Mark Scheme Pure Mathematics Year 1 (AS) Unit Test 4 .
Mark schemePure Mathematics Year 1 (AS) Unit Test 4: TrigonometryMarksAOsPearsonProgression Stepand Progressdescriptor A 45 seen or implied in later working.B11.1b5thMakes an attempt to use the sine rule, for example, aSchemesin120sin 45 8x 34x 1States or implies that sin120 32and sin 45 22Makes an attempt to solve the equation for x.Possible steps could include:326136 oror16 x 6 8 x 216 x 6 4 x 116 x 6 8 x 2 8 3 x 2 3 16 2 x 6 2 or 4 6 x 6 16 x 6 or24 x 6 16 6 x 6 66 2 2 3 x 16 2 8 3 or 4 6 x 6 16 x 6 or12 x 3 8 6 x 3 6x 6 2 2 36 63 6 3or x or x o.e.16 4 616 2 8 38 6 12Makes an attempt to rationalise the denominator bymultiplying top and bottom by the conjugate.Possible steps could include:x 3 2 3 8 8 2 4 3 8x 48 12 6 8 6 12128 48x 36 4 680 3 2 4 32 4States the fully correct simplifed version for x. Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.Solve problemsinvolving surds incontext andcomplete simpleproofs involvingsurds
Mark schemex Pure Mathematics Year 1 (AS) Unit Test 4: Trigonometry9 6*20(7)1b1.1a3rdM13.1aUnderstand anduse the generalformula for thearea of a triangle.A11.1bStates or implies that the formula for the area of a triangle is111ab sin C or ac sin B or bc sin A222M11 9 6 9 6 4 1 8 3 sin15 or awrt 0.259 2 20 20 or1 awrt1.29 awrt1.58 sin15 or awrt 0.259 .2Finds the correct answer to 2 decimal places. 0.26(3)(10 marks)Notes1aAward ft marks for correct work following incorrect values for sin 120 and sin 45 1bExact value of area is 124 11 6200 6 2 . If 0.26 not given, award M1M1A0 if exact value seen. Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.
Mark schemeMarksAOsPearsonProgression Stepand ProgressdescriptorStates or implies that the angle at P is 74 B12.2a4thStates or implies the use of the cosine rule. For example,M11.1aM1ft1.1bM1ft1.1bA11.1bQ2aPure Mathematics Year 1 (AS) Unit Test 4: TrigonometrySchemep 2 q 2 r 2 2qr cos PMakes substitution into the cosine rule.Solve triangleproblems in arange of contextsp 2 7 2 152 2 7 15cos 74Makes attempt to simplify, for example, stating p 2 216.11.States the correct final answer. QR 14.7 km.(5)2bStates or implies use of the sine rule, for example, writingsin Q sin P qpM13.1a4thSolve triangleproblems in arange of contextsMakes an attempt to substitute into the sine rule.sin Q sin 74 1514.7M1ft1.1bSolves to find Q 78.77 A1ft1.1bMakes an attempt to find the bearing, for example, writingM1ft1.1bA1ft3.2abearing 180 – 78.77 – 33 States the correct 3 figure bearing as 068 (5)(10 marks)Notes2aAward ft marks for correct use of cosine rule using an incorrect initial angle.2bAward ft marks for a correct solution using their answer to part (a). Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.
Mark schemePure Mathematics Year 1 (AS) Unit Test 4: TrigonometryMarksAOsPearsonProgression Stepand ProgressdescriptorM12.15thM11.1bM11.1bSolve morecomplicatedtrigonometricequations in agiven intervalsuch as onesrequiring use thetan identity(degrees)A11.1bFinds one correct solution for x. (48.2 ,60 , 311.8 or 300 ).A11.1bFinds all other solutions to the equation.A11.1bQ3SchemeStates sin 2 x cos 2 x 1 or implies this by making asubstitution. 8 7cos x 6 1 cos2 x Simplifies the equation to form a quadratic in cos x.6cos 2 x 7 cos x 2 0Correctly factorises this equation. 3cos x 2 2cos x 1 0 or uses equivalent method forsolving quadratic (can be implied by correct solutions).Correct solution. cos x 21or23(6)(6 marks)Notes Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.
Mark schemeQ4aPure Mathematics Year 1 (AS) Unit Test 4: TrigonometryScheme 2 3 or awrt 3.46MarksAOsPearsonProgression Stepand ProgressdescriptorB11.1b4thDetermine exactvalues fortrigonometricfunctions in allfour quadrants(1)4bFigure 1Sine curve withmax 2 and min 2B1Sine curvetranslated 60 tothe right.2.2a4thB12.2aTransform thegraphs oftrigonometricfunctions usingstretches andtranslationsSin curve cutsx-axis at ( 120 ,0) and(60 , 0) and they-axis (0, 3 ).B12.2aAsymptotes fortan curve at x 90 andx 90 B11.1bTangent curve is‘flipped’.B12.2aUses the valueof 2 tan ( 120 )to deduce nointersection in3rd quadrant(can beimplied).B12.2aTangent curvecuts x-axis at( 180 , 0),(0, 0) andB11.1b Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.
Mark schemePure Mathematics Year 1 (AS) Unit Test 4: Trigonometry(180 , 0).(7)4c4dStates that solutions to the equation 2sin( x 60 ) tan x 0will occur where the two curves intersect.States that there are two solutions in the given interval.B1ft3.1a4thUse intersectionpoints of graphsto solve equationsA12.2a(2)4thUse intersectionpoints of graphsto solve equations(10 marks)Notes4bIgnore any portion of curve(s) outside 180 x 180 4cAward both marks for correctly stating that there are two solutions even if explanation is missing. Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.
Mark schemePure Mathematics Year 1 (AS) Unit Test 4: TrigonometryQSchemeMarksAOsPearsonProgression Stepand Progressdescriptor5Makes an attempt to begin solving the equation. For example,sin 3 204states that 4 3cos 3 20M12.15thsin to write,cos 41tan 3 20 4 33M12.1Solve morecomplicatedtrigonometricequations in agiven intervalsuch as onesrequiring use thetan identity(degrees)States or implies use of the inverse tangent. For example, 1 3 20 tan 1 or 3 20 30 3 M11.1bShows understanding that there will be further solutions in thegiven range, by adding 180 to 30 at least once.M11.1bM11.1bA11.1b Uses the identity tan 3 20 30 , 210 , 390 ,. (ignore any out of rangevalues).Subtracts 20 and divides each answer by 3. 10 190 370 , , ,. (ignore any out of range values). 3 3 3 States the correct final answers to 1 decimal place.3.3 , 63.3 , 123.3 cao(6)(6 marks)Notes Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.
Mark schemeQ6aPure Mathematics Year 1 (AS) Unit Test 4: TrigonometrySchemeAny reasonable explanation.MarksAOsPearsonProgression Stepand ProgressdescriptorB12.34thFor example, the student did not correctly find all values of 2x3which satisfy cos 2 x . Student should have subtracted2150 from 360 first, and then divided by 2.Solve simpletrigonometricequations in agiven interval(degrees)N.B. If insufficient detail is given but location of error iscorrect then mark can be awarded from working in part (b).(1)6bx 75 B12.2ax 105 B12.2a4thSolve simpletrigonometricequations in agiven interval(degrees)(2)(3 marks)Notes6aAward the mark for a different explanation that is mathematically correct, provided that the explanation is clearand not ambiguous. Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.
Mark schemeQ7aPure Mathematics Year 1 (AS) Unit Test 4: TrigonometryMarksAOsPearsonProgression Stepand ProgressdescriptorCorrectshape of sinecurvethrough(0, 0).B13.1a4thSine curvehas maxvalue of1and min2B13.1aB13.1aSchemeFigure 2value of Transform thegraphs oftrigonometricfunctions usingstretches andtranslations12Sine curvehas a periodof 2 (can beimplied by 5completecycles) andpassesthrough(1,0),(2,0),.,(10,0).(3)7bStudent states that the buoy will be 0.4 m above the still waterlevel 10 times.B13.2a7thUse functions inmodelling(includingcritiquing)(1) Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.
Mark scheme7cPure Mathematics Year 1 (AS) Unit Test 4: TrigonometrySensible and correct reason. For example:B13.2bA buoy would not move up and down at exactly the same rateduring each oscillation.7thUse functions inmodelling(includingcritiquing)The period of oscillation is likely to change each oscillation.The maximum (or minimum) height is likely to change withtime.Waves in the sea are not uniform.(1)(5 marks)Notes7cAward the mark for a different explanation that is mathematically correct. For example, stating that the buoywould not move exactly vertically each time. Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.
Award the mark for a different explanation that is mathematically correct, provided that the explanation is clear and not ambiguous. Mark scheme Pure Mathematics Year 1 (AS) Unit Test 4: Trigonometry
A level Mathematics specimen papers - Paper 2 Pure Mathematics mark scheme 1 9MA0/02: Pure Mathematics Paper 2 Mark scheme Question Scheme Marks AOs 1 1 2) 2 r M1 1.1a A1 225 22. 24 r 1.1b length of minor arc ) dM1 3.1a 36 ab A1 1.1b (4) 1 Alt 1 2(4.8) 2 r M1 1.1
A level Mathematics specimen papers - Paper 1 Pure Mathematics mark scheme 1 9MA0/01: Pure Mathematics Paper 1 Mark scheme Question Scheme Marks AOs 1 (a) 1.09811 ( ) 2 R B1 1.1b M1 1.1b 1 5 4 (3 dp) A1 1.1b (3) (b) Any valid reason, for example Increas
CSEC English A Specimen Papers and Mark Schemes: Paper 01 92 Mark Scheme 107 Paper 02 108 Mark Scheme 131 Paper 032 146 Mark Scheme 154 CSEC English B Specimen Papers and Mark Schemes: Paper 01 159 Mark Scheme 178 Paper 02 180 Mark Scheme 197 Paper 032 232 Mark Scheme 240 CSEC English A Subject Reports: January 2004 June 2004
Matthew 27 Matthew 28 Mark 1 Mark 2 Mark 3 Mark 4 Mark 5 Mark 6 Mark 7 Mark 8 Mark 9 Mark 10 Mark 11 Mark 12 Mark 13 Mark 14 Mark 15 Mark 16 Catch-up Day CORAMDEOBIBLE.CHURCH/TOGETHER PAGE 1 OF 1 MAY 16 . Proverbs 2—3 Psalms 13—15 Psalms 16—17 Psalm 18 Psalms 19—21 Psalms
H567/03 Mark Scheme June 2018 6 USING THE MARK SCHEME Please study this Mark Scheme carefully. The Mark Scheme is an integral part of the process that begins with the setting of the question paper and ends with the awarding of grades. Question papers and Mark Schemes are d
Examiners should mark according to the mark scheme not according to their perception of where the grade boundaries may lie. All marks on the mark scheme should be used appropriately. All marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, i.e. if the answer matches the mark scheme.
Mark scheme for Paper 1 Tiers 3-5, 4-6, 5-7 and 6-8 National curriculum assessments ALL TIERS Ma KEY STAGE 3 2009. 2009 KS3 Mathematics test mark scheme: Paper 1 Introduction 2 Introduction This booklet contains the mark scheme for paper 1 at all tiers. The paper 2 mark scheme is printed in a separate booklet. Questions have been given names so that each one has a unique identifi er .
the mark scheme should be used appropriately. All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, i.e. if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate’s response is not worthy of credit according to the mark scheme.
