elementary surds, graphs of linear equations, linear equation problems - One Line Questions

1. What is the slope of the line represented by the equation $2x + 3y = 6$? -2/3
2. Which of the following points is on the line $y = 3x - 1$? (2, 5)
3. Which of the following points lies on the line $x - y = 2$? (3, 1)
4. Rationalize the denominator of $\frac{1}{\sqrt{7} - \sqrt{3}}$ $\frac{\sqrt{7} + \sqrt{3}}{4}$
5. Rationalize the denominator of $\frac{3}{\sqrt{5}}$ $\frac{3\sqrt{5}}{5}$
6. Rationalize the denominator of $\frac{1}{2 + \sqrt{3}}$ $2 - \sqrt{3}$
7. If $x = \sqrt{5} + \sqrt{2}$ and $y = \sqrt{5} - \sqrt{2}$, what is the value of $x^2 - y^2$? $8\sqrt{10}$
8. If $x = \sqrt{10} - \sqrt{7}$, find the value of $x + \frac{1}{x}$ $2\sqrt{10}$
9. If $x = 3 - \sqrt{2}$, find the value of $x - \frac{1}{x}$ $2\sqrt{2}$
10. If $x = \sqrt{3}$, what is the value of $x^3$? $3\sqrt{3}$
11. Simplify the expression: $\sqrt{18} + \sqrt{50} - \sqrt{32}$ $4\sqrt{2}$
12. What is the value of $(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b})$? $a - b$
13. Find the equation of a line with slope 2 and y-intercept 5. $y = 2x + 5$
14. Which of the following equations represents a line passing through the origin (0,0)? $y = 2x$
15. If $x-y=1$ and $x+y=5$, find the value of x. 3
16. If a line passes through points (1, 2) and (3, 6), what is its slope? 2
17. The graph of $y = -x + 3$ has a slope of: -1
18. What is the value of $(\sqrt{3} + \sqrt{2})^2 + (\sqrt{3} - \sqrt{2})^2$?
19. The sum of two consecutive integers is 35. Find the smaller integer. 16
20. Solve the equation: $2x + 3 = 7$ 2
21. What is the y-intercept of the line $y = 2x + 4$? 4
22. Solve: $4(x-1) = 12$ 3
23. If $x$ is an integer such that $2x + 1 < 7$, what is the largest possible value of $x$? 2
24. What is the value of $(\sqrt{12})^2 \div (\sqrt{3})^2$? 4
25. Solve for x: $5x - (x+3) = 9$ 3
26. Simplify: $\sqrt{72} \div \sqrt{8}$ 3
27. Solve for y: $5y - 2 = 18$ 4
28. Simplify: $\frac{\sqrt{27}}{\sqrt{3}}$ 3
29. If $x+y=10$ and $x-y=2$, find the value of y. 4
30. If the point (a, 3) lies on the line $x + y = 7$, find the value of a. 4
31. If $x = \sqrt{7}$, find the value of $x^2 - 3$. 4
32. If $a = 2 + \sqrt{3}$, find the value of $a + \frac{1}{a}$ 4
33. Find the value of $x$ if $3x - 5 = 10$ 5
34. If $x+4 = 9$, find the value of $x$. 5
35. If $x = \sqrt{2}$, find the value of $(x^2 + 1)^2$ 9
36. If $\frac{x}{2} + \frac{x}{3} = 5$, what is the value of $x$? 5
37. If the point (4, k) lies on the line $3x - y = 5$, find the value of k. 7
38. What is the value of $\sqrt{16} + \sqrt{9}$? 7
39. Find x: $\frac{2x}{5} = 4$ 10
40. The difference between two numbers is 5. If the larger number is 12, find the smaller number. 7
41. Simplify: $\sqrt{50} \times \sqrt{2}$ 10
42. A number when added to 5 gives 12. Find the number. 7
43. If $\frac{1}{\sqrt{x}} = \frac{1}{3}$, find the value of x. 9
44. What is the sum of a number and its double if the result is 21? 7
45. Two numbers differ by 3. Their sum is 15. Find the larger number. 8
46. Find the x-intercept of the line $2x + 3y = 12$. 6
47. Evaluate: $(\sqrt{5})^2 \times (\sqrt{2})^2$ 10
48. A number is 7 more than another number. Their sum is 23. Find the smaller number. 7
49. If the sum of three consecutive integers is 30, find the middle integer. 10
50. The graph of the equation $x+y=0$ passes through which quadrant(s)? II and IV