Algebra
1. Which of the following is a quadratic equation?
a) x + 2 = 0
b) 2x + 3 = 0
c) x^2 – 3x + 2 = 0
Answer: c) x^2 – 3x + 2 = 0
2. Which of the following is the formula for the quadratic formula?
a) x = (-b + sqrt(b^2 – 4ac)) / 2a
b) x = (-b – sqrt(b^2 + 4ac)) / 2a
c) x = (-b + sqrt(b^2 – 4ac)) / a
Answer: a) x = (-b + sqrt(b^2 – 4ac)) / 2a
3. Which of the following is a linear equation?
a) x^2 + 2x + 1 = 0
b) 3x – 4 = 0
c) 2x^3 – 4x^2 + x – 1 = 0
Answer: b) 3x – 4 = 0
4. Which of the following is the slope-intercept form of a linear equation?
a) y = mx + b
b) x = y – b / m
c) y = m / x + b
Answer: a) y = mx + b
5. Which of the following is the y-intercept of the linear equation y = 2x + 3?
a) 2
b) 3
c) (0,3)
Answer: b) 3
6. Which of the following is a solution to the equation x^2 – 5x + 6 = 0?
a) x = 2 or x = 3
b) x = -2 or x = -3
c) x = 2 or x = -3
Answer: a) x = 2 or x = 3
7. Which of the following is the equation of a vertical line?
a) y = mx + b
b) x = c
c) y = c
Answer: b) x = c
8. Which of the following is a factor of the polynomial x^2 – 4x – 21?
a) (x + 3)(x + 7)
b) (x – 3)(x + 7)
c) (x – 3)(x – 7)
Answer: a) (x + 3)(x + 7)
9. Which of the following is the degree of the polynomial 2x^3 – 3x^2 + 4x – 1?
a) 2
b) 3
c) 4
Answer: b) 3
10. Which of the following is the solution to the equation 2x – 4 = 6x + 2?
a) x = -1
b) x = 2
c) x = -3
Answer: c) x = -3
11. Which of the following is a binomial?
a) x^2 – 2x + 1
b) 3x^2 + 2x + 1
c) x + 2
Answer: c) x + 2
12. Which of the following is a trinomial?
a) x + 2
b) x^2 – 2x + 1
c) x^3 + 3x^2 + 2x + 1
Answer: c) x^3 + 3x^2 +
13. Which of the following is the standard form of a quadratic equation?
a) ax^2 + bx + c = 0
b) x^2 + px + q = 0
c) x^2 + bx + c = 0
Answer: a) ax^2 + bx + c = 0
14. Which of the following is the vertex form of a quadratic equation?
a) y = ax^2 + bx + c
b) y = a(x – h)^2 + k
c) y = a(x + h)^2 + k
Answer: b) y = a(x – h)^2 + k
15. Which of the following is the discriminant of a quadratic equation?
a) b^2 – 4ac
b) -b ± sqrt(b^2 – 4ac) / 2a
c) a(x – h)^2 + k
Answer: a) b^2 – 4ac
16. Which of the following is a system of linear equations?
a) x^2 + y^2 = 25, 2x – y = 1
b) y = 3x – 2, y = -2x + 5
c) 2x^2 – y = 3, x + y = 7
Answer: b) y = 3x – 2, y = -2x + 5
17. Which of the following is the solution to the system of equations 2x + 3y = 7 and x – y = 2?
a) (3,1)
b) (2,3)
c) (-1,3)
Answer: a) (3,1)
18. Which of the following is the slope of the line 4x – 2y = 6?
a) 2
b) -2
c) 4
Answer: c) 4
19. Which of the following is the y-intercept of the line y = -3x + 2?
a) 2
b) -3
c) (0,2)
Answer: a) 2
20. Which of the following is the slope of the line passing through the points (2,3) and (4,5)?
a) 2
b) 1/2
c) 1
Answer: c) 1
21. Which of the following is the equation of the line passing through the point (-2,5) and having a slope of 3?
a) y = 3x – 11
b) y = 3x + 11
c) y = -3x + 11
Answer: b) y = 3x + 11
22. Which of the following is the equation of the line perpendicular to the line y = 2x – 3 and passing through the point (4,5)?
a) y = -1/2x + 7
b) y = -2x + 13
c) y = 1/2x + 3
Answer: a) y = -1/2x + 7
23. Which of the following is the equation of the circle with center (3,-4) and radius 5?
a) (x – 3)^2 + (y + 4)^2 = 25
b) (x + 3)^2 + (y – 4)^2 = 25
c) (x – 3)^2 + (y – 4)^2 = 25
Answer: c) (x – 3)^2 + (y-4)^2 = 25
24. Which of the following is the slope-intercept form of a linear equation?
a) ax + by = c
b) y = mx + b
c) x^2 + y^2 = r^2
Answer: b) y = mx + b
25. Which of the following is the standard form of a linear equation?
a) ax + by = c
b) y = mx + b
c) x^2 + y^2 = r^2
Answer: a) ax + by = c
26. Which of the following is the solution to the equation 2x – 5 = 7?
a) x = 6
b) x = 12
c) x = -1
Answer: a) x = 6
27. Which of the following is the solution to the equation 3x + 4 = 19?
a) x = 5
b) x = 15
c) x = 23/3
Answer: a) x = 5
28. Which of the following is the equation of the parabola with vertex (1,-2) and focus (1,2)?
a) (y + 2)^2 = 4(x – 1)
b) (x – 1)^2 = 4(y + 2)
c) (x – 1)^2 = -4(y + 2)
Answer: a) (y + 2)^2 = 4(x – 1)
29. Which of the following is the equation of the ellipse with center (2,-3), major axis of length 10 and minor axis of length 6?
a) (x – 2)^2 / 25 + (y + 3)^2 / 9 = 1
b) (x – 2)^2 / 9 + (y + 3)^2 / 25 = 1
c) (x – 2)^2 / 36 + (y + 3)^2 / 100 = 1
Answer: c) (x – 2)^2 / 36 + (y + 3)^2 / 100 = 1
30. Which of the following is the equation of the hyperbola with center (-3,2), vertices (-3,5) and (-3,-1), and foci (-3,6) and (-3,-2)?
a) (y – 2)^2 / 9 – (x + 3)^2 / 16 = 1
b) (x + 3)^2 / 9 – (y – 2)^2 / 16 = 1
c) (y – 2)^2 / 16 – (x + 3)^2 / 9 = 1
Answer: b) (x + 3)^2 / 9 – (y – 2)^2 / 16 = 1
