SAT Practice Questions

The student wants to provide a historical overview of the two theories. Which choice most effectively uses relevant information from the no…

The side lengths are labeled as follows: a b c The angle opposite the side labeled c is a right angle. For the right triangle shown, \(a = …

One angle is a right angle. The length of the side opposite the right angle is c. The lengths of the other 2 sides are as follows: 9 6 In t…

Triangle \(A B C\) is similar to triangle \(D E F\), where angle \(A\) corresponds to angle \(D\), and angles \(C\) and \(F\) are right ang…

One angle is a right angle. The measure of a second angle is x°. The length of the side opposite the right angle is 73. The length of the s…

One angle is a right angle. The length of the side opposite the right angle is 19. The lengths of the other 2 sides are as follows: b 4 Whi…

One angle is a right angle. The measure of the other 2 angles are as follows: 45° 45° The lengths of the 2 sides adjacent to the right angl…

One angle is a right angle. The lengths of the sides adjacent to the right angle are as follows: 3 7 The lengths of the legs of a right tri…

A right triangle has legs with lengths of \(11\) centimeters and \(9\) centimeters. What is the length of this triangle's hypotenuse, in ce…

Angle upper C is a right angle. The length of side upper A upper B is 171. The length of side upper B upper C is 35. In the right triangle …

One angle is a right angle. The measure of a second angle is x°. The length of the leg opposite the angle with measure x° is 26. The length…

One angle is a right angle. The length of the side opposite the right angle is 21. The length of one side adjacent to the right angle is 6.…

A right triangle has legs with lengths of \(28\) centimeters and \(20\) centimeters. What is the length of this triangle's hypotenuse, in c…

Angle upper Z is a right angle. The length of side upper X upper Z is 27. The length of side upper Y upper Z is 35. Triangle \(X Y Z\) show…

One leg of a right triangle has a length of \(43.2\) millimeters. The hypotenuse of the triangle has a length of \(196.8\) millimeters. Wha…

One angle is a right angle. The measure of a second angle is x°. The lengths of the 2 sides adjacent to the right angle are as follows: 15 …

Triangle \(F G H\) is similar to triangle \(J K L\), where angle \(F\) corresponds to angle \(J\) and angles \(G\) and \(K\) are right angl…

In right triangle \(R S T\), the sum of the measures of angle \(R\) and angle \(S\) is \(90\) degrees. The value of \(\sin (R)\) is \(\frac…

In \(\triangle ABC\), \(\angle B\) is a right angle and the length of \(\overline{BC}\) is \(136\) millimeters. If \(\cos A = \frac{3}{5}\)…

One angle is a right angle. The measure of a second angle is x°. The lengths of the 2 sides adjacent to the right angle are as follows: 32 …

The length of a rectangle’s diagonal is \(5\sqrt{17}\), and the length of the rectangle’s shorter side is \(5\). What is the length of the …

Angle upper A upper C upper B is a right angle. The length of side upper A upper B is 42. The length of side upper A upper C is 41. What is…

Angle upper R is a right angle. The length of side upper R upper S is 18. In triangle \(Q R S\) shown, \(Q R < R S\). Which expression repr…

The perimeter of an equilateral triangle is \(624\) centimeters. The height of this triangle is \(k \sqrt{3}\) centimeters, where \(k\) is …

\(R S = 20\) \(S T = 48\) \(T R = 52\) The side lengths of right triangle \(R S T\) are given. Triangle \(R S T\) is similar to triangle \(…

Which of the following expressions is equivalent to \((\sin 24^{\circ}) (\cos 66^{\circ}) + (\cos 24^{\circ}) (\sin 66^{\circ})\)?

In triangle \(X Y Z\), the measure of angle \(X\) is \(90^{\circ}\). Point \(W\) lies on segment \(Y Z\), and segment \(W X\) is perpendicu…

Triangle \(A B C\) is similar to triangle \(D E F\), where angle \(A\) corresponds to angle \(D\) and angle \(C\) corresponds to angle \(F\…

A square is inscribed in a circle. The radius of the circle is \(\frac{20 \sqrt{2}}{2}\) inches. What is the side length, in inches, of the…

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…

Angle upper S is a right angle. The length of side upper R upper T is 53. In the triangle shown, \(R S = \sqrt{105}\). What is the value of…

Triangle \(A B C\) is similar to triangle \(D E F\), where angle \(A\) corresponds to angle \(D\) and angles \(C\) and \(F\) are right angl…

In triangle \(X Y Z\), angle \(Y\) is a right angle, the measure of angle \(Z\) is \(33^{\circ}\), and the length of \(\overline{YZ}\) is \…

One angle is a right angle. The measure of a second angle is x°. The length of the hypotenuse is 23. The length of the leg opposite the ang…

A right triangle has legs with lengths of \(24\) centimeters and \(21\) centimeters. If the length of this triangle's hypotenuse, in centim…

In triangle \(X Y Z\), angle \(Z\) is a right angle and the length of \(\overline{YZ}\) is \(24\) units. If \(\tan X = \frac{12}{35}\), wha…

In triangle \(A B C\), angle \(B\) is a right angle. The length of side \(A B\) is \(10 \sqrt{37}\) and the length of side \(B C\) is \(24 …

The perimeter of an equilateral triangle is \(852\) centimeters. The three vertices of the triangle lie on a circle. The radius of the circ…

A rectangle is inscribed in a circle, such that each vertex of the rectangle lies on the circumference of the circle. The diagonal of the r…

An isosceles right triangle has a perimeter of \(94 + 94 \sqrt{2}\) inches. What is the length, in inches, of one leg of this triangle?

\(R S = 440\) \(S T = 384\) \(T R = 584\) The side lengths of right triangle \(R S T\) are given. Triangle \(R S T\) is similar to triangle…

One angle is a right angle. The measure of a second angle is x°. The length of the hypotenuse is 28. The length of the leg adjacent to the …

An isosceles right triangle has a hypotenuse of length \(58\) inches. What is the perimeter, in inches, of this triangle?

In triangle \(J K L\), \(\cos (K) = \frac{24}{51}\) and angle \(J\) is a right angle. What is the value of \(\cos (L)\)?

The length of side upper A upper B is 54. The measure of angle upper B is 30°. Angle upper C is a right angle. Right triangle \(A B C\) is …

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

Triangle \(A B C\) is similar to triangle \(D E F\), where \(A\) corresponds to \(D\) and \(C\) corresponds to \(F\). Angles \(C\) and \(F\…

For two acute angles, \(\angle Q\) and \(\angle R\), \(\cos (Q) = \sin (R)\). The measures, in degrees, of \(\angle Q\) and \(\angle R\) ar…

\(4 x = 20\) \(- 3 x + y = - 7\) The solution to the given system of equations is \((x, y)\). What is the value of \(x + y\)?

\(y = 12 x - 20\) \(y = 28\) What is the solution \((x, y)\) to the given system of equations?

\(4 x - 3 y = 5\) \(x = 8\) What is the solution \((x, y)\) to the given system of equations?

Connor has \(c\) dollars and Maria has \(m\) dollars. Connor has \(4\) times as many dollars as Maria, and together they have a total of \(…

For the first line in the system: The line slants gradually down from left to right. The line passes through the following points: (negativ…

\(s + 7 r = 27\) \(r = 3\) What is the solution \((r, s)\) to the given system of equations?

\(x = 5\) \(y = x - 8\) Which of the following points \((x, y)\) is the solution to the given system of equations in the xy -plane?

For the first line in the system: The line slants sharply down from left to right. The line passes through the following points: (0 comma 8…

\(x = 4\) \(y = 5 - x\) The solution to the given system of equations is \((x, y)\). What is the value of \(y\)?

\(10 x = 110\) \(6 x - 63 = y\) The solution to the given system of equations is \((x, y)\). What is the value of \(y\)?

\(x = 8\) \(x + 3 y = 26\) The solution to the given system of equations is \((x, y)\). What is the value of \(y\)?

\(y = 4 x - 9\) \(y = 19\) What is the solution \((x, y)\) to the given system of equations?

\(3 x = 12\) \(- 3 x + y = - 6\) The solution to the given system of equations is \((x, y)\). What is the value of \(y\)?

\(5 x = 15\) \(- 4 x + y = - 2\) The solution to the given system of equations is \((x, y)\). What is the value of \(x + y\)?

For the first line in the system: The line slants gradually down from left to right. The line passes through the following points: (0 comma…

For the first line in the system: The line slants gradually down from left to right. The line passes through the following points: (0 comma…

\(x + y = 125\) \(x + y + y = 155\) The solution to the given system of equations is \((x, y)\). What is the value of \(y\)?

\(y = - 3 x\) \(4 x + y = 15\) The solution to the given system of equations is \((x, y)\). What is the value of \(x\)?

For the first line in the system: The line is horizontal. The line passes through the following points: (negative 4 comma 3) (0 comma 3) (2…

\(x = 10\) \(y = x + 21\) The solution to the given system of equations is \((x, y)\). What is the value of \(y\)?

For the first line in the system: The line slants sharply down from left to right. The line passes through the following points: (0 comma 3…

\(y = 4\) \(x = y + 6\) The solution to the given system of equations is \((x, y)\). What is the value of \(x\)?

\(x + y = 18\) \(5 y = x\) What is the solution \((x, y)\) to the given system of equations?

For the first line in the system: The line slants sharply down from left to right. The line passes through the following points: (4 comma 1…

\(y = - \frac{1}{9} x\) \(y = \frac{1}{2} x\) The solution to the given system of equations is \((x, y)\). What is the value of \(x\)?

\(y = 2 x + 10\) \(y = 2 x - 1\) At how many points do the graphs of the given equations intersect in the xy -plane?

\(y = 6 x + 3\) One of the two equations in a system of linear equations is given. The system has infinitely many solutions. Which equation…

Two customers purchased the same kind of bread and eggs at a store. The first customer paid \(12.45\) dollars for \(1\) loaf of bread and \…

\(6 x + 7 y = 28\) \(2 x + 2 y = 10\) The solution to the given system of equations is \((x, y)\). What is the value of y ?

\(2 a + 8 b = 198\) \(2 a + 4 b = 98\) The solution to the given system of equations is \((a, b)\). What is the value of \(b\)?

\(3 y = 4 x + 17\) \(- 3 y = 9 x - 23\) The solution to the given system of equations is \((x, y)\). What is the value of \(39 x\)?

A bus traveled on the highway and on local roads to complete a trip of \(160\text{ miles}\). The trip took \(4\text{ hours}\). The bus trav…

At how many points do the graphs of the equations \(y = x + 20\) and \(y = 8 x\) intersect in the xy -plane?

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

The combined original price for a mirror and a vase is \(\$ 60\). After a \(25 \%\) discount to the mirror and a \(45 \%\) discount to the …

A proposal for a new library was included on an election ballot. A radio show stated that \(3\) times as many people voted in favor of the …

A company that provides whale-watching tours takes groups of \(21\) people at a time. The company’s revenue is \(80\) dollars per adult and…

\(y = \frac{1}{3} x - 14\) \(y = - x + 18\) The solution to the given system of equations is \((x, y)\) . What is the value of \(x\)?

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

\(y = 3 x + 9\) \(3 y = 8 x - 6\) The solution to the given system of equations is \((x, y)\). What is the value of \(x - y\)?

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

\(x + 3 y = 29\) \(3 y = 11\) The solution to the given system of equations is \((x, y)\). What is the value of \(x\)?

\(y - 9 x = 13\) \(5 x = 2 y\) What is the solution \((x, y)\) to the given system of equations?

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

\(8 x + y = 5\) \(y = 9 x + 1\) The solution to the given system of equations is \((x, y)\). What is the value of \(x\)?

\(x + 3 = - 2 y + 5\) \(x - 3 = 2 y + 7\) The solution to the given system of equations is \((x, y)\). What is the value of \(2 x\)?

\(x + 2 y = 6\) \(x - 2 y = 4\) The solution to the given system of equations is \((x, y)\). What is the value of \(x\)?

Which of the following systems of linear equations has no solution?

A wire with a length of \(106\) inches is cut into two parts. One part has a length of \(x\) inches, and the other part has a length of \(y…

\(3 x + 6 = 4 y\) \(3 x + 4 = 2 y\) The solution to the given system of equations is \((x, y)\). What is the value of \(y\)?

The sum of a number \(x\) and \(7\) is twice as large as a number \(y\). The number \(y\) is \(3\) less than the number \(x\). Which system…

\(- 15 x + 25 y = 65\) One of the two equations in a system of linear equations is given. The system has infinitely many solutions. Which o…