Further Calculus Past Papers Unit 3 Outcome 2
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1 PSf Further Calculus Past Papers Unit 3 utcome 2 Multiple Choice Questions Each correct answer in this section is worth two marks. 1. Differentiate 3 cos ( 2 π ) 6 with respect to. A. 3 sin(2) B. 3 sin(2 π 6 ) C. 6 sin(2 π 6 ) D. 6 sin(2 π 6 ) Ke utcome Grade Facilit Disc. Calculator Content Source C 3.2 C NC C20 HSN 096 PSf Written Questions [END F MULTIPLE CHICE QUESTINS] 2. Differentiate sin with respect to. 4 hsn.uk.net Page 1 Questions marked c SQA
2 PSf 3. Given that f () = (5 4) 2 1, evaluate f (4). 3 Part Marks Level Calc. Content Answer U3 C2 5 1 C CN C P2 Q8 2 A/B CN C pd: differentiate power pd: differentiate 2nd function pd: evaluate f () (5 4) f (4) = Given f () = cos 2 sin 2, find f () Given that f () = 5(7 2) 3, find the value of f (4). 4 hsn.uk.net Page 2 Questions marked c SQA
3 PSf 6. Differentiate sin 2 with respect to Find the derivative, with respect to, of 1 + cos If f () = cos , find f (). 4 hsn.uk.net Page 3 Questions marked c SQA
4 PSf 9. Differentiate cos 2 with respect to Find d d given that = 1 + cos Given f () = (sin + 1) 2, find the eact value of f ( π 6 ). 3 hsn.uk.net Page 4 Questions marked c SQA
5 PSf 12. Find the equation of the tangent to the curve = 2 sin( π 6 ) at the point where = π 3. 4 Part Marks Level Calc. Content Answer U3 C2 4 C CN C5, C20 = π P2 Q6 pd: find derivative 2 ss: know derivative at =... represents grad. 3 pd: find corresponding -coordinate 4 ic: state equation of tangent 1 1 d d = 2 cos( π 6 ) 2 m = 3 3 = π 3 = = 3( π 3 ) 13. Find d and hence find the eact value of d Differentiate sin 3 with respect to. Hence find sin 2 cos d. 4 hsn.uk.net Page 5 Questions marked c SQA
6 PSf 15. Find 1 (7 3) 2 d. 2 Part Marks Level Calc. Content Answer U3 C2 2 A/B CN C22, C c 3(7 3) 2000 P2 Q pd: integrate function pd: deal with function of function (7 3) Evaluate 0 3 ( 2 + 3) 2 d (a) Evaluate π 2 0 cos 2 d. 3 (b) Draw a sketch and eplain our answer. 2 hsn.uk.net Page 6 Questions marked c SQA
7 PSf 18. (a) Show that (cos + sin ) 2 = 1 + sin 2. 1 (b) Hence find (cos + sin ) 2 d Find ( cos ) d. 4 hsn.uk.net Page 7 Questions marked c SQA
8 PSf 20. (a) B writing sin 3 as sin(2 + ), show that sin 3 = 3 sin 4 sin 3. 4 (b) Hence find sin 3 d (a) Find the derivative of the function f () = (8 3 ) 2 1, < (b) Hence write down d. 1 (8 3 ) 2 1 Part Marks Level Calc. Content Answer U3 C2 (a) 2 A/B CN C (8 3 ) P1 Q10 (b) 1 A/B CN C (8 3 ) c 1 2 pd: process differentiation pd: use the chain rule 3 ic: interpret answer from (a) (8 3 ) f () or 2 3 (8 3 ) 1 2 hsn.uk.net Page 8 Questions marked c SQA
9 PSf 22. The curve = f () passes through the point ( 12 π, 1) and f () = cos 2. Find f () The graph of = f () passes through the point ( π 9, 1 ). If f () = sin(3) epress in terms of. 4 Part Marks Level Calc. Content Answer U3 C2 4 A/B NC C18, C23 = 1 3 cos(3) P1 Q8 1 ss: know to integrate 2 pd: integrate 3 ic: interpret ( π 9, 1) 4 pd: process 1 = sin(3) d stated or implied b cos(3) 1 = 1 3 cos( 3π 9 ) + c or equiv. 4 c = A curve for which d ( d = 3 sin(2) passes through the point 5π 12, ) 3. Find in terms of. 4 Part Marks Level Calc. Content Answer U3 C2 4 A/B CN C18, C23 = 3 2 cos(2) P2 Q10 pd: integrate trig function pd: integrate composite function 3 ss: use given point to find c 4 pd: evaluate c sin(2) d stated or implied b cos(2) 3 3 = 3 2 cos( π) + c 4 c = ( 0 4) hsn.uk.net Page 9 Questions marked c SQA
10 PSf 25. A point moves in a straight line such that its acceleration a is given b a = 2(4 t) 1 2, 0 t 4. If it starts at rest, find an epression for the velocit v where a = dv dt. 4 Part Marks Level Calc. Content Answer U3 C2 4 C NC C18, C22 V = 4 3 (4 t) P2 Q8 1 ss: know to integrate acceleration 2 pd: integrate 3 ic: use initial conditions with const. of int. 4 pd: process solution 1 V = (2(4 t) 1 2 ) dt stated or implied b (4 t) = 2 1 (4 0) c 4 c = hsn.uk.net Page 10 Questions marked c SQA
11 PSf 27. hsn.uk.net Page 11 Questions marked c SQA
12 PSf 28. hsn.uk.net Page 12 Questions marked c SQA
13 PSf 29. [END F WRITTEN QUESTINS] hsn.uk.net Page 13 Questions marked c SQA
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