| y |
-4 |
31 |
4 |
68 |
12 |
| x |
-2 |
3 |
0 |
4 |
2 |
a. y = 2x2 + 7
b. y = x3 + 4
c. y = 2x
d. y = 3x + 1
5. If 2x + 3y = 13 and 4x - y = 5, then 3x + 2y =
a. 2
b. 3
c. 6
d. 12
Intermediate Algebra
1. A: From the starting expression, compute:
2. B: Compute as follows: (3 - 2 x 2)2 = (3 - 4)2 = (-1)2 = 1.
3. C: Evaluate as follows:
(3x-2)3 = 33 x ( x -2)3 = 27 x (1 / x2)3 = 27x 1 / x8 = 27x -8
4. B: The easiest pair to test is the third: y = 4 and x = 0. Substitute these values in each of the given equations and evaluate. Choice B gives 4 = 0 + 4, which is a true statement. None of the other answer choices is correct this number set.
5. D: Solving for y in the second equation gives y = 4x-5. If we plug this into the first equation we get 2x + 3(4x-5) = 13. Solving for this equation gives us 14x = 28, or x = 2. Then, plug the value of x into either equation to solve for y. y = 3. Therefore, 3x + 2y = 12.
College Algebra
1. In a rectangular x, y coordinate system, what is the intersection of two lines formed by the equations y = 2x + 3 and y = x - 5?
a. (5, 3)
b. (8, 13)
c. (-4, 13)
d. (-8, -13)
2. A function f(x) is defined by f(x) = 2x2 + 7. What is the value of 2f(x) - 3?
a. 4x2 + 11
b. 4x4 + 11
c. x2 + 11
d. 4 x2 + 14
3. If x and y are positive integers, which of the following expressions is equivalent to (xy)7y - (xy)y ?
a. (xy) 6y
b. (xy) 7y-1
c. (xy)y [(xy)71:44 PM 9/11/2012 -1]
d. (xy)y[(xy)6y -1]
4. Which equation is represented by the graph shown below?
a. y = 5 / 3 x + 2
b. y = - 5/3 x - 2
c. y = - 5/3 x + 2
d. y = 5/3 x -2
5. The graph below, not drawn to scale, shows a straight line passing through the origin. Point P1 has the (x,y) coordinates (-5,-3). What is the x-coordinate of point P2 if its y-coordinate is 3?
a. 0.8
b. 1
c. 5
d. 3
Geometry
1. Which of the following expressions represents the ratio of the area of a circle to its circumference?
a.πr 2
b. πr 2 / 2π
c. 2πr / r 2
d. r / 2
2. The sides of a triangle are equal to integral numbers of units. Two sides are 4 and 6 units long, respectively; what is the minimum value for the triangle's perimeter?
a. 10 units
b. 11 units
c. 12 units
d. 13 units
3. The two shortest sides of a right triangle are 6 and 8 units long, respectively. What is the length of the perimeter?
a. 10 units
b. 18 units
c. 24 units
d. 14 units
4. What is the area of an isosceles triangle inscribed in a circle of radius r if the base of the triangle is the diameter of the circle?
a. r2
b. 2r2
c. πr2
d. 2πr
5. If the area of a right triangle is 20 ft2, which of the following represent the possible measurements for the base and height of the triangle?
a. B = 4 ft; H = 5 ft
b. B = 10 ft; H = 2 ft
c. B = 8 ft; H = 5 ft
d. B = 15 ft; H = 3 ft
Answers
Writing Skills
1. C: Answer C as this phrase tells the reader where the man appeared. Answer A creates a run-on sentence, answer B is redundant, and choice D creates a disagreement of verb tense.
2. B: The original and answer C are slang usage, and D, suggesting that the villagers had only then noticed the monkeys, is inappropriate.
3. B: As the clause following the conjunction and is dependent, the comma is not employed.
4. D: The action described in the portion of the sentence following the conjunction is contrary to expectation, since the villagers hunted less despite the generous payments, and but reflects that contradiction better than any of the other choices.
5. D: The correct spelling for the possessive pronoun.
6. C: Answer C implies that the action that follows is a consequence of the one that precedes, i.e., the man raised his price because the villagers were losing interest.
7. A: No comma is used to set off a dependent clause.
Reading Skills
7. C: The first paragraph states that the main purpose of DST it to make better use of daylight.
8. A: Energy conservation is discussed as a possible benefit of DST, not a negative effect of it.
9. D: The first paragraph states that DST involves setting clocks forward one hour in the spring and one hour backward in the fall.
10. B: The last sentence in paragraph four notes that agricultural and evening entertainment interests have historically been opposed to DST.
11. D: The passage gives examples of both good and bad effects extra daylight can have on health.
Numerical Skills
1. C: 16.5 x 4/3 = 22.
6. B: The lowest score, 68, is eliminated. The average of the remaining four grades is (75 +88 + 86 + 90) divided by 4, which comes to 84.75.
Rounding up to the nearest integer gives a final grade of 85. Since this value is unique, all the other answers are incorrect.
7. A: The band's share, 25% of $20,000,000, is $5,000,000. After the agent's share is subtracted, the band gets (1-0.15) x $5,000,000 = 0.85 x $5,000,000 = $4,250,000
and each band member gets one fifth of that, or $850,000.
15. A: Negative numbers represent segments extending to the left of zero on the number line. Adding a negative number to another negative number extends the segment even further to the left, or into "negative territory". To add two negative numbers, add the magnitudes and retain the negative sign. For example (-3) + (-5) = -8.
17. B: The reciprocal of 5 is 1/5. When numbers are multiplied by their reciprocals, the result is always 1. Thus, 5 x (1/5) = 1.
Elementary Algebra
1. A: From the starting expression, compute:
2. B: Compute as follows: (3 - 2 x 2)2 = (3 - 4)2 = (-1)2 = 1.
3. C: Evaluate as follows:
(3x-2)3 = 33 x ( x -2)3 = 27 x (1 / x2)3 = 27x 1 / x8 = 27x -8
4. B: The easiest pair to test is the third: y = 4 and x = 0. Substitute these values in each of the given equations and evaluate. Choice B gives 4 = 0 + 4, which is a true statement. None of the other answer choices is correct this number set.
5. D: Solving for y in the second equation gives y = 4x-5. If we plug this into the first equation we get 2x + 3(4x-5) = 13. Solving for this equation gives us 14x = 28, or x = 2. Then, plug the value of x into either equation to solve for y. y = 3. Therefore, 3x + 2y = 12.
Intermediate Algebra
1. B: The equation has a negative slope (-3) and a positive intercept (+2).
A has a positive slope and goes through the origin, so the intercept is zero.
C has a negative slope but goes through the origin, so the intercept is zero.
D has a positive slope and a positive intercept.
2. A: Since the second line, , is a vertical, the intersection must occur at a point where y = 3. If x = -1.5, the equation describing the line is satisfied:(2x [-1.5] + 3)=0
B. The equation for the first line is not satisfied:(2 x 1.5) + 3 ≠ 0
C-D. None of these points satisfy the condition y = 3, and thus they will not be traversed by the second line.
3. A: For the line to be parallel to the x-axis, the slope must be 0. This condition is met if y has a constant value. B-D. y varies with x for all of these, and is therefore not parallel to the x-axis.
4. A: As defined, the line will be described by the equation . Expression A fits this equation (9 = 4 x 2 + 1). The others do not.
B. -1 ≠ 4 x 0 + 1
C. 0 ≠ 4 x 0 + 1
D. 4 ≠ 4 x 1 + 1
College Algebra
1. D: At the point of intersection, the y-coordinates are equal on both lines so that 2x + 3 = x - 5. Solving for x, we have x = -8. Then, evaluating y with either equation yields
y = 2(-8) + 3 = -16 + 3 = -13 or y = -8 - 5 = -13
2. A: Evaluate as follows: 2f(x) - 3 = 2 (2x2 + 7) - 3 = 4x2 + 14 - 3 = 4x2 + 11.
3. D: Remember that when you multiply like bases, you add the exponents, and when you divide like bases, you subtract the exponents. (xy)7y - (xy)y = (xy)y [(xy)7y-y - 1] = (xy)y [(xy) 6y - 1]
4. C: The line in the graph has a negative slope and a positive y-axis intercept, so the factor multiplying the variable x, or the slope, must be negative, and the constant, or y-intercept, must be positive.
5. C: Since the line is straight, the slope is the same throughout. Thus, if 5 y-units are traversed in going from x = -3 to x = 0 (where y increases from -5 to 0, to reach the origin), then 5 y-units will be traversed in going from x = 0 to x = 3 .
Geometry
1. D: The area of the circle is ?r2 while the circumference is 2?r. Taking the ratio of these two expressions and reducing gives:
Ratio = πr2 / 2πr = r/2
2. D: The sides of a triangle must all be greater than zero. The sum of the lengths of the two shorter sides must be greater than the length of the third side. Since we are looking for the minimum value of the perimeter, assume the longer of the two given sides, which is 6, is the longest side of the triangle. Then the third side must be greater than 6 - 4 = 2. Since we are told the sides are all integral numbers, the last side must be 3 units in length. Thus, the minimum length for the perimeter is 4+6+3 = 13 units.
3. C: The hypotenuse must be the longest side of a right triangle, so it must be the lengths of the other two sides that are given as 6 and 8 units. Calculate the length of the hypotenuse, H, from the Pythagorean Theorem: H2 = S12 + S22 = 62 + 82 = 36 + 64 = 100 , which yields H = 10 and the perimeter equals 10+6+8 = 24.
4. A: The area of a triangle equals half the product of base times height. Since the base passes through the center, we have base = 2 r and height = r, so that the area A is
5. C: The formula for the area of a triangle is 1/2bh, or one-half the base times the height. This means that the product of the two sides will actually be twice the number that is provided as the area, i.e., 20 x 2 or 40. Although the actual base and height aren't provided, only one answer choice offers two numbers that equal a product of 40 - 8 and 5.
ASSET test breakdown | Paying for College Information
by Enoch Morrison
Last Updated: 05/08/2013
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