Advanced level 2023 northwest regional mock pure mathematics with statistics 2
Advanced level 2023 northwest regional mock pure mathematics with statistics 2
The following table shows values of two variablesx andy obtained in an experiment.
i x [1 3 4 5
y | 17.1 28.0 32.9 31.9 25.0 S’
(a) Use the trapezium’rule to evaluate/5ydx
The variables x and y obey alaw ofthe form y= ax2+bx.
(b) By plotting a suitable straight line graph, estimate the values of the constants a andb.
JOmarks
4. (i)Given thatthe x-axis is a tangentto the circle(E):x2+y2-r ax+by= c, atthe point(2, 0) andthat
(F) passesthroughthe point(5,3), findthe valuesofthe constants a,b and c.
^ (ii) Prove by mathematical induction that 72+2 is divisible by 3 for all integers n> 1.
*
(5, 5)marks
5. (i) Consider the complex number z wherez — x+iy.
0
GiventhatRe(~”r)— ,showthatthelocusofzis a circle and statethecentreandradiusofthecircle.
(ii) Given the complex number vv=1+V3i
Findthe magnitude and argumentof w.
Hence or otherwise express —-in the form a 4-bi where a and b are real numbers.
W
(5, 5)marks
6. (i)) Given that g(6)= cos5#+V3sin50,
(a) expressg(0) in the form Rcos(59 — a) whereR> 0 and 00 <a< 90°,
(b) show that cos50+ \/3sin5f? + 8 < 10
(ii) Show that h*n?*+S’~~T~= tan4x.
cos6x-cos2x u
Hence., solve for x in the interval 0 < X ^the equation sin6x-eos6x = cos2x-sin2x.
