National 5 Mathematics Past Papers By Topic

National 5 MathematicsPast Papers by TopicV.1Contents:Expressions & FormulaeSurds & Indices. .Scientific Notation .Algebra . .Completing the Square Algebraic Fractions. Volumes .Gradient (See Straight Line) .Circles . .Page13578102415RelationshipsThe Straight Line .Function Notation .Solving Equations/Inequations .Simultaneous Equations .Change the Subject . .Quadratic Functions. .Properties of Shapes (See Circles). .Similar Shapes. .Trigonometry (Graphs and Equations) .Trig Identities . .24303133373815505460ApplicationsTriangle Trigonometry. .Converse of Pythagoras Vectors . .Percentages Fractions and BODMAS .Statistics 697071788284

This book of past paper questions by topic is made freely available by Zeta Maths forteachers and learners, to be used for educational purposes.The questions have been made available by and are copyright of the SQA. To obtainpast papers by years visit the SQA website at www.sqa.org.uk.The questions marked PP are practice papers produced by www.maths180.com. Visitthe website for 100’s of free video lessons for National 5 and Higher Maths.The answers and worked solutions in these documents have been collated from avariety of sources and are not the authorship of Zeta Maths Ltd.For easy navigation of the document, the contents page is linked to each chapter andthe chapter headings at the top of each page are linked back to the contents page.

PP A P1Ans2017P2Ans2016 P2Ans2016 P1Ans2015P1Ans2015 P1Ans2014P2Ans2014P1SNational 5: Surds and Indiceswww.zetamaths.com3332232331

PP AP2AnsNational 5: Surds and IndicesPP B P1Ans2PP BP1Ans2Ans2PP C P12224/334 33PP E P1AnsPP DP1AnsPP DP1Ans2Ans3(a) 25 2www.zetamaths.com(b) t 1/22

Ans2018 SP P2National 5: Scientific Notation291.5 102015 P23Ans2Ans2016 P22-98 10PP B P22www.zetamaths.com3

3AnsPP E P2AnsNational 5: Scientific NotationAnsPP F P13www.zetamaths.com4

AnsPP CP1AnsPP B P1AnsPP A P1AnsPP A P1Ans2017P1Ans2015 P1Ans2014 P1National 5: Algebrawww.zetamaths.com23323335

PP E P1National 5: Algebra2016P2Ans3Ans22017 P21(a) (2x 5)(2x – 5)2𝑥 5(b) 𝑥 22AnsPPAP1Ans3PP B P113AnsPP C P1Ans2PP F P11Ans2www.zetamaths.com6

2(a)𝑦 (𝑥 4)2 3223PP C P1AnsPP AP1Ans2016 P2Ans2014 P1Ans2018 SP P1National 5: Algebra (Completing the Square)2Ans1www.zetamaths.com7

PP B P1Ans2017P1Ans2016 P2Ans2015P2Ans2015P1Ans2014 P2Ans2018 SP P1National 5: Algebraic Fractions333310s3www.zetamaths.com228

AnsNational 5: Algebraic FractionsPP C P2133AnsPP DP2AnsPP DP1Ans4AnsPP F P23www.zetamaths.com9

2018SP P2National 5: Volume of SolidsAns5870cm3Ans2014 P25www.zetamaths.com10

National 5: Volume of SolidsAns2016 P25Ans2017 P25www.zetamaths.com11

National 5: Volume of Solids4AnsPP A P23AnsPP B P25www.zetamaths.com12

PP C P2National 5: Volume of Solids2Ans3AnsPP D P25www.zetamaths.com13

National 5: Volume of SolidsPP E P23Ans3AnsPP F P25www.zetamaths.com14

2018 SP P2National 5: Circles3(a) 864cm(b) 131cm22018 SP P1Ans31Ans3(a) r -5(b) r 10.6cmwww.zetamaths.com15

National 5: CirclesAns2014 P25Ans2015 P24www.zetamaths.com16

National 5: CirclesAns2016 P13Ans2017 P23PP A P25www.zetamaths.com17

AnsNational 5: CirclesAnsPP B P24AnsPP C P24www.zetamaths.com18

National 5: CirclesPP E P2AnsPP D P144Ans4www.zetamaths.com19

National 5: CirclesAnsPP F P24www.zetamaths.com20

National 5: Circles - Angle PropertiesAns2015 P1339⁰Ans2016 P2374⁰www.zetamaths.com21

National 5: Circles - Angle PropertiesAns2017 P1326⁰AnsPP C P23www.zetamaths.com22

National 5: Circles - Angle PropertiesAnsPP F P13www.zetamaths.com23

2014 P1National 5: Straight Line3Ans12014 P122015P1Ans23www.zetamaths.com24

2016 P1AnsNational 5: Straight Line3Ans1Ans2017 P13www.zetamaths.com25

2Ans2017 P2National 5: Straight Line3AnsPP A P1AnsPP A P13AnsPP B P13www.zetamaths.com26

PP C P1National 5: Straight Line212AnsPPDP1Ans2PP D P13www.zetamaths.com27

3AnsPP D P1AnsNational 5: Straight LinePP F P1AnsPP E P133Ans1www.zetamaths.com28

PP F P1National 5: Straight Line2Ans1www.zetamaths.com29

AnsPP C P1AnsPP B P1AnsPPB P1Ans2017 P1Ans2015 P2Ans2018 SP P1National 5: Function Notation22 552210www.zetamaths.com231230

3Ans2015 P2National 5: Solving Equations/Inequations3Ans2017 P1Ans2016 P133AnsPPB P1AnsPP A P12www.zetamaths.com31

33AnsPP F P1AnsPP E P1National 5: Solving Equations/Inequationswww.zetamaths.com32

National 5: Simultaneous Equations2014 P2113Ans2015 P1Ans42016 P1114www.zetamaths.com33

AnsNational 5: Simultaneous Equations4AnsPP a P1Ans2017 P13PP C P1113www.zetamaths.com34

AnsNational 5: Simultaneous EquationsPP D P211Ans4PP E P26www.zetamaths.com35

AnsNational 5: Simultaneous EquationsAnsPP F P23www.zetamaths.com36

AnsPP F P2AnsPP C P2AnsPP B P2AnsPP A P1Ans2017P1Ans2016 P2Ans2014P2National 5: Change the Subjectwww.zetamaths.com333323237

2018 SP P1National 5: Quadratic Functions2𝑦 (𝑥 4)2 3Ans2Two real and distint roots.2018 SP P1Ans2018 SPP1Ans(a)2𝑎 52014 P12www.zetamaths.com38

2014 P1AnsNational 5: Quadratic Functions42015 P1Ans3111www.zetamaths.com39

National 5: Quadratic FunctionsAns(a)(i) -2(ii) -42015 P2(b) x 212(a) (i) 2x 1(ii) proof(b) X 2.8cm22016 P1Ans2016 P1Ans4www.zetamaths.com340

2016 P1AnsNational 5: Quadratic Functions13(a) (2x 1)(x 8)(b) Proof(c) 2cm and 9cm2017 P1Ans312www.zetamaths.com41

33PP A P1AnsPP A P1Ans2017 P2AnsNational 5: Quadratic Functions22Ans1AnsPP A P24www.zetamaths.com42

PP A P2National 5: Quadratic FunctionsPP B P1Ans52Ans1www.zetamaths.com43

444PP D P1AnsPP C P2AnsPP C P2AnsPP B P2National 5: Quadratic Functions21Ans2www.zetamaths.com44

PP 2 P DNational 5: Quadratic Functions124PP D P2AnsPPDP2Ans234www.zetamaths.com45

4AnsPP E P1AnsNational 5: Quadratic Functionswww.zetamaths.com46

National 5: Quadratic Functions2PP E P11Ans2www.zetamaths.com47

National 5: Quadratic Functions4AnsPP EP2AnsPP E P15AnsPP F P12www.zetamaths.com48

National 5: Quadratic FunctionsPP F P122Ans3PP F P222Ans3www.zetamaths.com49

2018 SP P2National 5: Similar ShapesAns33456mlAns2014 P233072cm3www.zetamaths.com50

National 5: Similar ShapesAns2015 P24225cm2Ans2016 P23www.zetamaths.com51

National 5: Similar ShapesAns2017 P136.5cmAnsPP C P23www.zetamaths.com52

National 5: Similar ShapesPP F P2AnsPP E P231Ans3www.zetamaths.com53

2018 SP P2National 5: Trig Graphs and EquationsAns470.5, 289.53Ans2014 P2Ans2014 P12www.zetamaths.com54

National 5: Trig Graphs and Equations23Ans2016 P2Ans2015 P1Ans2015 P12PP a P11www.zetamaths.com55

2017 P2AnsNational 5: Trig Graphs and Equations113AnsPP A P2Ans4www.zetamaths.com56

National 5: Trig Graphs and EquationsPP B P2AnsPP B P122Ans4PP C P12www.zetamaths.com57

3AnsPP C P2AnsNational 5: Trig Graphs and Equations333AnsPP E P2AnsPPEP1AnsPP D P2AnsPP D P12www.zetamaths.com58

National 5: Trig Graphs and EquationsPP F P2AnsPP F P1123Ans1www.zetamaths.com59

2232AnsPP E P2AnsPP C P2AnsPP A P2Ans2016 P1National 5: Trig Identitieswww.zetamaths.com60

2018 SP P2National 5: Triangle Trigonometry4Ans2(a) 29⁰(b) 249⁰2018 SP P2Ans2015 P243www.zetamaths.com61

AnsNational 5: Triangle Trigonometry9.8cmAns2014 P138cm2014 P23Ans2(a)(b)84.8⁰155.2⁰Ans2015 P230.78kmwww.zetamaths.com62

National 5: Triangle TrigonometryAns2015 P2423.8kmAns2016 P2378⁰www.zetamaths.com63

National 5: Triangle TrigonometryAns2016 P246.8cmAns2017 P1232cm22017 P23www.zetamaths.com64

AnsNational 5: Triangle Trigonometry413mAns2017 P249.9kmAnsPPA P258.5kmwww.zetamaths.com65

National 5: Triangle TrigonometryAnsPP A P25237.76cm2190.8kmPP C P2AnsPP B P253Ans3www.zetamaths.com66

PP D P2National 5: Triangle TrigonometryAns3AnsPP E P24PP E P25www.zetamaths.com67

AnsNational 5: Triangle TrigonometryPP F P11Ans3www.zetamaths.com68

PP F P2National 5: Triangle Trigonometry2Ans4www.zetamaths.com69

National 5: Converse of PythagorasAns2014 P24Ans2017 P23www.zetamaths.com70

2018 SP P1National 5: Vectors11𝒃 𝒂2(𝒃 𝒂)37 22Ans2014 P1Ans2018 Sp P1Ans(a)(b)www.zetamaths.com71

National 5: Vectors2Ans2015 P2Ans2014 P222015 P22www.zetamaths.com72

AnsNational 5: Vectors2016 P1Ans2016 P121Ans3(a) (8, 4, 0)(b) 7www.zetamaths.com73

National 5: VectorsAns2016 P21v–uB (0, 6, 6), C (3, 3, 9)Ans2017 P2Ans2017 P12223www.zetamaths.com74

National 5: Vectors2017 P21(a)(b)d–c𝒅 3122PP A P1Ans2𝒄1PP B P1Ans2www.zetamaths.com275

AnsNational 5: Vectors10AnsPP B P24AnsPP D P13www.zetamaths.com76

National 5: VectorsPP E P223AnsPP F P1Ans1www.zetamaths.com77

397 miles3600 00035902015 P2Ans2014 P2Ans2014 P1Ans2018 SP P2National 5: Percentages3 3503Ans2016 P2Ans2015 P2Ans3www.zetamaths.com78

3 136934200335PP C P2AnsPP B P2AnsPP B P2AnsPP A P2Ans2017 P2Ans2017 P2National 5: Percentageswww.zetamaths.com479

3400g3 165 0003AnsPP E P2AnsPP D P2AnsPP D P1AnsNational 5: Percentageswww.zetamaths.com80

3750gAnsPP F P2AnsPP F P1National 5: Percentages3 25 073.75www.zetamaths.com81

AnsPP A P1Ans2017 P1Ans2016 P1Ans2015 P1Ans2014 P1Ans2018 SPP1National 5: Fractions and BODMASwww.zetamaths.com22222282

AnsPPCP1AnsPP B P1AnsPP F P1AnsPP E P1AnsPP DP1AnsPP C P1AnsPP B P2National 5: Fractions and BODMASwww.zetamaths.com223322283

National 5: Statistics2014 P2131(i) 𝑥̅ 56.5(ii) s 2.4(b)No, standard deviation is greater. No, times are more spread out.Ans2015P1Ans(a)3a 82015 P13Ans2(a)Median 19.5, SIQR 4.5(b)Valid comments – On average the second round’s scores are higher. The second round’s scores are more consistent.www.zetamaths.com84

National 5: Statistics2016 P24Ans2(a)Mean 13 minutes,Standard Deviation 5.7 minutes(b)Valid comments – On average, Sophie waited longer. Sophie’s waiting times were less spread out.Ans2017 P1216Ans2017 P14a 3, b 2www.zetamaths.com85

National 5: StatisticsPP A P24PP B P1Ans23Ans12www.zetamaths.com86

National 5: StatisticsPP B P24Ans21PP C P1111Ans2www.zetamaths.com87

National 5: StatisticsPP D P12Ans21PP D P2311www.zetamaths.com88

AnsNational 5: StatisticsAnsPP F P12www.zetamaths.com89

past papers by years visit the SQA website at www.sqa.org.uk. The questions marked PP are practice papers produced by www.maths180.com. Visit the website for 100’s of free video lessons for National 5 and Higher Maths. The answers and worked solutions in these documents have been collated from a