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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread If z1 = 4 - 1 and z2 = 2i , find in each case the two possible values of z3 so that the points representing z1, z2,z3 form an isosceles right angled triangle with right angle at : z1
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Prove that the point z1 ,z2, z3 are collinear if (z3 - z1)/ ( z2 - z1 ) is real Hence show that the points representing 5 = 8i , 13 + 20i, and 19 + 29i are collinear
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Let z = 1 + cosE + isinE a) Show that |z| = 2cosE/2 and argz = E/2 b) Hence show taht z^-1 = 1/2 - 1/2 itanE/2
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Let z = cisE and w = cisB, that is |z| = |w| = 1. Evaluate z + w in mod-arg form and hence show that arg(z+w) = 1/2 (arg z + arg w) The hint given is to use sums to products Answer is z + w = 2cos((E-B)/2) cis((E+B)/2)
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Sorry, z^4 - 2z^3 + 7z^2 - 4z + 10 = 0
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Find the values of a for which z - ai is factor of the equation Is it factor theorem ?? Seems tedious?
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread If 4 - tanE = 5sinEcosE, show that x = tanE is a root of the equation x^3 - 4x^2 + 6x - 4 = 0
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Find the values p and q given that 1 + 2i is a root of the equation z^3 + pz + q = 0, where p and q are real.
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Find and describe the locus of points in the Argand diagram which correspond to zz(conjugate) = (Re( z - 1 + 3i))^2 LHS is z times z (conjugate) Answer is a parabola with focus at the origin and the directrix at x = 1
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread P (2ap, ap^2) and Q (2aq, aq^2) are variable point on the parabola x^2 = 4ay. R is the intersection of the tangent at P and the line through Q parallel to the axis of the parabola, while U is the intersection of the tangent at Q...
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread How to solve for z: z^2 - z + ( 1 + i) = 0 Using The Quadratic method with finding out lander . Really confused on what to do.
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Use the discriminant to show that mx - y - m^2 = 0 touches the parabola x^2 = -4y for all values of m Hence find the equations of the tangents to x^2 = -4y through the point A (1,2)
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Find the parameters of the points of contact of the tangents to x = 10t , y = 5t^2 from the point P (24,-5) Not sure how to approach this question.
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Have a line that intesects the coordinate axes at ( 0 , 2a + ap^2) and (2ap + ap^3 , 0 ) Now find the area of the triangle formed by the two intercepts and the origin. So using 1/2 . length . width I get A = 1/2 a^2 ( 2 +...
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread SOlve integral of (16 - x^2)^1/2 dx using the substitution x = 4sinE
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Use mathematical induction to prove that for all positive integers n: a + (a+ d) + (a + 2d) + ... + ( a + ( n - 1 )d) = 1/2 . n (2a + (n - 1)d)
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread A straight line passes through the point 2,1 and has positive x and y int at P and Q respectivley. Let Angle ORQ = a where O is the origin. So the A of the Triange = (2tan a + 1 )^2 / 2tan a Now how do I show that this area is...
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread PQ is a diameter on the given circle and S is a point on the circumference. T is the point on PQ such that PS = PT . Let Angle SPT = alpha a) Show that the are A of triangle SPT is A = 1/2 d^2 cos^2a sina, where d is the...
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I was able to do the first and second derivative but am struggling with the 3rd.
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    Cambridge Prelim MX1 Textbook Marathon/Q&A

    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread If y = sin x prove i) y' = sin(pi/2 + x) ii) y'' = sin ( pi +x ) iii) y''' = sin (3pi/2 + x ) Hence deduce an expression for y^n
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