) are positive constants, which equation could define \(f\)?

The functions \(f\) and \(g\) are defined by the equations below, where \(x \ge 0\). Which of the following equations displays, as a consta…

A set designer is hammering nails along the top edge of a wall. Starting at one end of the edge, the designer hammers a nail every \(\frac{…

The perimeter of an isosceles right triangle is \(52+52\sqrt{2}\) inches. What is the length, in inches, of the hypotenuse of this triangle?

The table shows three values of \(x\) and their corresponding values of \(g(x)\), where \(g(x)=\frac{f(x)}{x+3}\) and \(f\) is a linear fun…

In the figure shown, points A, B, C, and E lie on the circle, and \(AB < BC.\) Segment AC is perpendicular to segment BE at point D, and \(…

\(13x+50=180\) Which equation has the same solution as the given equation?