1. What is the slope of the line passing through the points (3, 4) and (7, 8)?
A. 1
B. 2
C. 3
D. 4
2. Which of the following is the equation of a line that is parallel to y = 2x + 3 and passes through the point (4, -1)?
A. y = -1/2x - 3
B. y = 2x - 9
C. y = 2x + 5
D. y = -2x + 3
3. What is the x-coordinate of the vertex of the parabola given by the equation y = x^2 - 6x + 8?
A. -2
B. 2
C. 3
D. 6
4. What is the value of sin(60°)?
A. 1/2
B. √2/2
C. √3/2
D. √3/3
5. What is the solution to the equation 2x + 3 = 9x - 5?
A. -1/7
B. 2/7
C. 3/7
D. 5/7
6. What is the sum of the first 10 terms of the arithmetic sequence 2, 5, 8, 11, ... ?
A. 305
B. 310
C. 315
D. 320
7. What is the area of a circle with radius 5?
A. 25π
B. 50π
C. 75π
D. 100π
8. Which of the following is the equation of the line that passes through the point (3, 5) and is perpendicular to the line y = -2x + 1?
A. y = 2x + 1
B. y = -1/2x + 6
C. y = -1/2x + 3/2
D. y = 2x - 1
9. What is the value of log10(1000)?
A. 1
B. 2
C. 3
D. 4
10. What is the solution to the equation x^2 + 3x - 4 = 0?
A. x = -4, 1
B. x = -4, -1
C. x = -3, 4
D. x = -1, 4
A. 1
B. 2
C. 3
D. 4
2. Which of the following is the equation of a line that is parallel to y = 2x + 3 and passes through the point (4, -1)?
A. y = -1/2x - 3
B. y = 2x - 9
C. y = 2x + 5
D. y = -2x + 3
3. What is the x-coordinate of the vertex of the parabola given by the equation y = x^2 - 6x + 8?
A. -2
B. 2
C. 3
D. 6
4. What is the value of sin(60°)?
A. 1/2
B. √2/2
C. √3/2
D. √3/3
5. What is the solution to the equation 2x + 3 = 9x - 5?
A. -1/7
B. 2/7
C. 3/7
D. 5/7
6. What is the sum of the first 10 terms of the arithmetic sequence 2, 5, 8, 11, ... ?
A. 305
B. 310
C. 315
D. 320
7. What is the area of a circle with radius 5?
A. 25π
B. 50π
C. 75π
D. 100π
8. Which of the following is the equation of the line that passes through the point (3, 5) and is perpendicular to the line y = -2x + 1?
A. y = 2x + 1
B. y = -1/2x + 6
C. y = -1/2x + 3/2
D. y = 2x - 1
9. What is the value of log10(1000)?
A. 1
B. 2
C. 3
D. 4
10. What is the solution to the equation x^2 + 3x - 4 = 0?
A. x = -4, 1
B. x = -4, -1
C. x = -3, 4
D. x = -1, 4
Answers & Comments
1. B. The slope is (8-4)/(7-3) = 4/4 = 1, which is also the slope of the line y = 2x + b. Solving for b using the point (4,-1), we get y = 2x - 9 as the equation of the line.
2. B. The x-coordinate of the vertex of y = x^2 - 6x + 8 is given by x = -(-6)/(2*1) = 3. So the vertex is (3,2).
3. C. sin(60°) = √3/2.
4. D. Solving for x, we get x = 5/7 as the solution.
5. C. The sum of the first 10 terms of an arithmetic sequence is (first term + last term)/2 * number of terms. The last term is 2 + (10-1)*3 = 29, so the sum is (2+29)/2 * 10 = 155.
6. A. The area of a circle with radius 5 is π*5^2 = 25π.
7. C. The equation of the line perpendicular to y = -2x + 1 and passing through (3,5) has slope 1/2. Its equation is y - 5 = 1/2(x - 3), which simplifies to y = 1/2x + 7/2.
8. B. log10(1000) = 3, since 10^3 = 1000.
9. A. The quadratic factors as (x-1)(x+4) = 0, so the solutions are x = 1 and x = -4.
10. To solve the equation x^2 + 3x - 4 = 0, we can use factoring or the quadratic formula.
Factoring:
We need to find two numbers that multiply to -4 and add up to 3. These numbers are 4 and -1. Therefore, we can factor the equation as (x+4)(x-1) = 0.
Using the zero product property, we set each factor to zero:
x+4 = 0 or x-1 = 0
Solving for x, we get:
x = -4 or x = 1
Therefore, the solution to the equation is x = -4, 1.
The answer is (A).