Free SAT Math Level 2 Subject Test Practice Questions with Answers - Sample 1

50 SAT Math subject level 2 sample questions with answers, similar to actual SAT math test questions. Detailed solutions with full explanations are available at the solutions page.

Two dice are tossed. What is the probability that the sum of the two dice is greater than 3?
A) \(\frac{1}{4}\)
B) \(\frac{3}{4}\)
C) \(\frac{5}{6}\)
D) \(\frac{11}{12}\)
E) \(1\)
Solution on Video
If \(L\) is a line through the points \((2,5)\) and \((4,6)\), what is the value of \(k\) so that the point \((7,k)\) is on the line \(L\)?
A) \(0\)
B) \(5\)
C) \(6\)
D) \(\frac{15}{2}\)
E) \(11\)
Solution on Video
Find a negative value of \(k\) so that the graph of \(y = x^2 - 2x + 7\) and the graph of \(y = kx + 5\) are tangent.
A) \(-4\sqrt{2}\)
B) \(-2 - 2\sqrt{2}\)
C) \(-2\)
D) \(-\sqrt{2}\)
E) \(-2 + \sqrt{2}\)
Solution on Video
Which of these graphs is closest to the graph of \[f(x) = \frac{|4 - x^2|}{x + 2}\]
The circle \((x - 3)^2 + (y - 2)^2 = 1\) has center \(C\). Point \(M(4,2)\) is on the circle. \(N\) is another point on the circle so that angle \(MCN\) is \(30^\circ\). Find the coordinates of \(N\).

A) \(\left(3 + \frac{\sqrt{3}}{2}, \frac{5}{2}\right)\)
B) \(\left(\frac{5}{2}, 3 + \frac{\sqrt{3}}{2}\right)\)
C) \(\left(3 - \frac{\sqrt{3}}{2}, \frac{3}{2}\right)\)
D) \(\left(\frac{3}{2}, 3 - \frac{\sqrt{3}}{2}\right)\)
E) \((4, 3)\)
Solution on Video
Vectors \(\mathbf{u}\) and \(\mathbf{v}\) are given by \(\mathbf{u} = (2, 0)\) and \(\mathbf{v} = (-3, 1)\). What is the length of vector \(\mathbf{w} = -\mathbf{u} - 2\mathbf{v}\)?
A) \(10\)
B) \(6\)
C) \(\sqrt{26}\)
D) \(2\sqrt{5}\)
E) \(2\)
Solution on Video
What is the smallest distance between the point \((-2,-2)\) and a point on the circumference of the circle given by \[(x - 1)^2 + (y - 2)^2 = 4\]
A) \(3\)
B) \(4\)
C) \(5\)
D) \(6\)
E) \(7\)
Solution on Video
What is the equation of the horizontal asymptote of the function \[f(x) = \frac{2}{x + 2} - \frac{x + 3}{x + 4}\]
A) \(-4\)
B) \(-2\)
C) \(-1\)
D) \(0\)
E) \(1\)
The lines \(x + 3y = 2\) and \(-2x + ky = 5\) are perpendicular for \(k =\)
A) \(-3\)
B) \(-2\)
C) \(-1\)
D) \(0\)
E) \(\frac{2}{3}\)
If \(f(x) = (x - 1)^2\) and \(g(x) = \sqrt{x}\), then \((g \circ f)(x) =\)
A) \(|x - 1|\)
B) \(x - 1\)
C) \(1 - x\)
D) \(\sqrt{x}(x - 1)^2\)
E) \((\sqrt{x} - 1)^2\)
The domain of \(f(x) = \frac{\sqrt{4 - x^2}}{\sqrt{x^2 - 1}}\) is given by the interval
A) \((-2, 2)\)
B) \((-1, 2)\)
C) \((-2, -1) \cup (1, 2)\)
D) \((-2, 2) \cup (-1, 1)\)
E) \([-2, -1) \cup (1, 2]\)
The area of the circle \(x^2 + y^2 - 8y - 48 = 0\) is
A) \(96\pi\)
B) \(64\pi\)
C) \(48\pi\)
D) \(20\pi\)
E) \(\pi\)
Solution on Video
The \(y\)-coordinates of all intersection points of the parabola \(y^2 = x + 2\) and the circle \(x^2 + y^2 = 4\) are given by
A) \(2, -2\)
B) \(0\)
C) \(0, \sqrt{3}, -\sqrt{3}\)
D) \(1, 2, -1\)
E) \(1, -2, 1\)
What is the smallest positive zero of \(f(x) = \frac{1}{2} - \sin\left(3x + \frac{\pi}{3}\right)\)?
A) \(\pi\)
B) \(\frac{\pi}{3}\)
C) \(\frac{\pi}{6}\)
D) \(\frac{\pi}{18}\)
E) \(\frac{\pi}{36}\)
If \(x - 1\), \(x - 3\), and \(x + 1\) are all factors of a cubic polynomial \(P(x)\), which must also be a factor?
I) \(x^2 + 1\)
II) \(x^2 - 1\)
III) \(x^2 - 4x + 3\)
A) II and III only
B) I and II only
C) III only
D) II only
E) I only
A cylinder of radius 5 cm is inside a cylinder of radius 10 cm. Both have height 20 cm. What is the volume between them?
A) \(1000\)
B) \(500\pi\)
C) \(1000\pi\)
D) \(1500\pi\)
E) \(2000\pi\)
A data set has standard deviation 1. If each value is multiplied by 4, the new standard deviation is
A) \(0.25\)
B) \(0.50\)
C) \(1\)
D) \(2\)
E) \(4\)
A cardboard cone has height 8 cm and radius 6 cm. If cut along the slant height to form a sector, what is its central angle in degrees?
A) \(216\)
B) \(180\)
C) \(90\)
D) \(36\)
E) \(1.2\)
If \(\sin x = -\frac{1}{3}\) and \(\pi \le x \le \frac{3\pi}{2}\), then \(\cot(2x) =\)
A) \(8\)
B) \(4\sqrt{2}\)
C) \(2\sqrt{2}\)
D) \(\sqrt{2}\)
E) \(\frac{7}{4\sqrt{2}}\)
Which functions satisfy \(f(x) = f^{-1}(x)\)?
I) \(f(x) = -x\)
II) \(f(x) = \sqrt{x}\)
III) \(f(x) = -\frac{1}{x}\)
A) III and II only
B) III and I only
C) III only
D) II only
E) I only
If \(f(x) = \frac{1}{x - 2}\), which graph is closest to \(|f(x)|\)?
In triangle \(ABC\), \(\sin A = \frac{1}{5}\), \(\cos B = \frac{2}{7}\). Then \(\cos C =\)
A) \(\frac{\sqrt{45} - 2\sqrt{24}}{35}\)
B) \(\frac{\sqrt{45} + 2\sqrt{24}}{35}\)
C) \(\frac{7\sqrt{24} + 10}{35}\)
D) \(0.85\)
E) \(1\)
Find the sum: \[\sum_{k=1}^{100} (3 + k)\]
A) \(300\)
B) \(5050\)
C) \(5300\)
D) \(5350\)
E) \(5400\)
What \(x\) makes \(x\), \(\frac{x}{x+1}\), \(\frac{3x}{(x+1)(x+2)}\) a geometric sequence?
A) \(2\)
B) \(1\)
C) \(\frac{1}{2}\)
D) \(\frac{1}{4}\)
E) \(-\frac{1}{2}\)
As \(x\) increases from \(\frac{\pi}{4}\) to \(\frac{3\pi}{4}\), \(|\sin(2x)|\)
A) always increases
B) always decreases
C) increases then decreases
D) decreases then increases
E) constant
When \(ax^3 + bx^2 + cx + d\) is divided by \(x - 2\), the remainder equals
A) \(d\)
B) \(a - b + c - d\)
C) \(8a + 4b + 2c + d\)
D) \(-8a + 4b - 2c + d\)
E) \(a + b + c + d\)
A committee of 6 is formed from 5 male and 8 female teachers randomly. Probability of equal gender representation:
A) \(\frac{1}{10}\)
B) \(\frac{140}{429}\)
C) \(\frac{150}{429}\)
D) \(\frac{160}{429}\)
E) \(\frac{170}{429}\)
The range of \(f(x) = -|x - 2| - 3\) is
A) \(y \ge 2\)
B) \(y \le -3\)
C) \(y \ge -3\)
D) \(y \le -2\)
E) \(y \ge -2\)
The period of \(f(x) = 3 \sin^2(2x + \frac{\pi}{4})\) is
A) \(4\pi\)
B) \(3\pi\)
C) \(\pi\)
D) \(\frac{\pi}{2}\)
E) \(\frac{\pi}{3}\)
3 out of 10 TVs are defective. If 2 are selected randomly, probability exactly 1 is defective:
A) \(\frac{7}{15}\)
B) \(\frac{1}{10}\)
C) \(\frac{1}{2}\)
D) \(\frac{1}{3}\)
E) \(1\)
In triangle \(ABC\), \(B = 50^\circ\), \(A = 32^\circ\), \(BC = 150\). Length of \(AB\):
A) \(232\)
B) \(250\)
C) \(260\)
D) \(270\)
E) \(280\)
For \(x^3 - 2x^2 + 3kx + 18\) divided by \(x - 6\) to have zero remainder, \(k =\)
A) \(0\)
B) \(1\)
C) \(5\)
D) \(-9\)
E) \(-10\)
Pump A empties a pool in 4 hours, pump B in 6 hours. Together, time to empty 50%:
A) 1 hour 12 min
B) 1 hour 20 min
C) 2 hours 30 min
D) 3 hours
E) 5 hours
The graph of \(r = 10 \cos \theta\) in polar coordinates is
A) a circle
B) an ellipse
C) a horizontal line
D) a hyperbola
E) a vertical line
If \((2 - i)(a - bi) = 2 + 9i\), with \(a,b\) real, then \(a =\)
A) \(3\)
B) \(2\)
C) \(1\)
D) \(0\)
E) \(-1\)
Perpendicular lines \(L_1\) and \(L_2\) intersect at \((2,3)\). If \(L_1\) passes through \((0,2)\), \(L_2\) must pass through:
A) \((0,3)\)
B) \((1,1)\)
C) \((3,1)\)
D) \((5,0)\)
E) \((6,7)\)
A square pyramid inscribed in a cube with surface area 24 cm². Pyramid volume:

A) \(\frac{1}{3}\)
B) \(\frac{8}{3}\)
C) \(6\)
D) \(4\)
E) \(8\)
The graph defined by \(x = \cos^2 t\), \(y = 3 \sin t - 1\) is
A) a circle
B) a hyperbola
C) a vertical line
D) part of a parabola
E) an ellipse
A) \(33\)
B) \(32\)
C) \(30\)
D) \(1\)
E) \(0\)
For \(x > 0\), \(x \ne 1\), \(\log_{16}(x) =\)
A) \(8 \log_2(x)\)
B) \(4 \log_2(x)\)
C) \(0.5 \log_2(x)\)
D) \(0.25 \log_2(x)\)
E) \(0.125 \log_2(x)\)
The value of \(k\) making \(f(x)\) continuous:

A) \(\frac{1}{3}\)
B) \(1\)
C) \(2\)
D) \(5\)
E) \(6\)
If \(\log_b(a) = x\), \(\log_b(c) = y\), and \(4x + 6y = 8\), then \(\log_b(a^2 \cdot c^3) =\)
A) \(0\)
B) \(1\)
C) \(2\)
D) \(3\)
E) \(4\)
The point \((0, -2, 5)\) lies on the
A) \(z\)-axis
B) \(x\)-axis
C) \(xy\)-plane
D) \(yz\)-plane
E) \(xz\)-plane
Curve \(C: y = \sqrt{9 - x^2}, x \ge 0\). Area bounded by \(C\), x-axis, and y-axis:
A) \(\frac{\pi}{4}\)
B) \(\frac{9\pi}{4}\)
C) \(\frac{9\pi}{2}\)
D) \(9\pi\)
E) \(\frac{81\pi}{4}\)
In a plane, 6 points with no three collinear. How many triangles?
A) \(2\)
B) \(3\)
C) \(6\)
D) \(18\)
E) \(20\)
Find \(a, b, c\).
A) \(2, -1, 3\)
B) \(1, -2, 3\)
C) \(3, -2, 1\)
D) \(1, 2, 3\)
E) \(1, 2, -3\)
Sum of repeating decimals \(0.\overline{35} + 0.\overline{25}\) as a fraction in lowest terms. Product of numerator and denominator:
A) \(3465\)
B) \(2475\)
C) \(680\)
D) \(670\)
E) \(660\)
\(\sin(\tan^{-1} \sqrt{2}) =\)
A) \(0.82\)
B) \(0.83\)
C) \(0.84\)
D) \(0.85\)
E) \(0.86\)
If \(8^x = 2\) and \(3^{x+y} = 81\), then \(y =\)
A) \(\frac{1}{3}\)
B) \(\frac{9}{3}\)
C) \(\frac{11}{3}\)
D) \(\frac{13}{3}\)
E) \(4\)
Let \(f(x) = -\frac{x^2}{2}\). If the graph is translated 2 units up and 3 units left to get \(g(x)\), then \(g\left(\frac{1}{2}\right) =\)
A) \(0\)
B) \(-\frac{1}{8}\)
C) \(-\frac{2}{8}\)
D) \(-\frac{33}{8}\)
E) \(\frac{13}{8}\)

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