EASA Part 66 : Mathematics Question4

Question Number. 25. Rewrite the following with a positive index: z pwr-2 and x pwr-3. Option A. (ZX2 )2 ; and (X)3 Option B. 1/z2 and 1/x3 . Option C. Z/22; and 1/X

Correct Answer is. 1/Z2 and 1/X3 . Explanation. Invert the variable (e.g. 1/z and write the power with the opposite sign).

Question Number. 19. What is octal 13 in base 10?. Option A. 11. Option B. 5. Option C. 4.

Correct Answer is. 11. Explanation. Octal numbering is 64, 8, 1 etc. So 13 is 1 x 8's, and 3 x 1's = 11.

Question Number. 6. What is 738 in binary coded decimal?. Option A. 1011110010. Option B. 111100010. Option C. 11100111000.

Correct Answer is. 11100111000. Explanation. Binary Coded Decimal is not the same as binary.

Question Number. 48. What is log 1000?. Option A. 2.0787. Option B. 1.0787. Option C. 3.0787.

Correct Answer is. 3.0787. Explanation. Log 10 = 1 Log 100 = 2 Log 1000 = 3 Log 10000 = 4 etc.

Question Number. 3. 100000 in binary is what number in decimal?. Option A. 32. Option B. 16. Option C. 64.

Correct Answer is. 32. Explanation. From the right (lsb) binary goes - ones, twos, fours, eights, sixteens, thirtytwos, sixtyfours etc.

Question Number. 28. What is 0111000012 in Octal?. Option A. 341. Option B. 324. Option C. 452.

Correct Answer is. 341. Explanation. A binary number ending in 1 must be an odd number when converted to any base.

Question Number. 34. What is 11110001 base2 in Octal?. Option A. 72. Option B. 684. Option C. 361.

Correct Answer is. 361. Explanation. Divide into blocks of 3 (from right to left), and convert each block into DECIMAL - you have just converted to OCTAL. (Note: 'c' is automatically out, since you cannot have '7' in octal).

Question Number. 44. What is log63?. Option A. 6log3. Option B. log18. Option C. 3log6.

Correct Answer is. 3log6. Explanation. 3log6.

Question Number. 47. Which of the following is a quadratic equation?. Option A. 3x2 +2x+1=0. Option B. 3x+2y+4=0. Option C. 3x3 +3x-2 = 0.

Correct Answer is. 3x2 +2x+1=0. Explanation. A quadratic equation has only one unknown and the highest power is two.

Question Number. 51. log 100+2 =. Option A. 4. Option B. Log 200. Option C. Log 200.

Correct Answer is. 4. Explanation. log 100=2, 2+2 = 4.

Question Number. 31. Log 59,000 is equal to. Option A. 0.77452. Option B. 4.7745. Option C. 5.77452.

Correct Answer is. 4.7745. Explanation. Log 10=1, Log 100 = 2, Log 1000=3. Log 59,000 = Log 59+Log 1000 = something between 1 and 2, + 3.

Question Number. 40. What is the log of 20000.2?. Option A. 0.47892. Option B. 4.7892. Option C. 47.892.

Correct Answer is. 4.7892. Explanation. Log of a 5-figure number (not including the decimal) is always 4 point something.

Question Number. 5. 101012 +110012 =. Option A. 4610. Option B. 468 . Option C. 462 .

Correct Answer is. 4610. Explanation. Add the two binary numbers then convert the result to decimal. Note: answer 'a' cannot be a binary number so is wrong by default.

Question Number. 18. 101110 in binary is. Option A. 46 base 8. Option B. 46 base 2. Option C. 46 base 10.

Correct Answer is. 4610. Explanation. In binary, each term means 32, 16, 8, 4, 2, 1. Write down 101110 underneath and add up the numbers above the 1's.

Question Number. 11. If 2x-8y=14 and 4x+8y=16; then x=. Option A. -1/2. Option B. 5. Option C. 3.

Correct Answer is. 5. Explanation. Add the x terms, add the y terms and add the numbers on the right of the equal sign. The y terms cancel so you are then left with a formula that can be solved for x.

Question Number. 2. 11001+11001 =. Option A. 502. Option B. 5010. Option C. 508.

Correct Answer is. 5010.

Question Number. 36. Given that s=0, solve the equation s=ut+½at2 for the two possible values of t. Option A. t=0, t=2u/a. Option B. t=0, t=a/2u. Option C. t=0, t=-2u/a.

Correct Answer is. t=0, t=-2u/a. Explanation. s=ut+½at2 Make s=0, 0=ut+½at2 Divide all terms by u, 0 = t + a/2ut2 Factorise, 0=t(1+a/2ut) So either t=0, or -2u/a=0 (so everything in the brackets=0).

Question Number. 35. If x2 -3=6, then x=. Option A. ±3. Option B. 18. Option C. ± 2.

Correct Answer is. ±3. Explanation. x2 =6 +3, x2 =9, x=+/-3.

Question Number. 7. (A+B)4 is (A+B)2 . Option A. (A+B)6 . Option B. (A+B)2 . Option C. A+B.

Correct Answer is. (A+B)2 . Explanation. Subtract the indices.

Question Number. 9. What is y in the formula shown? a=(X+B)/y. Option A. (a + X) / B. Option B. (X - B) /a. Option C. (X +B)/ a.

Correct Answer is. (X +B)/ a. Explanation. The A and y can be swapped in this situation.

Question Number. 24. (x+y)2 ÷ (x + y)8 has a base and exponent of. Option A. (x+y)10. Option B. (x+y)-6. Option C. (x+y)1/4.

Correct Answer is. (x+y)-6 . Explanation. If the bases are the same, keep it the same, but subtract the indices (exponents) if dividing.(Add the indices if multiplying).

Question Number. 15. Make x the subject of the formula in y = mx+c. Option A. (y-c)/m. Option B. y-c/m. Option C. y-m/c.

Correct Answer is. (y-c)/m. Explanation. Basic transposition.

Question Number. 38. What is log 0.1?. Option A. -0.1. Option B. 0. Option C. -1.

Correct Answer is. -1. Explanation. Log of 0.1 is always -1, (log 0.01 = -2, log 0.001 = -3 etc).

Question Number. 30. The characteristic of Log 0.698 is. Option A. 1. Option B. -1. Option C. -2.

Correct Answer is. -1. Explanation. The characteristic of a logarithm is the integral part of the logarithm. The mantissa is the decimal part. So, for example Log8(29345) = 4.94694 the characteristic is 4 and the mantissa 0.94694. The log definition y=bx, logb(y)=x. So 0.698 = 10powerx. x must be -1.*** (i.e minus one-point-something).

Question Number. 43. What is the characteristic of 5.74?. Option A. 1. Option B. -1. Option C. 0.

Correct Answer is. 0. Explanation. If you find the Log of 5.74, it will be 0.--- The '0' is the characteristic.

Question Number. 39. What is log 1?. Option A. 10. Option B. 1. Option C. 0.

Correct Answer is. 0. Explanation. Log of 1 is always 0.

Question Number. 52. Log 100/2 =. Option A. Log 200. Option B. Log 98. Option C. 1.

Correct Answer is. 1. Explanation. log 100=2, 2/2 = 1.

Question Number. 10. 67 divided by 127 is equal to. Option A. 1/2. Option B. 1/20. Option C. 1/128.

Correct Answer is. 1/128. Explanation. Cannot subtract the indices when the base is different. 127 =27 x67 . Now cancel the 67 top and bottom. 1/27 = 1/(2x2x2x2x2x2x2) = 1/128.

Question Number. 42. What is 101112 -10012 ?. Option A. 1100 2 . Option B. 1110 2 . Option C. 1010 2 .

Correct Answer is. 11102 .

Question Number. 4. D in hexidecimal is what number in decimal?. Option A. 17. Option B. 13. Option C. 8.

Correct Answer is. 13. Explanation. In hexidecimal, 10 is A, 11 is B, 12 is C, 13 is D, 14 is E and 15 is F.

Question Number. 22. Hexadecimal is base. Option A. 16. Option B. 8. Option C. 2.

Correct Answer is. 16. Explanation. Hexadecimal is base 16.

Question Number. 26. 100112 =. Option A. 292 . Option B. 1910. Option C. 3510.

Correct Answer is. 1910. Explanation. (1 * 16) + (0 * 8) + (0 * 4) + (1 * 2) + (1 * 1) = 19.

Question Number. 29. BCD format of numbering system has a base of. Option A. 8. Option B. 2. Option C. 10.

Correct Answer is. 2. Explanation. BCD is base 2.

Question Number. 27. y = 2x + 4, When x = -1, y =. Option A. 4. Option B. 2. Option C. 0.5.

Correct Answer is. 2. Explanation. y=2(-1)+4=-2+4 =+2.

Question Number. 53. Log 100+cos60. Option A. 0.25. Option B. 25. Option C. 2.5.

Correct Answer is. 2.5. Explanation. Log 100=2, cos60=0.5, 2+0.5=2.5.

Question Number. 1. Solve the following equations for x: 4x+8y=64 2x-8y=86. Option A. 125. Option B. 25. Option C. 5.

Correct Answer is. 25. Explanation. Add like terms to eliminate y term. Thus 6x = 150, x = 25.

Question Number. 12. 2x-3 = 4; x =. Option A. 7. Option B. -3. Option C. 3.50.

Correct Answer is. 3.50. Explanation. 2x-3=4, 2x=4+3, 2x=7, x=7/2=3.5.

Question Number. 46. Octal is the word given to what base?. Option A. 8. Option B. 2. Option C. 16.

Correct Answer is. 8.

Question Number. 17. Octal is to the base of. Option A. 2. Option B. 16. Option C. 8. .

Correct Answer is. 8. Explanation. Octal is base 8 numbering system

Question Number. 33. Given the log of A exceeds that of B by 4, find the correct statement about A and B. Option A. A is 4000 times the value of B. Option B. A is 10,000 times the value of B. Option C. A is 1000 times the value of B.

Correct Answer is. A is 10,000 times the value of B. Explanation. log 10=1, log 100=2, log 1000=3, log 10000=4, log 100,000=5.

Question Number. 37. What is Log 9-Log 3 + Log 4. Option A. Log 12. Option B. Log 10. Option C. Log 16.

Correct Answer is. Log 12. Explanation. Log 9 = 2Log3, therefore 2Log3-Log3 + Log 4 = Log3 + Log4 = Log(3 x 4) = Log12.

Question Number. 20. What type of equation is this? ax2 +bx+c = 0. Option A. Quadratic equation. Option B. Polynomic equation. Option C. Gradient of the line.

Correct Answer is. Quadratic equation. Explanation. Quadratic.

Question Number. 13. V = (a+b) r2 Find a. Option A. V - r2 - b. Option B. (V - b)/ r2 Option C. V / r2 - b.

Correct Answer is. V / r2 - b. Explanation. Basic transposition.

Question Number. 21. What is (X2 x X3 )3 ?. Option A. X36. Option B. X 15. Option C. X 10.

Correct Answer is. X 15. Explanation. X2 * X3 = X5 X5 raised to the power 3 is X15.

Question Number. 41. A quadratic equation has the real roots x=6 and x=9. Determine the equation which is satisfied by these roots. Option A. x2 -54x+15=0. Option B. x2 -15x+54=0. Option C. x2 +15x-15=0.

Correct Answer is. X2 -15x+54=0. Explanation. Change the sign of each root -6, -9. Coefficient of x is the addition, the constant is the multiplication. http://www.themathpage.com/alg/quadratic-equations.htm.

Question Number. 32. If 2x2 + kx-8 = 0 has two equal real roots, then. Option A. k is an imaginary number. Option B. k=±8. Option C. k=-8.

Correct Answer is. k is an imaginary number. Explanation. Because of the +/- part of the quadratic solution formula, it is not possible for the equation to have two equal roots. k is therefore an imaginary number.

Question Number. 8. log 9-log 3=. Option A. log 6. Option B. log 3. Option C. log 9.

Correct Answer is. log 3. Explanation. log 9 = log (3x3) = 2 log 3. 2 log 3-log 3 = log 3.

Question Number. 49. What is log AB?. Option A. log (A+B). Option B. log A+log B. Option C. Log A-Log B.

Correct Answer is. log A+log B. Explanation. External website.

Question Number. 50. What is LogA/B?. Option A. log A+Log B. Option B. log A-Log B. Option C. Log (A-B).

Correct Answer is. log A-Log B. Explanation. External website.

Question Number. 45. Solve for x: 5x-7=3. Option A. x=-4/5. Option B. x=-2. Option C. x=2.

Correct Answer is. x=2. Explanation. 5x-7 = 3add 7 to both sides to give 5x = 10 divide both sides by 5 to give x = 2.

Question Number. 23. y=mx+c can also be written. Option A. x=y-c/m. Option B. x=y/m+c. Option C. x=y/m-c.

Correct Answer is. x=y-c/m. Explanation. Basic transposition.

Question Number. 14. Make m the subject of the formula in y=mx+c. Option A. y-x/c. Option B. y-c/x. Option C. y+c/x.

Correct Answer is. y-c/x. Explanation. Basic transposition.

Question Number. 16. Make c the subject of the formula in y = mx+c. Option A. y-mx. Option B. mx-y. Option C. y+mx.

Correct Answer is. y-mx. Explanation. Basic transposition.