Convert \(4 \times 10^{-5}\) to decimal form:
A) -40,000
B) -200
C) 0.0004
D) 0.00004
E) 0.20
Which of the following is equivalent to \((x)(x)(x)(x^3)\), for all \(x\)?
A) \(4x\)
B) \(6x\)
C) \(x^6\)
D) \(4x^6\)
E) \(4x^4\)
There are 15 balls in a box: 8 green, 4 blue, and 3 white. One green ball and one blue ball are removed. If a ball is then selected at random from the remaining balls, what is the probability that it is blue?
A) \(\dfrac{3}{13}\)
B) \(\dfrac{4}{15}\)
C) \(\dfrac{3}{15}\)
D) \(\dfrac{4}{13}\)
E) \(\dfrac{2}{13}\)
The length of a rectangle is 3 times its width. If the width is 5 inches, what is the area of the rectangle in square inches?
A) 15
B) 20
C) 30
D) 75
E) 40
For all \(x>2\), simplify \(\dfrac{2x^2 + 2x - 12}{x-2}\):
A) \(2(x-2)\)
B) \(x+3\)
C) \(2(x+3)(x-2)\)
D) \(x-2\)
E) \(2(x+3)\)
If the hypotenuse of a right triangle is 10 inches and one leg is 5 inches, find the length of the other leg.
A) 5
B) \(5\sqrt{3}\)
C) \(5\sqrt{5}\)
D) 75
E) \(10 - \sqrt{5}\)
In the standard \((x,y)\) coordinate plane, the graph of \((x+3)^2 + (y+5)^2 = 16\) is a circle. What is the circumference of the circle?
A) \(4\pi\)
B) \(5\pi\)
C) \(3\pi\)
D) \(8\pi\)
E) \(25\pi\)
How many solutions are there to the equation \(x^2 - 7 = 0\)?
A) 1
B) 2
C) 4
D) 7
E) 14
A circle with center \((4,-5)\) is tangent to the y-axis. What is the radius of this circle?
A) 4
B) 5
C) \(\sqrt{41}\)
D) 16
E) 25
Angle \(A\) is acute and \(\sin(A) = \dfrac{11}{14}\). Find \(\cos(A)\).
A) \(\dfrac{3}{14}\)
B) \(\dfrac{\sqrt{3}}{14}\)
C) \(\dfrac{5\sqrt{3}}{14}\)
D) \(\sqrt{\dfrac{3}{14}}\)
E) \(\dfrac{5}{14}\)
Find the values of \(a\) and \(b\) satisfying \(-a|b+4|>0\).
A) \(a>0\) and \(b \ne -4\)
B) \(a>0\) and \(b \ne 4\)
C) \(a<0\) and \(b \ge -4\)
D) \(a<0\) and \(b \ne -4\)
E) \(a<0\) and \(b \le -4\)
In a shipment of televisions, \( \dfrac{1}{50} \) are defective. What is the ratio of defective to non-defective TVs?
A) \(\dfrac{1}{200}\)
B) \(\dfrac{1}{50}\)
C) \(\dfrac{1}{49}\)
D) \(\dfrac{49}{1}\)
E) \(\dfrac{50}{1}\)
Which of the following numbers is divisible by 4?
A) 214133
B) 510056
C) 322569
D) 952217
E) 214395
A particle travels \(1 \times 10^6\) meters per second for \(5 \times 10^{-6}\) seconds. How many meters has it traveled?
A) \(2 \times 10^{11}\)
B) \(5 \times 10^{12}\)
C) \(5 \times 10^{-12}\)
D) 5
E) \(5 \times 10^{-36}\)
The length of sides AB and AC in the triangle below are equal. What is the measure of \(\angle A\)?
A) 70°
B) 55°
C) 40°
D) 110°
E) 20°
ABC is an equilateral triangle. AH is perpendicular to BC and has length \(2\sqrt{3}\) inches. Find the area of \(\triangle ABC\).
A) 12
B) \(2\sqrt{3}\)
C) \(4\sqrt{3}\)
D) \(8\sqrt{3}\)
E) cannot be determined
If \(8y = 3x - 11\), then \(x = ?\)
A) \(\dfrac{88}{3}y\)
B) \(\dfrac{8}{3}y + 11\)
C) \(\dfrac{8}{3}y - 11\)
D) \(\dfrac{8y - 11}{3}\)
E) \(\dfrac{8y + 11}{3}\)
Solve for \(x\) in \(-2(x+8) = -2x + 20\). Which statement describes the solution set?
A) \(x=-2\) only
B) \(x=0\) only
C) \(x=20\) only
D) no solution
E) all real numbers
At what point do the lines \(2x+3y=5\) and \(x=-2\) intersect?
A) (-2,0)
B) (-2,5)
C) (0,5/3)
D) (0,5)
E) (-2,3)
The area of a trapezoid is \(A = \dfrac{1}{2} h (b_1 + b_2)\). If \(h=15\), \(A=105\), and \(b_1=22\), find the perimeter.
A) 8
B) 45
C) 60
D) 30
E) Does not exist
If you drive at 66 mph, how many miles do you travel in 99 minutes?
A) 1.5
B) 0.7
C) 65.34
D) 108.9
E) 150
If \(0 < x < 2 < y\), which must be true?
A) \(x < \dfrac{xy}{2} < y\)
B) \(0 < xy < 2x\)
C) \(x < xy < 2\)
D) \(0 < xy < 2\)
E) \(xy < y\)
In the right triangle below, what is \(\cos A\)?
A) 3/4
B) 4/3
C) 5/4
D) 3/5
E) 4/5
The graph of \(y = \dfrac{2}{x-3}\) is shown. Which is the best graphical representation of \(y = \dfrac{-2}{|x-3|}\)?
What is the slope of the line:
\(4x = -3y + 8\)
A) 4
B) \(-\dfrac{3}{4}\)
C) \(-\dfrac{4}{3}\)
D) 2
E) 8
In the figure below, \(B\) is on \(\overline{AD}\), \(\angle BAC = 26^\circ\) and \(\angle ACB = 131^\circ\). What is the measure of \(\angle CBD\)?
A) \(26^\circ\)
B) \(157^\circ\)
C) \(23^\circ\)
D) \(154^\circ\)
E) \(49^\circ\)
Which of the following is equal to \(\sqrt{45}\)?
A) 15
B) \(5\sqrt{3}\)
C) \(9\sqrt{5}\)
D) \(3\sqrt{5}\)
E) 3
What is the smallest value of \(x\) that satisfies the equation:
\(x(x+4) = -3\)
A) -1
B) 0
C) 1
D) 3
E) -3
A group of 7 friends are having lunch together. Each eats at least \(\dfrac{3}{4}\) of a pizza. What is the minimum number of whole pizzas needed?
A) 7
B) 5
C) 6
D) 28
E) 21
All axes have the same scale. Which graph shows the graph of \(y = -2x + 2\)?
The measures of angles \(A, B, C\) of a triangle are in the ratio \(3:4:5\). What is the largest angle?
A) \(75^\circ\)
B) \(15^\circ\)
C) \(12^\circ\)
D) \(90^\circ\)
E) \(60^\circ\)
There are \(n\) students. If \(r\%\) are 12 years or younger, which expression gives the number older than 12?
A) \(nr/100\)
B) \(n(1-r)\)
C) \(100(1-r)n\)
D) \(\dfrac{n(1-r)}{100}\)
E) \(\dfrac{n(100-r)}{100}\)
If \(x+4y = 5\) and \(5x+6y = 7\), then \(3x+5y = ?\)
A) 12
B) 6
C) 4
D) 2
E) 1
Which integer is nearest to \(\dfrac{\sqrt{2100}}{\sqrt{7}}\)?
A) 3
B) 30
C) 43
D) 150
E) 17
For all real \(x\), what is the minimum of \(1 + 2\cos(4x)\)?
A) 0
B) 1
C) -1
D) -2
E) -4
What is the largest possible product of two odd integers whose sum is 32?
A) 34
B) 64
C) 255
D) 256
E) 1024
If \((a+b)^2 = 25\) and \((a-b)^2 = 45\), find \(a^2 + b^2\).
A) 35
B) 70
C) 625
D) 2025
E) 4900
If \(a = 3\), evaluate \(\dfrac{2}{\dfrac{1}{7} + \dfrac{1}{a}}\).
A) 5
B) \(\dfrac{21}{10}\)
C) 20
D) 10
E) \(\dfrac{21}{5}\)
A company makes a profit equal to 25% of sales. The profit is divided equally among 4 owners. If sales = \$5,000,000, how much per owner?
A) 12,500
B) 312,500
C) 500,000
D) 1,250,000
E) 12,500,000
If \(x^3 + 2hx - 2 = 6\) when \(x=-2\), what is \(h\)?
A) 0
B) -2
C) -4
D) 4
E) 6
If \(-\dfrac{3}{a-3} = \dfrac{3}{a+2}\), find \(a\).
A) -3
B) -2
C) \(\dfrac{1}{2}\)
D) 2
E) 3
For what negative \(k\) does the system have no solutions?
\(2x + ky = 5\) \(kx + (k+4)y = 7\)
A) -2
B) -5
C) -4
D) -7
E) -1
The two legs of a right triangle measure 6 and 8 inches. What is the area of the circle passing through all vertices?
A) \(24\pi\)
B) \(25\pi\)
C) \(36\pi\)
D) \(64\pi\)
E) \(48\pi\)
If \(X\) and \(Y\) are acute angles such that \(\tan Y = \cot X\), what is \(X + Y\) in degrees?
A) \(90^\circ\)
B) \(45^\circ\)
C) \(60^\circ\)
D) \(30^\circ\)
E) \(120^\circ\)
The measures of the sides of the right triangle below are in inches. What is the value of \(x\)?
A) \(\dfrac{1}{\sqrt{3}}\)
B) \(\sqrt{2}\)
C) \(\sqrt{3}\)
D) \(\dfrac{6}{\sqrt{3}}\)
E) \(\dfrac{2}{\sqrt{3}}\)
Which of the graphs below is the solution set of \(-3x \le 12\)?
Which of the following lines is not parallel to \(6x - 2y = 10\)?
A) \(3x - y = 7\)
B) \(-6x + 2y = 20\)
C) \(3x + y = 7\)
D) \(6x - 2y = 5\)
E) \(x - \dfrac{y}{3} = 9\)
For what value of \(k\) does the equation below have no solutions?
\(2x + 3 = x - 2kx - 5\)
A) 1
B) 2
C) -1
D) 0.5
E) -0.5
\(|5 - 2| - |6 - 9| = ?\)
A) 6
B) 0
C) -8
D) 22
E) -6
What is the average of \(\dfrac{7}{8}\) and \(\dfrac{3}{4}\)?
A) \(\dfrac{13}{8}\)
B) \(\dfrac{5}{6}\)
C) \(\dfrac{5}{3}\)
D) \(\dfrac{5}{12}\)
E) \(\dfrac{13}{16}\)
A solution is made of water and pure acid. If 75% of the solution is water, how many liters of pure acid are in 20 liters?
A) 10
B) 15
C) 25
D) 5
E) 20
The total surface area of all six sides of this rectangular box is 128 in². What is \(x\)?
A) 6
B) 4
C) 16
D) 8
E) 12
The diagonal of a square measures 12 inches. What is the perimeter?
A) \(6\sqrt{2}\)
B) 72
C) \(24\sqrt{2}\)
D) 144
E) 48
The lengths in the rectangle below are in inches. What is the shaded area?
A) 70
B) 34
C) 21
D) 8
E) 38
In the right triangle \(ABC\), \(C\) is right and \(\angle B = 60^\circ\). If \(\overline{BC} = 20\) in, how long is \(\overline{AC}\)?
A) \(20\sqrt{3}\)
B) 20
C) \(\sqrt{3}\)
D) 40
E) \(\dfrac{20}{\sqrt{3}}\)
In the figure below, \(ABC\) is right. \(ABDE\) is a square of area 200 and \(BCGF\) is a square of area 100. What is \(\overline{AC}\)?
A) \(10\sqrt{3}\)
B) \(10\sqrt{2}\)
C) 300
D) 10
E) 15
If \(x = 2.0001\), which expression has the largest value?
A) \(\dfrac{2}{x+2}\)
B) \(\dfrac{2}{x-2}\)
C) \(\dfrac{x+2}{2}\)
D) \(\dfrac{2}{x}\)
E) \(\dfrac{x}{2}\)
In the rectangle below, \(\overline{AD} = 3\overline{AB}\). What is the slope of \(\overline{BD}\)?
A) 3
B) \(\dfrac{1}{3}\)
C) \(-\dfrac{1}{3}\)
D) -3
E) \(-\dfrac{1}{4}\)
What is the product of the two real solutions of the equation:
\(2x = 3 - x^2\)
A) 3
B) 2
C) -2
D) 6
E) -3
Which equation corresponds to the data in this table?
| x | y |
| -20 | -1/8 |
| -10 | -1/3 |
| 0 | 1/2 |
| 5 | 2/9 |
| 20 | 1/12 |
A) \(y = \dfrac{1}{x+2}\)
B) \(y = \dfrac{2}{x+4}\)
C) \(y = \dfrac{x-1}{x+2}\)
D) \(y = \dfrac{2}{x-2}\)
E) \(y = \dfrac{1}{2x+2}\)