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By Eva Shipton, Michael Kenwood, C.T. Moss, Charles Plumpton

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Multiple-choice tests: pure mathematics 47 28 These are well-known inverse curves and should be quickly sketched: Y = e" y = lnx This gives key A. sin tX =! (although the values of tX are not needed). The question is based on the fact that lsin xl ~ 1, giving 1 and 2 both incorrect, and so 3 is correct, giving key E. 30 The equation of a plane given in parametric form must have two parameters, so 1 is incorrect while 2 is correct. 3 is also correct as it is a correct perpendicular form of the equation of a plane.

The point (1, 1) lies E -17 + y2 - 4y = 0 and A outside both circles B C on the circumference of C1 D inside C1 but outside C2 E inside both circles inside C2 but outside C1 Multiple-choice tests: pure mathematics 49 7 Given that y = (In x ) 3 , then dy -= dx A 3lnx 3 B D 3(ln x) 2 c x2 X 3ln x 3(ln x) 2 E X 8 Given that lzl = 4 and arg z = - 2n/3, then z= A -2-i2j3 B -2+i2j3 D -2j3+i2 E -2+ij3 c -2j3-i2 9 The complete solution set of the inequality 2x 2 - 3x- 5 < 0 is A {x: -5/25/2} C {x: -1 < x < 5/2} D {x: x < 5/2} u {x: x > 1} E {x: 1 < x < 5/2} 10 All solutions ofthe equation sin(} = sin 21X are obtained by taking all integer values of n in lJ= A nn + ( -1)"1X B 2nn + ( -1)"21X C nn + ( -1)"21X D nn E 2nn ± 21X 50 Examinations in Mathematics ± 21X 11 When sin x = 3/5, cos x A E c =t =-!

9 Care is needed with this one. Use => dy = dy;dx dx dt dt dy dx 2t 2 = 3t2 = 3t" Then or 11 d 3 -d (ln4+3lnx]=-. X X Remainder= f( -3) = -27 + 18 + 3 + 6 = 0. 1l The more experienced candidate will probably 'spot' Eat once because of the impossibility of getting log x without log y from the given equation. It is always worth glancing through the answers to see if one is blatantly impossible as in this case. However, it does not take long to rearrange Multiple-choice tests: pure mathematics 43 (preferably mentally) the equation to give a linear one in each case, thus: y 2 /x 2 = 4x, 2 log y = log 4 + 3 log x, 1/x 3 = 4/y 2 , xy 2 = 4x 4 • 13 Area = Jo1 x 1 dx = [~3 x 4 1 2 3 12 ] 4 0 = 16 .

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