SAT Practice Questions

In triangle \(X Y Z\), angle \(Y\) is a right angle, point \(P\) lies on \(\overline{XZ}\), and point \(Q\) lies on \(\overline{YZ}\) such …

In convex pentagon \(A B C D E\), segment \(A B\) is parallel to segment \(D E\). The measure of angle \(B\) is \(139\) degrees, and the me…

Triangles \(P Q R\) and \(L M N\) are graphed in the xy -plane. Triangle \(P Q R\) has vertices \(P\), \(Q\), and \(R\) at \((4, 5)\), \((4…

In triangles \(L M N\) and \(R S T\), angles \(L\) and \(R\) each have measure \(60^{\circ}\), \(L N = 10\), and \(R T = 30\). Which additi…

\(y - 57 = p x\) The given equation relates the positive numbers \(p\), \(x\), and \(y\). Which equation correctly expresses \(y\) in terms…

\(\frac{x^{2}}{25} = 36\) What is a solution to the given equation?

\(\left|x - 2\right| = 9\) What is one possible solution to the given equation?

For the line in the system: The line slants sharply down from left to right. The line passes through the following points: (negative 2 comm…

\(x = 49\) \(y = \sqrt{x} + 9\) The graphs of the given equations intersect at the point \((x, y)\) in the xy -plane. What is the value of …

\(q - 29 r = s\) The given equation relates the positive numbers \(q\), \(r\), and \(s\). Which equation correctly expresses \(q\) in terms…

\(y = 76\) \(y = x^{2} - 5\) The graphs of the given equations in the xy -plane intersect at the point \((x, y)\). What is a possible value…

\(8 j = k + 15 m\) The given equation relates the distinct positive numbers \(j\), \(k\), and \(m\). Which equation correctly expresses \(j…

\(6 r = 7 s + t\) The given equation relates the variables \(r\), \(s\), and \(t\). Which equation correctly expresses \(s\) in terms of \(…

\((x + 2) (x - 5) (x + 9) = 0\) What is a positive solution to the given equation?

\(\frac{r}{38} = s + t\) The given equation relates the quantities \(r\), \(s\), and \(t\). Which equation correctly expresses \(r\) in ter…

\(x + 7 = 10\) \((x + 7)^{2} = y\) Which ordered pair \((x, y)\) is a solution to the given system of equations?

For the absolute value function in the system: Moving from left to right: The function slants sharply down to the point (negative 3 comma 4…

\(\left|x + 45\right| = 48\) What is the positive solution to the given equation?

For the curve in the system: Moving from left to right: The curve passes from quadrant 2 to quadrant 1. In quadrant 2, the curve trends up …

\(x^{2} = (22) (22)\) What is the positive solution to the given equation?

\(k^{2} - 53 = 91\) What is the positive solution to the given equation?

\(5 \left|x\right| = 45\) What is the positive solution to the given equation?

\(x = 3\) \(y = (15 - x)^{2}\) A solution to the given system of equations is \((x, y)\). What is the value of \(x y\)?

\(p + 34 = q + r\) The given equation relates the variables \(p\), \(q\), and \(r\). Which equation correctly expresses \(p\) in terms of \…

\(8 x^{2} - 40 = 32\) What is the positive solution to the given equation?

\(x + 5 = 14\) \(y = 4 x^{2} + 4\) At what point \((x, y)\) do the graphs of the equations in the given system intersect?

For the curve in the system: The curve passes from quadrant 2 to quadrant 1. In quadrant 2, the curve trends up gradually to the approximat…

For the parabola in the system: The parabola opens upward. The vertex is at point (4 comma 1). The parabola passes through the following po…

\(3 x^{2} - 15 x + 18 = 0\) How many distinct real solutions are there to the given equation?

\(\left|p\right| + 61 = 65\) Which value is a solution to the given equation?

\(7 m = 2 (n + p)\) The given equation relates the positive numbers \(m\), \(n\), and \(p\). Which equation correctly gives \(m\) in terms …

For the absolute value function: Moving from left to right: The function slants sharply down to the point (4 comma 2). The function then sl…

\(c - 7 = 25 p + k\) The given equation relates the positive numbers \(c\), \(p\), and \(k\). Which equation correctly expresses \(c\) in t…

\(b = 42 c f\) The given equation relates the positive numbers \(b\), \(c\), and \(f\). Which equation correctly expresses \(c\) in terms o…

\(\left|x - 5\right| = 10\) What is one possible solution to the given equation?

\(y = 5 x + 4\) \(y = 5 x^{2} + 4\) Which ordered pair \((x, y)\) is a solution to the given system of equations?

\(x = 8\) \(y = x^{2} + 8\) The graphs of the equations in the given system of equations intersect at the point \((x, y)\) in the xy -plane…

\(38 x^{2} = 38 (9)\) What is the negative solution to the given equation?

\(z^{2} + 10 z - 24 = 0\) What is one of the solutions to the given equation?

If \(4 \sqrt{2 x} = 16\), what is the value of \(6 x\)?

If \(\left|4 x - 4\right| = 112\), what is the positive value of \(x - 1\)?

\(- 4 x^{2} - 7 x = - 36\) What is the positive solution to the given equation?

\(14 j + 5 k = m\) The given equation relates the numbers \(j\), \(k\), and \(m\). Which equation correctly expresses \(k\) in terms of \(j…

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

\(y = 4 x\) \(y = x^{2} - 12\) A solution to the given system of equations is \((x, y)\), where \(x > 0\). What is the value of \(x\)?

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

\(5 x^{2} - 37 x - 24 = 0\) What is the positive solution to the given equation?

Which quadratic equation has exactly one distinct real solution?

\(x^{2} + y + 10 = 10\) \(8 x + 16 - y = 0\) The solution to the given system of equations is \((x, y)\). What is the value of \(x\)?

\(P = N (19 - C)\) The given equation relates the positive numbers \(P\), \(N\), and \(C\). Which equation correctly expresses \(C\) in ter…

\(y = x^{2} + 14 x + 48\) \(x + 8 = 11\) The solution to the given system of equations is \((x, y)\). What is the value of \(y\)?

\((5 x + 4) (2 x - 5) = 0\) Which of the following is a solution to the given equation?

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

\(3 x (x - 4) (x + 5) = 0\) What is one of the solutions to the given equation?

\(\frac{- 54}{w} = 6\) What is the solution to the given equation?

\(52 (x^{3} + 64) (x^{4} - 81) = 0\) How many distinct real solutions does the given equation have?

\(7 x^{2} - 20 x - 32 = 0\) What is the positive solution to the given equation?

\(p = \frac{k}{4 j + 9}\) The given equation relates the distinct positive numbers \(p\), \(k\), and \(j\). Which equation correctly expres…

\(\frac{(x + 9) (x - 9)}{x + 9} = 7\) What is the solution to the given equation?

\(b - 72 = \frac{x}{y}\) The given equation relates the positive numbers \(b\), \(x\), and \(y\). Which equation correctly expresses \(x\) …

\(x^{2} = - 841\) How many distinct real solutions does the given equation have?

\(7 m = 5 (n + p)\) The given equation relates the positive numbers \(m\), \(n\), and \(p\). Which equation correctly gives \(n\) in terms …

\(x^{2} - 12 x + 27 = 0\) How many distinct real solutions does the given equation have?

\((d - 30) (d + 30) - 7 = - 7\) What is a solution to the given equation?

\(x = 8 a (b + 9)\) The given equation relates the positive numbers \(a\), \(b\), and \(x\). Which equation correctly expresses \(a\) in te…

The equation \(12 t + b = c\) relates the variables \(t\), \(b\), and \(c\). Which of the following correctly expresses the value of \(c - …

\(v = - \frac{w}{150 x}\) The given equation relates the distinct positive numbers \(v\), \(w\), and \(x\). Which equation correctly expres…

\(y = (x - 2) (x + 4)\) \(y = 6 x - 12\) Which ordered pair \((x, y)\) is the solution to the given system of equations?

\(p = 20 + \frac{16}{n}\) The given equation relates the numbers \(p\) and \(n\), where \(n\) is not equal to \(0\) and \(p > 20\). Which e…

\(\frac{1}{7 b} = \frac{11 x}{y}\) The given equation relates the positive numbers \(b\), \(x\), and \(y\). Which equation correctly expres…

\(\frac{55}{x + 6} = x\) What is the positive solution to the given equation?

\(w^{2} + 12 w - 40 = 0\) Which of the following is a solution to the given equation?

\(x - 29 = (x - a) (x - 29)\) Which of the following are solutions to the given equation, where \(a\) is a constant and \(a > 30\)? I. \(a\…

In the \(xy\)-plane, a line with equation \(2y=4.5\) intersects a parabola at exactly one point. If the parabola has equation \(y=-4x^2+bx\…

\(5 x^{2} + 10 x + 16 = 0\) How many distinct real solutions does the given equation have?

\(- 9 x^{2} + 30 x + c = 0\) In the given equation, \(c\) is a constant. The equation has exactly one solution. What is the value of \(c\)?

\(y + k = x + 26\) \(y - k = x^{2} - 5 x\) In the given system of equations, \(k\) is a constant. The system has exactly one distinct real …

In the xy -plane, the graph of the equation \(y = - x^{2} + 9 x - 100\) intersects the line \(y = c\) at exactly one point. What is the val…

\(2 \left|4 - x\right| + 3 \left|4 - x\right| = 25\) What is the positive solution to the given equation?

\(x^{2} - 2 x - 9 = 0\) One solution to the given equation can be written as \(1 + \sqrt{k}\), where \(k\) is a constant. What is the value…

\((x - 47)^{2} = 1\) What is the sum of the solutions to the given equation?

\(- x^{2} + b x - 676 = 0\) In the given equation, \(b\) is a positive integer. The equation has no real solution. What is the greatest pos…

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

\(x^{2} + 7 x + 5 = 0\) One solution to the given equation can be written as \(x = \frac{- 7 + \sqrt{k}}{2}\), where \(k\) is a constant. W…

\(\left|- 5 x + 13\right| = 73\) What is the sum of the solutions to the given equation?

\(- 16 x^{2} - 8 x + c = 0\) In the given equation, \(c\) is a constant. The equation has exactly one solution. What is the value of \(c\)?

\(x^{2} - 34 x + c = 0\) In the given equation, \(c\) is a constant. The equation has no real solutions if \(c > n\). What is the least pos…

\(57 x^{2} + (57 b + a) x + a b = 0\) In the given equation, \(a\) and \(b\) are positive constants. The product of the solutions to the gi…

\(5 (x + 7) = 15 (x - 17) (x + 7)\) What is the sum of the solutions to the given equation?

If \(3 x^{2} - 18 x - 15 = 0\), what is the value of \(x^{2} - 6 x\)?

\(\left|x - 9\right| + 45 = 63\) What is the sum of the solutions to the given equation?

\(y = - 1.5\) \(y = x^{2} + 8 x + a\) In the given system of equations, \(a\) is a positive constant. The system has exactly one distinct r…

\(y = - 2.5\) \(y = x^{2} + 8 x + k\) In the given system of equations, \(k\) is a positive integer constant. The system has no real soluti…

\(\sqrt{k - x} = 58 - x\) In the given equation, \(k\) is a constant. The equation has exactly one real solution. What is the minimum possi…

\((x - 1)^{2} = - 4\) How many distinct real solutions does the given equation have?

\(\frac{x^{2}}{\sqrt{x^{2} - c^{2}}} = \frac{c^{2}}{\sqrt{x^{2} - c^{2}}} + 39\) In the given equation, \(c\) is a positive constant. Which…

\(64 x^{2} + b x + 25 = 0\) In the given equation, \(b\) is a constant. For which of the following values of \(b\) will the equation have m…

\(64 x^{2} - (16 a + 4 b) x + a b = 0\) In the given equation, \(a\) and \(b\) are positive constants. The sum of the solutions to the give…

\(x^{2} - 40 x - 10 = 0\) What is the sum of the solutions to the given equation?

In the xy -plane, a line with equation \(2 y = c\) for some constant \(c\) intersects a parabola at exactly one point. If the parabola has …