Here are the answers to each of the questions you provided:
1. 102.4886 rounded off to four significant figures:
C. 102.5
2. Which statement is correct?
C. 100.00 has five significant figures
3. Most significant digit of 0.2015:
C. 2
4. Solve for the value of x in xxxxxxxx = 10
This equation seems incomplete, so unable to determine an answer.
5. If 9xx = 27yy and 8yy = 16zz, what is x:y:z?
A. 1:3:6
6. If 3xx = 4yy, then 3xx² / 4yy² = ?
C. 27/64
7. If log xx = − 1⁄nn, then the value of x is:
B. 10−1⁄nn
8. Three people step off together with steps of 75 cm, 80 cm, and 90 cm. The minimum
distance they should walk is:
C. 7200 cm (LCM of 75, 80, and 90)
9. Absolute value of the complex number 3 + 4i:
C. 5 (using the formula √(a² + b²) for complex numbers)
10. Solve for x in √20 − xx = xx
B. -4, 5
11. Solve for x in xx + yy = 7 and xx² + 2yy² = 34
C. 2
12. Ordered triples of real numbers (x, y, z) satisfying the system of equations: C. I and
II
13. Solve for the constant m in xx² − 4xx + 3mm = 0, if one root exceeds the other by 2
B. 3
14. Which is a prime number?
B. 313
15. If yy = xx + 1⁄xx, then the equation (xx² − 3xx + 1)(xx² − 5xx + 1) = 6xx² reduces to:
B. yy² − 8yy + 7 = 0
16. Solve for x in xx²/3 + xx−2/3 = 17/4.
C. -8
17. If aa + 2bb + 4cc = 0, then the equation aa² + bb + cc = 0:
B. has both the roots complex
18. Two or more equations are equal if and only if they have the same:
A. solution set
19. Solve for x: √xx + xx − √1 − xx = 1
C. 16/25
20. Which state is NOT correct?
C. 00 = 1
21. The equation whose roots are twice the roots of xx² − 3xx + 3 = 0 is:
B. xx² − 6xx + 12 = 0
22. Solve for x in 38.5xx = 6.5(xx−2)
A. -2.10
23. Simplify: log xx + log xx³ + log xx⁵
C. 9 log xx
24. Given the equation 2xx² + xx − 10 = 0, find the product of roots:
C. -5
25. Given: logaa xx = 5yy + logaa yy. Find the value of x.
B. xx = 5aa
26. If the sum of the roots of a quadratic equation is 12 and the product is 36, then what
is the difference of the roots?
D. 6
27. What is the logarithm of a negative number?
D. complex
28. Solve for x: xx−3 − 9xx−3/2 + 8 = 0.
C. 8
29. Solve for x: 1.4 = (0.0613/xx)¹³²
B. 0.04751
30. The surface area A of a hollow cone is given by A=πrL. Determine the surface area
when r=3.0 cm and L=8.5 cm.
B. 80.1 cm²
31. Solve for x if 8xx = 2(yy + 2) and 16(3xx − yy) = 4yy
C. 3
32. What are the roots of the cubic equation xx³ − 8xx − 3 = 0?
C. x = -3, -0.38, 2
33. What is most nearly the value of x that satisfies the expression 17.3 = e¹¹ˣ?
B. 2.6
34. What is the solution of the equation 50xx² + 5(xx − 2)² = −1?
D. no solution
35. Which of the following is a happy number?
D. 100
36. How many real solutions does the equation xx⁷ + 14xx⁵ + 16xx³ + 30xx − 560 = 0
have?
C. 5
37. What is the discriminant of the equation 4xx² − 8xx + 5 = 0?
D. -8
38. How many positive real roots are in the equation 4xx³ − 2xx² + xx − 3 = 0?
B. 1
39. What is the natural logarithm of exy?
B. xy
40. What is the value of (0.001)²/³?
D. antilog[2/3 log(0.001)]
41. Factor the expression 3xx³ − 3xx² − 18xx
A. 3xx(xx − 3)(xx + 2)
42. Which of the following best describes 8 + 0ii?
B. real number
43. Simplify the given fraction: (3xx−1)/(xx²−1) − (xx+3)/(xx²+3xx+2) − 1/(xx+2)
B. 1/(xx+1)
44. Find the equation whose roots are the reciprocal of the roots of 2xx² − 3xx − 5 = 0.
A. 5xx² − 3xx − 2 = 0
45. Resolve (xx+2)/(xx²−7xx+12) into partial fractions.
A. 6/(xx−4) − 2/(xx−3)
46. One root of the equation 5xx² + 13xx + mm = 0 is the reciprocal of the other. What is
m?
D. 1/6
47. Which of the following is the complete factor of xx⁴ + 5xx² − 36?
B. (xx − 2)(xx + 2)(xx² + 9)
48. Divide xx⁴ − 10xx² − 9xx − 20 by xx − 4. What is the remainder?
C. 45
49. If one root of 9xx² − 6xx + kk = 0 exceeds the other by 2, find the value of k.
A. 6
50. What is the quadratic equation if the product and sum of its roots are -32 and -4,
respectively?
B. xx² − 4xx − 32 = 0
This is a long set of questions, and I've covered the first 50 here. If you need help with the
remaining ones, feel free to ask!
