SSC CAPFS and DP - elementary surds, graphs of linear equations, linear equation problems Online Test (MCQ Quiz)

1. Simplify the expression: $\sqrt{18} + \sqrt{50} - \sqrt{32}$

A) $4\sqrt{2}$ B) $6\sqrt{2}$ C) $2\sqrt{2}$ D) $8\sqrt{2}$

2. If $x = \sqrt{5} + \sqrt{2}$ and $y = \sqrt{5} - \sqrt{2}$, what is the value of $x^2 - y^2$?

A) $2\sqrt{10}$ B) $4\sqrt{10}$ C) $8\sqrt{10}$ D) $10\sqrt{2}$

3. 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) $\frac{\sqrt{7} - \sqrt{3}}{10}$

4. What is the value of $(\sqrt{3} + \sqrt{2})^2 + (\sqrt{3} - \sqrt{2})^2$?

A) 10 B) 12 C) 5 D) 6

5. If $a = 2 + \sqrt{3}$, find the value of $a + \frac{1}{a}$

A) 4 B) 3 C) 5 D) 2

6. Solve the equation: $2x + 3 = 7$

A) 2 B) 3 C) 4 D) 5

7. Find the value of $x$ if $3x - 5 = 10$

A) 4 B) 5 C) 6 D) 7

8. If $\frac{x}{2} + \frac{x}{3} = 5$, what is the value of $x$?

A) 5 B) 6 C) 7 D) 8

9. A number when added to 5 gives 12. Find the number.

A) 6 B) 7 C) 8 D) 9

10. The sum of two consecutive integers is 35. Find the smaller integer.

A) 16 B) 17 C) 18 D) 19

11. 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

12. Which of the following points lies on the line $x - y = 2$?

A) (3, 1) B) (1, 3) C) (0, -2) D) (2, 2)

13. 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

14. 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

15. What is the y-intercept of the line $y = 2x + 4$?

A) 2 B) 4 C) -2 D) -4

16. Simplify: $\sqrt{72} \div \sqrt{8}$

A) 3 B) 4 C) 5 D) 6

17. If $x = \sqrt{3}$, what is the value of $x^3$?

A) $3\sqrt{3}$ B) $9\sqrt{3}$ C) 9 D) 27

18. Evaluate: $(\sqrt{5})^2 \times (\sqrt{2})^2$

A) 7 B) 10 C) 25 D) 50

19. If $\frac{1}{\sqrt{x}} = \frac{1}{3}$, find the value of x.

A) 6 B) 9 C) 12 D) 18

20. What is the value of $\sqrt{16} + \sqrt{9}$?

A) 5 B) 7 C) 12 D) 25

21. Solve for y: $5y - 2 = 18$

A) 3 B) 4 C) 5 D) 6

22. If $x+4 = 9$, find the value of $x$.

A) 4 B) 5 C) 13 D) 36

23. What is the sum of a number and its double if the result is 21?

A) 6 B) 7 C) 8 D) 9

24. Two numbers differ by 3. Their sum is 15. Find the larger number.

A) 6 B) 7 C) 8 D) 9

25. If $x-y=1$ and $x+y=5$, find the value of x.

A) 1 B) 2 C) 3 D) 4

26. 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

27. 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) $y = 3x + 3$

28. Find the x-intercept of the line $2x + 3y = 12$.

A) 6 B) 4 C) 12 D) 3

29. If a line passes through points (1, 2) and (3, 6), what is its slope?

A) 1 B) 2 C) 3 D) 4

30. Simplify: $\frac{\sqrt{27}}{\sqrt{3}}$

A) 3 B) 9 C) 27 D) 81

31. If $x = \sqrt{2}$, find the value of $(x^2 + 1)^2$

A) 4 B) 9 C) 16 D) 25

32. 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) $\frac{\sqrt{5}}{5}$

33. 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) $\sqrt{a} - \sqrt{b}$

34. 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) $\frac{2\sqrt{7}}{\sqrt{10} - \sqrt{7}}$

35. Solve: $4(x-1) = 12$

A) 2 B) 3 C) 4 D) 5

36. Find x: $\frac{2x}{5} = 4$

A) 5 B) 10 C) 15 D) 20

37. A number is 7 more than another number. Their sum is 23. Find the smaller number.

A) 7 B) 8 C) 9 D) 10

38. 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

39. 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

40. If $x+y=10$ and $x-y=2$, find the value of y.

A) 3 B) 4 C) 5 D) 6

41. The graph of $y = -x + 3$ has a slope of:

A) 1 B) -1 C) 3 D) -3

42. Which of the following points is on the line $y = 3x - 1$?

A) (1, 1) B) (1, 2) C) (2, 5) D) (0, -1)

43. 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

44. 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) $y = 5x - 2$

45. 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

46. Simplify: $\sqrt{50} \times \sqrt{2}$

A) 5 B) 10 C) 25 D) 100

47. If $x = \sqrt{7}$, find the value of $x^2 - 3$.

A) 3 B) 4 C) 7 D) 10

48. Rationalize the denominator of $\frac{1}{2 + \sqrt{3}}$

A) $2 - \sqrt{3}$ B) $2 + \sqrt{3}$ C) $\frac{2 - \sqrt{3}}{7}$ D) $\frac{2 + \sqrt{3}}{7}$

49. What is the value of $(\sqrt{12})^2 \div (\sqrt{3})^2$?

A) 2 B) 3 C) 4 D) 12

50. 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) $\frac{-2\sqrt{2}}{7}$

elementary surds, graphs of linear equations, linear equation problems - Online Test

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