national 5 mathematics past papers by topic...past papers by years visit the sqa website at . the...
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V.1
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
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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.
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National 5: Surds and Indices
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National 5: Surds and Indices
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(a) 25 2 (b) t = 1/2
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National 5: Scientific Notation
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1.5 × 109
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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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National 5: Algebraic Fractions
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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: Volume of Solids
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National 5: Volume of Solids
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National 5: Circles
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National 5: Circles
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National 5: Circles
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National 5: Circles
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National 5: Circles
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National 5: Circles
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National 5: Circles - Angle Properties
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39⁰
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74⁰
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National 5: Circles - Angle Properties
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National 5: Circles - Angle Properties
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National 5: Straight Line
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National 5: Straight Line
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National 5: Straight Line
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National 5: Straight Line
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National 5: Straight Line
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National 5: Straight Line
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National 5: Function Notation
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National 5: Solving Equations/Inequations
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National 5: Solving Equations/Inequations
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National 5: Simultaneous Equations
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National 5: Simultaneous Equations
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National 5: Simultaneous Equations
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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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(a) 𝑦 = (𝑥 − 4)2 + 3
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Two real and distint roots.
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𝑎 = 5
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National 5: Quadratic Functions
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National 5: Quadratic Functions
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s (a)(i) -2 (ii) -4 (b) x = 2
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s (a) (i) 2x = 1 (ii) proof
(b) X = 2.8cm
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National 5: Quadratic Functions
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s (a) (2x + 1)(x + 8) (b) Proof (c) 2cm and 9cm
20
17
P1
1
2
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National 5: Quadratic Functions
42
www.zetamaths.com
An
s
20
17
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3
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s
PP
A P
1
3
An
s
PP
A P
1
2
2
1
An
s
PP
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2
4
An
s
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National 5: Quadratic Functions
43
www.zetamaths.com
PP
A P
2
5
An
s
PP
B P
1
2
1
An
s
![Page 46: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/46.jpg)
National 5: Quadratic Functions
44
www.zetamaths.com
PP
B P
2
4
An
s
PP
C P
2
4
An
s
PP
C P
2
4
An
s
PP
D P
1
2
1
2
An
s
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National 5: Quadratic Functions
45
www.zetamaths.com
PP
2 P
D
1
2
2
An
s
PP
D
P2
4
An
s
PP
D P
2
3
4
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National 5: Quadratic Functions
46
www.zetamaths.com
An
s
P
P E
P1
4
An
s
![Page 49: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/49.jpg)
National 5: Quadratic Functions
47
www.zetamaths.com
PP
E P
1
2
1
2
An
s
![Page 50: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/50.jpg)
National 5: Quadratic Functions
48
www.zetamaths.com
PP
E P
1
5
An
s
PP
E
P2
4
An
s
PP
F P
1
2
An
s
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National 5: Quadratic Functions
49
www.zetamaths.com
PP
F P
1
2
2
3
An
s
PP
F P
2
2
2
3
An
s
![Page 52: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/52.jpg)
National 5: Similar Shapes
50
www.zetamaths.com
20
18
SP
P2
3
An
s
3456ml
20
14
P2
3
An
s
3072cm3
![Page 53: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/53.jpg)
National 5: Similar Shapes
51
www.zetamaths.com
20
15
P2
4
An
s
225cm2
20
16
P2
3
An
s
![Page 54: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/54.jpg)
National 5: Similar Shapes
52
www.zetamaths.com
20
17
P1
3
An
s
6.5cm
PP
C P
2
3
An
s
![Page 55: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/55.jpg)
National 5: Similar Shapes
53
www.zetamaths.com
PP
E P
2
3
An
s
PP
F P
2
1
3
An
s
![Page 56: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/56.jpg)
National 5: Trig Graphs and Equations
54
www.zetamaths.com
20
18
SP
P2
4
An
s
70.5, 289.5
20
14
P1
2
An
s
20
1
4 P
2
3
An
s
![Page 57: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/57.jpg)
National 5: Trig Graphs and Equations
55
www.zetamaths.com
20
15
P1
2
An
s
20
15
P1
2
An
s
20
1
6 P
2
3
An
s
PP
a P
1
1
![Page 58: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/58.jpg)
National 5: Trig Graphs and Equations
56
www.zetamaths.com
An
s
20
17
P2
1
1
4
An
s
PP
A P
2
3
An
s
![Page 59: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/59.jpg)
National 5: Trig Graphs and Equations
57
www.zetamaths.com
PP
B P
1
2
An
s
PP
B P
2
2
4
An
s
PP
C P
1
2
![Page 60: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/60.jpg)
National 5: Trig Graphs and Equations
58
www.zetamaths.com
An
s
PP
C P
2
3
An
s
PP
D P
1
2
An
s
PP
D P
2
3
An
s
PP
E P1
3
An
s
PP
E P
2
3
An
s
![Page 61: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/61.jpg)
National 5: Trig Graphs and Equations
59
www.zetamaths.com
PP
F P
1
1
An
s
PP
F P
2
2
3
1
An
s
![Page 62: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/62.jpg)
National 5: Trig Identities
60
www.zetamaths.com
20
16
P1
2
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s
PP
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2
2
An
s
PP
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2
3
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s
PP
E P
2
2
An
s
![Page 63: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/63.jpg)
National 5: Triangle Trigonometry
61
www.zetamaths.com
20
18
SP
P2
4
2
An
s (a) 29⁰ (b) 249⁰
20
15
P2
4
An
s
20
18
SP
P2
3
![Page 64: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/64.jpg)
National 5: Triangle Trigonometry
62
www.zetamaths.com
An
s 9.8cm
2
01
4 P
1
3
An
s
8cm
20
14
P2
3
2
An
s (a) 84.8⁰ (b) 155.2⁰
20
15
P2
3
An
s
0.78km
![Page 65: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/65.jpg)
National 5: Triangle Trigonometry
63
www.zetamaths.com
20
15
P2
4
An
s
23.8km
20
16
P2
3
An
s
78⁰
![Page 66: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/66.jpg)
National 5: Triangle Trigonometry
64
www.zetamaths.com
20
16
P2
4
An
s
6.8cm
20
17
P1
2
An
s
32cm2
20
17
P2
3
![Page 67: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/67.jpg)
National 5: Triangle Trigonometry
65
www.zetamaths.com
An
s 413m
2
01
7 P
2
4
An
s
9.9km
PP
A P
2
5
An
s
8.5km
![Page 68: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/68.jpg)
National 5: Triangle Trigonometry
66
www.zetamaths.com
PP
A P
2
5
An
s
237.76cm2
PP
B P
2
5
An
s
190.8km
PP
C P
2
3
3
An
s
![Page 69: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/69.jpg)
National 5: Triangle Trigonometry
67
www.zetamaths.com
PP
D P
2
3
An
s
PP
E P
2
4
An
s
PP
E P
2
5
![Page 70: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/70.jpg)
National 5: Triangle Trigonometry
68
www.zetamaths.com
An
s
PP
F P
1
1
3
An
s
![Page 71: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/71.jpg)
National 5: Triangle Trigonometry
69
www.zetamaths.com
PP
F P
2
2
4
An
s
![Page 72: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/72.jpg)
National 5: Converse of Pythagoras
70
www.zetamaths.com
2
01
4 P
2
4
An
s
20
17
P2
3
An
s
![Page 73: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/73.jpg)
National 5: Vectors
71
www.zetamaths.com
20
18
SP
P1
1 1
An
s (a) 𝒃− 𝒂 (b) 2(𝒃− 𝒂)
20
18
Sp
P1
3
An
s
7 2
20
14
P1
2
An
s
![Page 74: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/74.jpg)
National 5: Vectors
72
www.zetamaths.com
20
14
P2
2
An
s
20
15
P2
2
An
s
20
15
P2
2
![Page 75: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/75.jpg)
National 5: Vectors
73
www.zetamaths.com
An
s
2
01
6 P
1
2
An
s
20
16
P1
1 3
An
s (a) (8, 4, 0) (b) 7
![Page 76: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/76.jpg)
National 5: Vectors
74
www.zetamaths.com
20
16
P2
1
An
s
v – u
20
17
P1
2
An
s
B (0, 6, 6), C (3, 3, 9)
20
17
P2
2
An
s
23
![Page 77: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/77.jpg)
National 5: Vectors
75
www.zetamaths.com
20
17
P2
1 2
An
s
(a) d – c
(b)3
2𝒅−
1
2𝒄
PP
A P
1
1 2
An
s
PP
B P
1
2
![Page 78: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/78.jpg)
National 5: Vectors
76
www.zetamaths.com
An
s 10
P
P B
P2
4
An
s
PP
D P
1
3
An
s
![Page 79: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/79.jpg)
National 5: Vectors
77
www.zetamaths.com
PP
E P
2
2 1
An
s
PP
F P
1
3
An
s
![Page 80: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/80.jpg)
National 5: Percentages
78
www.zetamaths.com
20
18
SP
P2
3
An
s
97 miles
20
14
P1
3
An
s
600 000
20
14
P2
3
An
s
590
20
15
P2
3
An
s
20
15
P2
3
An
s
£350
20
16
P2
3
An
s
![Page 81: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/81.jpg)
National 5: Percentages
79
www.zetamaths.com
20
17
P2
3
An
s
£1369
20
17
P2
3
An
s
4200
PP
A P
2
3
An
s
PP
B P
2
3
An
s
PP
B P
2
5
An
s
PP
C P
2
4
![Page 82: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/82.jpg)
National 5: Percentages
80
www.zetamaths.com
An
s
P
P D
P1
3
An
s
400g
PP
D P
2
3
An
s
£165 000
PP
E P
2
3
An
s
![Page 83: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/83.jpg)
National 5: Percentages
81
www.zetamaths.com
PP
F P
1
3
An
s
750g
PP
F P
2
3
An
s
£25 073.75
![Page 84: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/84.jpg)
National 5: Fractions and BODMAS
82
www.zetamaths.com
20
18
SP
P1
2
An
s
20
14
P1
2
An s
20
15
P1
2
An
s
20
16
P1
2
An
s
20
17
P1
2
An
s
PP
A P
1
2
An
s
![Page 85: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/85.jpg)
National 5: Fractions and BODMAS
83
www.zetamaths.com
PP
B P
2
2
An
s
PP
C P
1
2
An
s
PP
D
P1
3
An
s
PP
E P
1
3
An
s
PP
F P
1
2
An
s
PP
B P
1
2
An s
PP
C
P
1 2
An
s
![Page 86: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/86.jpg)
National 5: Statistics
84
www.zetamaths.com
20
14
P2
1
3
1
An
s
(a) (i) �̅� = 56.5 (ii) s = 2.4
(b) No, standard deviation is greater. No, times are more spread out.
20
15
P1
3
An
s a = 8
20
15
P1
3 2
An
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.
![Page 87: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/87.jpg)
National 5: Statistics
85
www.zetamaths.com
20
16
P2
4 2
An
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
![Page 88: National 5 Mathematics Past Papers by Topic...past papers by years visit the SQA website at . The questions marked PP are practice papers produced by . Visit the website for 100’s](https://reader035.vdocuments.net/reader035/viewer/2022070706/5e9db9e018449450de46e528/html5/thumbnails/88.jpg)
National 5: Statistics
86
www.zetamaths.com
PP
A P
2
4 2
An
s
PP
B P
1
3 1 2
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