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National 5 Mathematics Past Papers by Topic
Contents: Expressions & Formulae Page
Surds & Indices.……………………………………. 1 Scientific Notation……………………………….. 3 Algebra………………..………………………………. 5 Completing the Square………………………… 7 Algebraic Fractions.……………………………… 8 Volumes………………………………………………. 10 Gradient (See Straight Line)…………………. 24 Circles….………………………………………………. 15
Relationships
The Straight Line………………………………….. 24 Function Notation……………………………….. 30 Solving Equations/Inequations…………….. 31 Simultaneous Equations………………………. 33 Change the Subject………………………….….. 37 Quadratic Functions.……………………………. 38 Properties of Shapes (See Circles)..………. 15 Similar Shapes..……………………………………. 50 Trigonometry (Graphs and Equations)…. 54 Trig Identities…………………………………..….. 60
Applications Triangle Trigonometry..………………………. 69 Converse of Pythagoras……………………… 70 Vectors….……………………………………………. 71 Percentages………………………………………… 78 Fractions and BODMAS………………………. 82 Statistics……………………………………………… 84
ThisbookofpastpaperquestionsbytopicismadefreelyavailablebyZetaMathsforteachersandlearners,tobeusedforeducationalpurposes.ThequestionshavebeenmadeavailablebyandarecopyrightoftheSQA.ToobtainpastpapersbyyearsvisittheSQAwebsiteatwww.sqa.org.uk.ThequestionsmarkedPParepracticepapersproducedbywww.maths180.com.Visitthewebsitefor100’soffreevideolessonsforNational5andHigherMaths.The answers andworked solutions in these documents have been collated from avarietyofsourcesandarenottheauthorshipofZetaMathsLtd.Foreasynavigationofthedocument,thecontentspageislinkedtoeachchapterandthechapterheadingsatthetopofeachpagearelinkedbacktothecontentspage.
National 5: Surds and Indices
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(a) 25 2 (b) t = 1/2
National 5: Scientific Notation
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1.5 × 109
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8 ×10-9
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National 5: Scientific Notation
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National 5: Algebra
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National 5: Algebra
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(b)2𝑥+5
𝑥+2
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National 5: Algebra (Completing the Square)
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(a) 𝑦 = (𝑥 − 4)2 + 3
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National 5: Algebraic Fractions
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10s
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National 5: Algebraic Fractions
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National 5: Volume of Solids
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870cm3
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National 5: Volume of Solids
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National 5: Volume of Solids
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National 5: Circles
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(b) 131cm
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National 5: Circles
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National 5: Circles
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39⁰
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74⁰
National 5: Circles - Angle Properties
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26⁰
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National 5: Circles - Angle Properties
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National 5: Straight Line
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National 5: Function Notation
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National 5: Simultaneous Equations
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National 5: Change the Subject
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National 5: Quadratic Functions
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Two real and distint roots.
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National 5: Quadratic Functions
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National 5: Quadratic Functions
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National 5: Quadratic Functions
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National 5: Quadratic Functions
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National 5: Quadratic Functions
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National 5: Similar Shapes
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3456ml
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3072cm3
National 5: Similar Shapes
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225cm2
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6.5cm
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National 5: Trig Graphs and Equations
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70.5, 289.5
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National 5: Trig Identities
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National 5: Triangle Trigonometry
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National 5: Triangle Trigonometry
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0.78km
National 5: Triangle Trigonometry
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23.8km
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78⁰
National 5: Triangle Trigonometry
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6.8cm
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32cm2
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National 5: Triangle Trigonometry
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9.9km
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8.5km
National 5: Triangle Trigonometry
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237.76cm2
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190.8km
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National 5: Triangle Trigonometry
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National 5: Converse of Pythagoras
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National 5: Vectors
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7 2
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National 5: Vectors
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v – u
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B (0, 6, 6), C (3, 3, 9)
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23
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(a) d – c
(b)3
2𝒅−
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National 5: Percentages
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97 miles
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600 000
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590
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£350
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£1369
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4200
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400g
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£165 000
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750g
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£25 073.75
National 5: Fractions and BODMAS
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National 5: Fractions and BODMAS
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National 5: Statistics
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(a) (i) �̅� = 56.5 (ii) s = 2.4
(b) No, standard deviation is greater. No, times are more spread out.
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s (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.
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s
(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.
20
17
P1
2
An
s
16
20
17
P1
4
An
s
a = 3, b = 2
National 5: Statistics
86
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PP
A P
2
4 2
An
s
PP
B P
1
3 1 2
An
s
National 5: Statistics
87
www.zetamaths.com
PP
B P
2
4 2
An
s
PP
C P
1
1 1 1 1 2
An
s
National 5: Statistics
88
www.zetamaths.com
PP
D P
1
2 2
An
s
PP
D P
2
1 3 1 1
National 5: Statistics
89
www.zetamaths.com
An
s
P
P F
P1
2
An
s
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