elementary surds, graphs of linear equations, linear equation problems - Question Bank

1. If the sum of three consecutive integers is 30, find the middle integer.
A) 9
B) 10
C) 11
D) 12
2. Solve for x: $5x - (x+3) = 9$
A) 2
B) 3
C) 4
D) 5
3. If $x = 3 - \sqrt{2}$, find the value of $x - \frac{1}{x}$
A) $2\sqrt{2}$
B) $-2\sqrt{2}$
C) $\frac{2\sqrt{2}}{7}$
D) $\frac{-2\sqrt{2}}{7}$
4. What is the value of $(\sqrt{12})^2 \div (\sqrt{3})^2$?
A) 2
B) 3
C) 4
D) 12
5. Rationalize the denominator of $\frac{1}{2 + \sqrt{3}}$
A) $2 - \sqrt{3}$
B) $2 + \sqrt{3}$
C) $\frac{2 - \sqrt{3}}{7}$
D) $\frac{2 + \sqrt{3}}{7}$
6. If $x = \sqrt{7}$, find the value of $x^2 - 3$.
A) 3
B) 4
C) 7
D) 10
7. Simplify: $\sqrt{50} \times \sqrt{2}$
A) 5
B) 10
C) 25
D) 100
8. If the point (a, 3) lies on the line $x + y = 7$, find the value of a.
A) 3
B) 4
C) 5
D) 6
9. Find the equation of a line with slope 2 and y-intercept 5.
A) $y = 2x + 5$
B) $y = 5x + 2$
C) $y = 2x - 5$
D) $y = 5x - 2$
10. The graph of the equation $x+y=0$ passes through which quadrant(s)?
A) I and III
B) II and IV
C) I and II
D) III and IV
11. Which of the following points is on the line $y = 3x - 1$?
A) (1, 1)
B) (1, 2)
C) (2, 5)
D) (0, -1)
12. The graph of $y = -x + 3$ has a slope of:
A) 1
B) -1
C) 3
D) -3
13. If $x+y=10$ and $x-y=2$, find the value of y.
A) 3
B) 4
C) 5
D) 6
14. The difference between two numbers is 5. If the larger number is 12, find the smaller number.
A) 5
B) 6
C) 7
D) 8
15. If $x$ is an integer such that $2x + 1 < 7$, what is the largest possible value of $x$?
A) 2
B) 3
C) 4
D) 5
16. A number is 7 more than another number. Their sum is 23. Find the smaller number.
A) 7
B) 8
C) 9
D) 10
17. Find x: $\frac{2x}{5} = 4$
A) 5
B) 10
C) 15
D) 20
18. Solve: $4(x-1) = 12$
A) 2
B) 3
C) 4
D) 5
19. If $x = \sqrt{10} - \sqrt{7}$, find the value of $x + \frac{1}{x}$
A) $2\sqrt{10}$
B) $2\sqrt{7}$
C) $\frac{2\sqrt{10}}{\sqrt{10} - \sqrt{7}}$
D) $\frac{2\sqrt{7}}{\sqrt{10} - \sqrt{7}}$
20. What is the value of $(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b})$?
A) $a^2 - b^2$
B) $a - b$
C) $a + b$
D) $\sqrt{a} - \sqrt{b}$
21. Rationalize the denominator of $\frac{3}{\sqrt{5}}$
A) $\frac{3\sqrt{5}}{5}$
B) $\frac{3\sqrt{5}}{25}$
C) $3\sqrt{5}$
D) $\frac{\sqrt{5}}{5}$
22. If $x = \sqrt{2}$, find the value of $(x^2 + 1)^2$
A) 4
B) 9
C) 16
D) 25
23. Simplify: $\frac{\sqrt{27}}{\sqrt{3}}$
A) 3
B) 9
C) 27
D) 81
24. If a line passes through points (1, 2) and (3, 6), what is its slope?
A) 1
B) 2
C) 3
D) 4
25. Find the x-intercept of the line $2x + 3y = 12$.
A) 6
B) 4
C) 12
D) 3
26. Which of the following equations represents a line passing through the origin (0,0)?
A) $y = x + 1$
B) $y = 2x$
C) $y = x - 2$
D) $y = 3x + 3$
27. The graph of the equation $x = -3$ is a line parallel to which axis?
A) x-axis
B) y-axis
C) Both x-axis and y-axis
D) Neither x-axis nor y-axis
28. If $x-y=1$ and $x+y=5$, find the value of x.
A) 1
B) 2
C) 3
D) 4
29. Two numbers differ by 3. Their sum is 15. Find the larger number.
A) 6
B) 7
C) 8
D) 9
30. What is the sum of a number and its double if the result is 21?
A) 6
B) 7
C) 8
D) 9
31. If $x+4 = 9$, find the value of $x$.
A) 4
B) 5
C) 13
D) 36
32. Solve for y: $5y - 2 = 18$
A) 3
B) 4
C) 5
D) 6
33. What is the value of $\sqrt{16} + \sqrt{9}$?
A) 5
B) 7
C) 12
D) 25
34. If $\frac{1}{\sqrt{x}} = \frac{1}{3}$, find the value of x.
A) 6
B) 9
C) 12
D) 18
35. Evaluate: $(\sqrt{5})^2 \times (\sqrt{2})^2$
A) 7
B) 10
C) 25
D) 50
36. If $x = \sqrt{3}$, what is the value of $x^3$?
A) $3\sqrt{3}$
B) $9\sqrt{3}$
C) 9
D) 27
37. Simplify: $\sqrt{72} \div \sqrt{8}$
A) 3
B) 4
C) 5
D) 6
38. What is the y-intercept of the line $y = 2x + 4$?
A) 2
B) 4
C) -2
D) -4
39. If the point (4, k) lies on the line $3x - y = 5$, find the value of k.
A) 5
B) 6
C) 7
D) 8
40. The graph of the equation $y = 5$ is a line parallel to which axis?
A) x-axis
B) y-axis
C) Both x-axis and y-axis
D) Neither x-axis nor y-axis
41. Which of the following points lies on the line $x - y = 2$?
A) (3, 1)
B) (1, 3)
C) (0, -2)
D) (2, 2)
42. What is the slope of the line represented by the equation $2x + 3y = 6$?
A) -2/3
B) 2/3
C) 3/2
D) -3/2
43. The sum of two consecutive integers is 35. Find the smaller integer.
A) 16
B) 17
C) 18
D) 19
44. A number when added to 5 gives 12. Find the number.
A) 6
B) 7
C) 8
D) 9
45. If $\frac{x}{2} + \frac{x}{3} = 5$, what is the value of $x$?
A) 5
B) 6
C) 7
D) 8
46. Find the value of $x$ if $3x - 5 = 10$
A) 4
B) 5
C) 6
D) 7
47. Solve the equation: $2x + 3 = 7$
A) 2
B) 3
C) 4
D) 5
48. If $a = 2 + \sqrt{3}$, find the value of $a + \frac{1}{a}$
A) 4
B) 3
C) 5
D) 2
49. What is the value of $(\sqrt{3} + \sqrt{2})^2 + (\sqrt{3} - \sqrt{2})^2$?
A) 10
B) 12
C) 5
D) 6
50. Rationalize the denominator of $\frac{1}{\sqrt{7} - \sqrt{3}}$
A) $\frac{\sqrt{7} + \sqrt{3}}{4}$
B) $\frac{\sqrt{7} - \sqrt{3}}{4}$
C) $\frac{\sqrt{7} + \sqrt{3}}{10}$
D) $\frac{\sqrt{7} - \sqrt{3}}{10}$
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