EASA Part 66 : Mathematics Question1

Question Number. 6. The sum of complex numbers a+bi and a'+b'i are. Option A. (a+b)+(a'+b')i. Option B. (a+a')i+(b+b'). Option C. (a+a')+(b+b')i.

Correct Answer is. (a+b)+(a'+b')i. Explanation. Add the real numbers to each other, then add the imaginary numbers to each other, and keep them separate.

Question Number. 14. Starting from zero amplitude, the cosine curve repeats itself between. Option A. -180 and 180 degree. Option B. -90 and 270 degrees. Option C. 0 and 360 degree.

Correct Answer is. -90 and 270 degrees. Explanation. Sketch the cosine curve and see. Neither 0 or -180 degrees are zero amplitude.

Question Number. 23. If cos 60 is 0.5, what is sin 30?. Option A. 0.5. Option B. None of the above. Option C. 0.866.

Correct Answer is. 0.5. Explanation. Cos θ = sin (90-θ).

Question Number. 19. A right angled triangle has sides 6cm, 8cm and 10 cm. What is the sine of the angle between the 8cm side and the 10 cm side?. Option A. 0.75. Option B. 0.6. Option C. 0.8.

Correct Answer is. 0.6. Explanation. A 6,8,10 triangle is 2 x the 3, 4, 5 triangle which is a right angled triangled triangle with hypotenuse 5. For our triangle the hypotenuse will be 10. The angle we are considering has an opposite side of 6 and sine of an angle is the opposite/hypotenuse. Hence the answer is 6/10 = 0.6.

Question Number. 6. Cos A =. Option A. 1.2. Option B. 0.6. Option C. 0.8.

Correct Answer is. 0.8. Explanation. S.O.H.C.A.H.T.O.A.

Question Number. 18. 57.3 degrees is equal to. Option A. 2 radians. Option B. 1 radian. Option C. π radians.

Correct Answer is. 1 radian. Explanation. This is worth learning.

Question Number. 20. Sin 90 =. Option A. Infinity. Option B. 1. Option C. 0.

Correct Answer is. 1. Explanation. Sin 90 = 1, Cos 90 = 0, tan 90 = infinity.

Question Number. 3. 10000 expressed as ten raised to a power would be. Option A. 105. Option B. 103. Option C. 104.

Correct Answer is. 104. Explanation. 10 * 10 *10 = 1000, 10 * 10 * 10 * 10 = 10000.

Question Number. 1. 5/16 + 3/32 expressed as a single fraction is. Option A. 13/32. Option B. 8/48. Option C. 15/512.

Correct Answer is. 13/32. Explanation. 5/16 = 10/32 , 10/32 + 3/32 = 13/32.

Question Number. 16. A right angled triangle has the two shortest sides of 5cm and 12 cm. What is the length of the longest side?. Option A. 17cm. Option B. 15cm. Option C. 13cm.

Correct Answer is. 13cm. Explanation. Use Pythagoras theorem The square on the hypotenuse is equal to the sum of the squares on the other two sides. 52 + 122 = h2 25 + 144 = h2 , h = √169 =13.

Question Number. 10. On a right angle triangle, the longest side is 20 cm and the shortest is 12 cm. What is the other side?. Option A. 13 cm. Option B. 18 cm. Option C. 16 cm.

Correct Answer is. 16 cm. Explanation. 3,4,5 triangle. Also applies to multiples of 3,4,5 such as 6,8,10 and 12,16,20.

Question Number. 4. 60 mm expressed as a percentage of 3 metres is. Option A. 2 %. Option B. 1.8 %. Option C. 0.5 %.

Correct Answer is. 2 %. Explanation. (60 * 100) / 3000.

Question Number. 22. Sin A is equal to. Option A. 3/4. Option B. 3/5. Option C. 4/5.

Correct Answer is. 3/5. Explanation. B&C is opposite to A, A&B is adjacent to A, A&C is hypotenuse, sin = o/h, cos = a/h , tan= o/a.

Question Number. 21. What size of angle has the same ratio for both the sine and the cosine?. Option A. 60 degrees. Option B. 0 degrees. Option C. 45 degrees.

Correct Answer is. 45 degrees. Explanation. An isosceles right angled triangle has two 45 degree angles. The size of the two sides that are not the hypotenuse are the same. This means that both the sine which is opposite/hypotenuse and the cosine which is adjacent/hypotenuseis the same as the adjacent = opposite in this case.

Question Number. 2. Dividing 41/2 by 2 1/6 gives the answer of. Option A. 21/3. Option B. 25/12. Option C. 54/26.

Correct Answer is. 54/26. Explanation. 41/2 = 9/2, 21/6 = 13/6 Turn one fraction up-side-down then multiply 9/2 x 6/13 = 54/26.

Question Number. 5. The average speed of an aircraft that travels 7200 miles in 12 hours is. Option A. 864 MPH. Option B. 167 MPH. Option C. 600 MPH.

Correct Answer is. 600 MPH. Explanation. 7200 /12.

Question Number. 2. Two angles of a triangle are 68o and 32o . Therefore the third angle must be. Option A. 114o . Option B. 80o . Option C. 63o .

Correct Answer is. 80o . Explanation. The sum of all the angles in a triangle is 180 degrees.

Question Number. 5. Sin ø =. Option A. A/C. Option B. B/C. Option C. C/A.

Correct Answer is. A /C. Explanation. S.O.H.C.A.H.T.O.A.

Question Number. 13. A sector with angle A is subtended to the centre point of a circle. Area of the sector is proportional to:. Option A. Angle A. Option B. Cos A. Option C. Sin A.

Correct Answer is. Angle A. Explanation. Area of a sector is proportional to the subtended angle of the sector.

Question Number. 3. Which of the following formulae are correct for the triangle shown?. Option A. A2 = C2 + B2 . Option B. B2 = C2 + A2 . Option C. C2 = A2 + B2 .

Correct Answer is. C2 = A2 + B2 . Explanation. Pythagoras theorem.

Question Number. 15. Choose the correct statement:. Option A. Cosec2 x-Cot2 x = 1. Option B. Sec2 x+tan2 x = 1. Option C. Cos2 x-Sin2 x = 1.

Correct Answer is. Cosec2 x-Cot2 x = 1. Explanation. See http://www.ilovemaths.com/2trigid.htm.

Question Number. 17. The trigonometrical ratio; adjacent divided by hypotenuse is. Option A. Sine. Option B. Tangent. Option C. Cosine.

Correct Answer is. Cosine. Explanation. Sin = Opp/Hyp, Cos = Adj/Hyp, Tan = Opp/Adj.

Question Number. 1. What is the tangent of 90o ?. Option A. Negative infinity. Option B. 0. Option C. Positive infinity.

Correct Answer is. Positive infinity. Explanation. Technically, the tan curve goes off the graph to + infinity at 90 degrees, but then comes back on at - infinity at the same point. Choose + infinity for the answer here (since it goes to +infinity first).

Question Number. 9. In a right-angle triangle, the cosine of an angle is. Option A. opposite divided by hypotenuse. Option B. adjacent divided by hypotenuse. Option C. opposite divided by adjacent.

Correct Answer is. adjacent divided by hypotenuse.

Question Number. 8. In a right-angle triangle, the tangent of an angle is. Option A. opposite divided by adjacent. Option B. adjacent divided by hypotenuse. Option C. opposite divided by hypotenuse.

Correct Answer is. opposite divided by adjacent. Explanation. S.O.H.C.A.H.T.O.A.

Question Number. 11. In a right triangle, SINE theta =. Option A. adjacent divided by hypotenuse. Option B. opposite divided by adjacent. Option C. opposite divided by hypotenuse.

Correct Answer is. opposite divided by hypotenuse.

Question Number. 7. In a right-angle triangle, the sine of an angle is. Option A. opposite divided by hypotenuse. Option B. adjacent divided by hypotenuse. Option C. opposite divided by adjacent.

Correct Answer is. opposite divided by hypotenuse. Explanation. S.O.H.C.A.H.T.O.A.

Question Number. 12. Complete the following: SINE a =. Option A. a squared times b squared. Option B. opposite side divided by the hypotenuse side. Option C. adjacent side divided by the opposite side.

Correct Answer is. opposite side divided by the hypotenuse side.

Question Number. 4. In a right-angled triangle the other two angles are both 45°. The length of the opposite side can be calculated by. Option A. cos 45° x length of the adjacent side of the triangle. Option B. cos 45° x length of the adjacent side of the triangle. Option C. sin 45° x length of the hypotenuse side of the triangle.

Correct Answer is. sin 45° x length of the hypotenuse side of the triangle. Explanation. sin 45o = opp/hyp opp = sin 45o / hyp.