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This is a pretest of basic algebra and arithmetic for High School level Mathematics
Questions and Answers
1.
Evaluate: 10 - 2(3)
A.
-13
B.
4
C.
16
D.
24
E.
None of the above
Correct Answer B. 4
Explanation The expression 10 - 2(3) can be simplified by performing the multiplication first. 2(3) equals 6, so the expression becomes 10 - 6. Subtracting 6 from 10 gives us 4. Therefore, the correct answer is 4.
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2.
-2^{3} =
A.
-8
B.
-6
C.
8
D.
6
E.
9
Correct Answer A. -8
3.
6 - 3^{2}
A.
-9
B.
-3
C.
3
D.
6
E.
9
Correct Answer B. -3
Explanation The correct answer is -3 because when you subtract 32 from 6, you get -26. Then, when you divide -26 by 9, you get -3.
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4.
Solve for x:3x - 3 = 9
A.
X = 10x = -6
B.
X = 6
C.
X = 4
D.
X = -6
E.
None of the above
Correct Answer B. X = 6
Explanation To solve the equation 3x - 3 = 9, we need to isolate the variable x. Adding 3 to both sides of the equation, we get 3x = 12. Then, dividing both sides by 3, we find that x = 4. Therefore, the correct answer is x = 4.
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5.
2k + 3 + 5k = 10What should be the first step to solving the equation?
A.
Substituting values in for k
B.
Subtracting 5k from both sides of the equation
C.
Subtracting 2k from 2k and 5k.
D.
Adding 2k to 5k
E.
Dividing both sides of the equation by 2
Correct Answer(s) A. Substituting values in for k B. Subtracting 5k from both sides of the equation D. Adding 2k to 5k
Explanation The first step to solving the equation 2k + 3 + 5k = 10 is to substitute values in for k. This means replacing all instances of k in the equation with the given values. Then, the next step is to subtract 5k from both sides of the equation to isolate the variable. Finally, adding 2k to 5k helps to combine like terms and simplify the equation further.
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6.
2(m - 3) = 3m + 3The first step to solving this equation should be
A.
Subtracting 3m from both sides of the equation
B.
Combining 2m with 3m
C.
Distributing the 2 into (m - 3)
D.
Subtracting 3 from both sides of the equation
E.
Substituting values into m
Correct Answer(s) C. Distributing the 2 into (m - 3) E. Substituting values into m
Explanation The correct answer is "Distributing the 2 into (m - 3)". This is the first step to solving the equation because it allows us to eliminate the parentheses and simplify the expression. By distributing the 2, we multiply it by both m and -3, resulting in 2m - 6. This step is necessary in order to combine like terms and further simplify the equation. The other options listed are not the first step because they do not address the need to distribute the 2.
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7.
Simplify: (2x^{3})^{2}
A.
2x^5
B.
2x^6
C.
4x^5
D.
4x^6
E.
None of the above
Correct Answer D. 4x^6
Explanation The expression (2x3)2 means we have to raise the quantity 2x3 to the power of 2. Simplifying this, we get (2x3)2 = 2^2 * (x^3)^2 = 4 * x^6. Therefore, the correct answer is 4x^6.
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8.
Write in simplest radical form: sqrt(200)
A.
10*sqrt(2)
B.
2*sqrt(10)
C.
5*sqrt(8)
D.
100*sqrt(2)
E.
None of the above
Correct Answer A. 10*sqrt(2)
Explanation The given expression sqrt(200) can be simplified by finding the largest perfect square that divides 200. In this case, the largest perfect square is 100. Therefore, we can rewrite sqrt(200) as sqrt(100 * 2). Taking the square root of 100 gives us 10, and we are left with sqrt(2). Hence, the simplest radical form of sqrt(200) is 10*sqrt(2).
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9.
What is the slope of the equation,y = -2x + 3
Correct Answer -2
Explanation The slope of a linear equation is the coefficient of the x term. In the given equation, y = -2x + 3, the coefficient of the x term is -2. Therefore, the slope of the equation is -2.
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10.
What is the y-intercept of the equation,y + 2x = 6
Correct Answer 6
Explanation The y-intercept of an equation represents the point where the line intersects the y-axis. To find the y-intercept, we set x = 0 in the equation and solve for y. In this case, when x = 0, the equation becomes y + 2(0) = 6, which simplifies to y = 6. Therefore, the y-intercept of the equation y + 2x = 6 is 6.
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11.
What is the value of x in the following system of equations:3x - 2y = 03x + y = 9
Correct Answer 2 x=2
Explanation The given system of equations can be solved using the method of substitution. We can solve the second equation for y, which gives us y = 9 - 3x. Substituting this value of y into the first equation, we get 3x - 2(9 - 3x) = 0. Simplifying this equation, we get 3x - 18 + 6x = 0, which further simplifies to 9x - 18 = 0. Solving for x, we get x = 2. Therefore, the value of x in the given system of equations is 2.
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12.
Solve for x:x^{2} - x - 2 = 0
Correct Answer x = 2, x = -1 {2, -1}
Explanation The given equation is a quadratic equation in the form of ax^2 + bx + c = 0. To solve it, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 1, b = -1, and c = -2. Plugging these values into the quadratic formula, we get x = (1 ± √(1 - 4(1)(-2))) / 2(1). Simplifying further, x = (1 ± √(1 + 8)) / 2, which becomes x = (1 ± √9) / 2. This gives us two possible solutions: x = (1 + 3) / 2 = 2 and x = (1 - 3) / 2 = -1. Therefore, the answer is x = 2, x = -1, or {2, -1}.