EASA Part 66 : Mathematics Question6
Question Number. 10. (a * b)(a * b) =. Option A. a2 + 2ab + b2 . Option B. a2 b2. Option C. a2 + b2.
Correct Answer is. a2 b2 . Explanation. Do a x (a-b) (i.e. expand that bracket), then do b x (a-b) (i.e. expand that bracket too). Then gather together like terms. You will find that ab and -ab cancel.
Question Number. 31. Remove the brackets and simplify: (x-y)(x-y). Option A. x2 -2xy-y2 . Option B. x2 +y2 . Option C. x2 -2xy+y2 .
Correct Answer is. x2 -2xy+y2 . Explanation. Multiply both the x and the -y in the first bracket by both the x and -y in the second bracket. X2 -xy-yx + y2 x2 -2xy + y2 ( remember -x- = + and yx is the same as xy).
Question Number. 16. Factorise the following : 4x2 -6x-28 = 0. Option A. (4x-14) (x+2). Option B. (2x+7) (x-2). Option C. (2x2 +7) (x + 2).
Correct Answer is. (4x-14) (x + 2). Explanation. Expand each answer in turn until you get the question. Remember the smiley face.
Question Number. 22. (x + y + z)(x + y + z) =. Option A. 2(x + y + z). Option B. 2x + 2y +2z. Option C. (x + y + z)2 .
Correct Answer is. (x + y + z)2 .
Question Number. 23. If x in an equation equals Ly + 7cb, define the formula for finding the subject y. Option A. x-7cb/L. Option B. x-7cb/L. Option C. x-L/7cb.
Correct Answer is. x-7cb/L. Explanation. Subtract the 7cb (x-7cb) then divide all by L.
Question Number. 15. Factorise the following : x2 -x-6=0. Option A. (x-2)(x+3). Option B. (x-2)(x-3). Option C. (x+2)(x-3).
Correct Answer is. (x+2)(x-3). Explanation. Choose 2 numbers where the sum = -1 (the coefficient of x) and the product (multiple) is -6 (the constant). Alternatively, multiply out the answers a, b, c until you get the question.
Question Number. 2. Simplify the following (w + z)(x - y)(y - w) / (y - x)(w - y)(w + z). Option A. -1. Option B. 0. Option C. +1.
Correct Answer is. +1. Explanation. First cancel the (w+z) because they are the same. Then multiply out the top and bottom lines (remember the smiley face) and cancel what you can (everything cancels - leaving you with just 1/1=1).
Question Number. 21. Determine x in the following: (2x-1)(3x+2) = 0. Option A. 1.5, 1. Option B. 0.5, 3. Option C. -0.67, 0.5.
Correct Answer is. -0.67, 0.5. Explanation. Two values of x, either 2x-1 = 0 (2x = 1, x = 1/2) or 3x + 2 = 0 (3x = -2, x=-2/3).
Question Number. 14. The heat of a resistor is given by the equation h = I2 RT. Find the current I. Option A. . Option B. . Option C. .
Correct Answer is. . Explanation. h/RT Square root ALL.
Question Number. 1. Solve the following equation: 5x = 3x + 2. Option A. 3. Option B. 5. Option C. 1.
Correct Answer is. 1. Explanation. 5x-3x = 2, 2x = 2, x = 1.
Question Number. 24. 64y = 64 what does y =. Option A. 1. Option B. 0. Option C. 0.5. .
Correct Answer is. 1. Explanation. Anything to the power of 1 is itself
Question Number. 28. simplify (a+b)(a-c)(b-c) divided by (b+a)(c-a)(c-b). Option A. -1. Option B. (a+b)(a-c)(b-c). Option C. 1.
Correct Answer is. 1. Explanation. Because this is a series of multiplications on both top and bottom we can do the following: (a+b)/(b+a) = 1 (a-c)/(c-a) =(a-c)/-(a-c) = -1 (b-c)/-(b-c) = -1 hence the result is 1x-1x-1 =1.
Question Number. 20. 27y = 3 so y is equal to:. Option A. 1/9. Option B. 1/3. Option C. 9/1.
Correct Answer is. 1/9. Explanation. 3/27 = 1/9.
Question Number. 19. 12x/2y + 14 = 50, When y = 2, solve for x. Option A. 11.6. Option B. 14. Option C. 12.
Correct Answer is. 12. Explanation. 12x/(2x2) = 50-14. 12x = 36 x 4. 12x = 144. x = 144/12 = 12.
Question Number. 17. Solve for x in the equation: 3(x + 2) = 30 + 2(x-4). Option A. 8. Option B. 16. Option C. 15.
Correct Answer is. 16. Explanation. Multiply out the bracket first. 3x + 6 = 30 + 2x-8. Then take all 'x' terms to left, and all 'non-x' terms to right. 3x-2x = 30-8-6 etc.
Question Number. 6. If y/x = 4 and y = 5 then x =. Option A. 20. Option B. 4/5. Option C. 1 ¼.
Correct Answer is. 1¼. Explanation. 5/x = 4, x = 5/4 = 1 1/4.
Question Number. 11. If y/x = 4 and x = 5 then y =. Option A. 1 ¼. Option B. 20. Option C. 4/5.
Correct Answer is. 20. Explanation. y/5 = 4. y = 5x4 = 20.
Question Number. 27. Simplify 5(x-2y) + 3(2y-x). Option A. 4x +4y. Option B. 2x +4y. Option C. 2x-4y.
Correct Answer is. 2x-4y. Explanation. Remove the brackets first: 5x-10y +6y-3x Collect like terms: 5x-3x +6y-10y = 2x-4y.
Question Number. 32. Evaluate (3X2 -6xy) / (x-2y). Option A. cannot be simplified further. Option B. 3x-3y. Option C. 3x.
Correct Answer is. 3x. Explanation. 3x2 -6xy=3x(x-2y) Dividing by x-2y leaves 3x.
Question Number. 8. 21=43- , is equal to. Option A. 21-43. Option B. 43+21. Option C. 43-21.
Correct Answer is. 43-21. Explanation. 21=43- , 21+ = 43, = 43-21.
Question Number. 3. Given 43-x = 21, find the value of x. Option A. 43-21. Option B. 43/21. Option C. 43+21.
Correct Answer is. 43-21. Explanation. 43 = 21 + x 43-21 = x.
Question Number. 18. 2x = 4(x-3), Evaluate x. Option A. 6. Option B. 0.5. Option C. 2.
Correct Answer is. 6. Explanation. Expand the bracket 2x = 4x-12, Take 4x to LHS 2x-4x = -12, -2x = -12, x = -12/-2 = 6
Question Number. 33. Evaluate (3a + 2b)(2a-3b). Option A. 6a2 -5ab-6b2 . Option B. 6a-5ab-6b. Option C. 6a2 + 5ab-6b2 .
Correct Answer is. 6a2 -5ab-6b2 . Explanation. Multiply 3a(2a-3b) =6a2 -9ab then multiply 2b(2a-3b) = 4ab-6b2 collect like terms to give 6a2 -5ab-6b2 .
Question Number. 9. Evaluate. 2X2 Z2 (3X-Z2 ) =. Option A. 6X2 z2 +3x-z2 . Option B. 6x2 z2 -2x2 z2 . Option C. 6x3 z2 -2x2 z4 .
Correct Answer is. 6x3 z2 -2x2 z4 . Explanation. Multiply out the brackets and add the indices where necessary.
Question Number. 25. Simplify 3a-2b +6a-3b-2a. Option A. 7a-5b. Option B. 7a +5b. Option C. 7a +b.
Correct Answer is. 7a-5b. Explanation. Collect together like terms: 3a +6a-2a-2b-3b = 7a-5b.
Question Number. 12. Determine x. Option A. 9.029. Option B. 9.570. Option C. 8.971.
Correct Answer is. 9.029. Explanation. Root of 81 is 9, so it must be 9.xxx (which rules out b). (Since the content of the brackets comes to a negative number, it is positive when it is squared).
Question Number. 5. Given that A = X+BY, what is Y equal to?. Option A. A-X add B. Option B. A-X divided by B. Option C. A-X minus B.
Correct Answer is. A-X divided by B. Explanation. Basic transposition.
Question Number. 4. Make L the subject of the formula 2pfL = x. Option A. L = 2pf. Option B. L = 2pf / x. Option C. L = x / 2pf.
Correct Answer is. L = x / 2pf. Explanation. Divide the x by 2pf.
Question Number. 29. Make P the subject of the formula I =PRT/100. Option A. P = IRT/100. Option B. P = 100I/RT. Option C. P = 100RT/I.
Correct Answer is. P = 100I/RT. Explanation. Multiply both sides by 100 then divide both sides by RT to get P =100I/RT.
Question Number. 13. Find L in the following expression. Option A. Q2 C / R2 . Option B. Q2 C2 / R. Option C. Q2 R2 C.
Correct Answer is. Q2 R2 C. Explanation. QxR to remove the R from RHS. Square both sides to remove the root from RHS. Multiply LHS by C to remove the C from RHS and you are left with L.
Question Number. 30. Make u the subject of the formula v2 = u2 + 2as. Option A. u = v-2as. Option B. u = √(v2 -2as). Option C. u = √(v2 +2as).
Correct Answer is. u = √(v2 -2as). Explanation. u = √(v2 -2as).
Question Number. 26. Simplify 3x-2xy-3y +5xy-2x +2y. Option A. x + 3xy-y. Option B. 5x + 3xy-y. Option C. x-3xy + y.
Correct Answer is. x + 3xy-y. Explanation. Collect together like terms: 3x-2x +5xy-2xy +2y-3y = x +3xy-y.
Question Number. 7. (x - 3)(x + 5)=. Option A. x2 +2x. Option B. x2 +2x-15. Option C. x2 -15.
Correct Answer is. x2 +2x-15. Explanation. Multiply x by x and +5, then multiply -3 by x and +5. Then gather together all like terms.