Maths C1 June 2016 MS Written

C1 JUNE 2016 MS WRITTEN

cl sl6 rat<1 . FindJ(-'- *-,,)0,giving each term in its sirnplest form. +; LLxs - +xL? <e' -t-+3x+C , LLSs(4)I-8f +11+ Cwww.mymathscloud.com

2. Express 9l'*I in the lorm 3r', giving/ in the form a-r i &, where a and b are constants.(2)(3.f**') . 3Lz*t ... J=6-.+2www.mymathscloud.com

3. (a) SimplifrJ5o - Jsgiving your answer in the form aJ2, where a is an integer.(2)(b) Hence, or otherwise, simplifyt2]1giving your answer in the form bJi , where D and c are integers and b I 1Jis(3)ar.) .fis ti - fi JZ - SJe - 3Jt = 2d2^www.mymathscloud.com

4.Figure IFigure 1 shows a sketch of part of the curve with equation y : f('r). The curve has amaximum point I at (-2, \ and a minimum point B at (3, 8) and passes through theorigin O.On separate diagrams, sketch the curve with equation(a) y: 3f(;r),(b) r: fQr) - a(3)On each diagram, show clearly the coordinates of the maximum and the minimum pointsand the coordinates of the point where the curve crosses the y-axrs.(2)^) 3{r:c) $rsb) f(l)-s f"A(-2,4)B(3. -8)(r7-zq1(o1*t)(3,-ru)www.mymathscloud.com

5. Solve the simultaneous equationsy+4x+l :0f+5x2+2x:0(6)=) q't o l- lt)L-f ) - 3_ ( rcrlt&&jf)t5dr-'?a-:q j 2-f!_L:[O)s t] aOwww.mymathscloud.com

6. A sequence ar az, at,... is defined byar: 4,a,*r=5-ka,, n)lwhere tis a constant.(a) Write down expressions for a, and a, in terms of ft.Find3(b) :,(1 + a") in terms of /e, giving your answer in its simplest form,100@) l@"*,+ka,)(2\(3)(1)-7t--u_++wL= $,-48+www.mymathscloud.com

7 . Given that.l2x)j!=3x,+6xr+!;. x>o- -dvfind z. Give each term in your answer in its simplified form.dx(6)L-a[ Lf _ +*t*'' {'+- {;*!'+i -tirI'3* tr:'www.mymathscloud.com

The straight line with equation y : 3x - 7 does not cross or touch the curve withequationy: 2px2 - Opx + 4p, where p is a constant.(a) Show that 4p2 - 20p + 9 < 0(b) Hence find the set of possible values ofp.(4)(4)-*- i*-b=) Lo't -6r- 5r-+4tF lrr.n- doer tdt cf,oss or rcotxJl r-rlnre =r b-2-lqElo--Gst$1tkd(trr$lo -www.mymathscloud.com

C1 JUNE 2016 MS WRITTEN

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