st ninian’s high school - mathsrevision · maths national 5 course ... 3. removing double...

MATHS

National 5 Course

Pupil Learning Log (Unit by Unit Approach)

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Teacher :

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I am unsure of this part of the course =

I do not understand this part of the course =

St Ninian’s High School

Success is 99% Perspiration and 1% Inspiration

Hard Work beats Talent every time when Talent doesn’t Work Hard

Expect to get out what you put in !

National 5 Checklist – TJ Book

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St. Ninian’s High School – Mathematics Dept

Rules for Completing Homework

Always write the date, Page No, Ex No, and a

heading.

Attempt all questions using the method and

working shown in class.

Self correct answers from the back of the

booklet.

Do any corrections.

Parents must then sign your jotter to ensure

that all questions have been attempted.

If you found any questions difficult – ask in class

the next day.


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N5 Chapter 2 - Percentages

1. Appreciation (Increase) and Depreciation (Decrease)

2. Compound Interest

3. Working Backwards ( Original Price)

Jumper costs £64 in a sale. ( 20% off everything)

P £

80% 64

100% 80£6480

100

4. I have successfully completed past paper questions on

this topic.

Topic Mark : %

1

2

3

4


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N5 Chapter 3 – Numerical Fractions

1. Revision of + , - , x Fractions

8 1

16 2

2 1 4 3 7 11

3 2 6 6 6 6

2 1 4 3 1

3 2 6 6 6

2 1 5 5 25 11 1 2

3 4 3 4 12 12

2. Division of Fractions

2 1 5 5 5 4 4 11 1 1

3 4 3 4 3 5 3 3


this topic.

Topic Mark : %

1

2

3


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N5 Chapter 8 – Trigonometric and Triangle Calculations

1. Area of ANY triangle (SAS)

2. Sine Rule – Finding a Length

3. Sine Rule – Finding an Angle

4. Cosine Rule – Finding a Length

1

2

3

4


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5. Cosine Rule – Finding an Angle

6. Mixed Questions


this topic.

Topic Mark : %

5

6

7


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N5 Chapter 11 – Statistics

1. Mode , Mean , Median and Range

2. Quartiles

3. Semi-Interquartile Range (SIQR)

4. Boxplot – 5-Figure Summary.

5. Standard Deviation – ( A measure of spread)

1

)( 2

2

n

n

xx

S


this topic.

Topic Mark : %

1

2

3

4

5

6


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N5 Chapter 6 – Best-Fit Line Only

1. Best-Fit Line


this topic.

Topic Mark : %

1

2


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N5 Chapter 15 – Vectors

1. Vectors & Scalars

2. Adding & Subtracting Vectors

3. Position Vector

4. Magnitude of a Vector (Simply Pythagoras Theorem!)

1

2

3

4


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5. Vector Journey

6. 3D - Vectors


this topic.

Topic Mark : %

5

6

3


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Unit Assessment – Applications

Unit 1 – Applications Assessment Details

Outcome 1.1 1.2 1.3 1.4 #2.1 #2.2

Content Trig Vectors % and

Fractions Statistics Reasoning Reasoning

Marks

Available 8 9 8 8 1 2

Threshold 4 5 4 4 1 1

Your

Score

Overall Mark ( Circle ) Pass Failed


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N5 Chapter 1 - Working with Brackets

1. Removing a single bracket

3( 2y – 4) – 2(y +3)

2. Removing Double Bracket -Multiplication Table

(2m – 1) (3m + 4)

3. Removing Double Brackets of the form

(k – 1)(k2 + 5k – 6)

4. Expanding and tidying up Cubic brackets.

(b – 1)3 = b

3 + 3b

2 + 3b - 1

5. Solving equations, containing Double Brackets

(x + 2)2 = x

2 + 64

6. I have successfully completed past paper questions

on this topic.

Topic Mark : %

1

2

3

4

5

6


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N5 Chapter 6 – Straight Line

1. Equation give gradient and y-intercept

y mx c

m = gradient

c = y - intercept

2. Equation given any two point 1 1(x ,y ) and 2 2(x ,y )

3. Straight Line in Real – Life

4. Determining the gradient given two points

2 1

2 1

y ym

x x

5. Straight Line of the form

y b m(x a) (a,b)

6. General form of Straight

ax by c 0


this topic.

Topic Mark : %

1

2

3

4

5

6

7


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N5 Chapter 7 – Factorisation

1. Common Factor

)3(262 2 yyyy

2. Difference of two squares

)4)(4(162 bbb

)7)(7(2982 2 ppp

3. Trinomials ( St. Andrews Cross Method))


this topic.

5. Can you make up an equation

6. Can you find angles in a polygon

Topic Mark : %

1

2

3

4

5

6


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N5 Chapter 9 – Algebraic Fractions

1. Equivalent & Simplifying Fractions

3

5 =

3 3( 1)

5 5( 1)

x x

x x

2

30( 1) 5

6( 1) ( +1)

x

x x

2. Factorising & Simplifying Fractions

3. Add and Subtracting Fractions

1

2

3


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4. Multiplication & Division Fractions


this topic.

Topic Mark : %

4

5


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N5 Chapter 13 – The Circle

1. Arc Length of a Circle

2. Sector Area of a Circle


this topic.

Topic Mark : %

1

2

3


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N5 Chapter 17 – Surds and Indices

1. What s a Surd ?

2. Simplifying a Surd

3. Rationalising the denominator containing a Surd

4. Conjugate Pairs (Extension)

1

2

3

4


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5. What are Indices

6. Adding & Subtracting Rules for Indices

7. Power of a Power

8. Negative and Positive Indices

9. Fraction Indices


this topic.

Topic Mark : %

5

6

7

8

9

10


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N5 Chapter 19 – Completing the Square

1. Completing the Square


this topic.

Topic Mark : %

1

2


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4+ Chapter 16 - Volume

1. Sphere

2. Cone

3. Pyramid


this topic.

Topic Mark : %

1

2

3

4


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Unit 2 – Expressions & Formulae Assessment Details

Outcome 1.1 1.2 1.3 1.4 #2.1 #2.2

Content Surds &

Indices Algebra

Algebraic

Fractions Geometry Reasoning Reasoning

Marks

Available 8 9 5 10 2 2

Threshold 4 5 3 5 1 1

Your

Score

Overall Mark ( Circle ) Pass Failed


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4+ Chapter 9 - Equations & Inequations

1. Revision 2 and 3 Equations

2. Harder Equation

3. Equations with Brackets

1

2

3


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4. Equations with Fractions

5. Equations with Harder Fractions

6. Solving Inequations (Inequalities)

The same as solving equations EXCEPT when dividing

by a negative FLIP sign.

Also NEVER put in an equal sign.


this topic.

Topic Mark : %

4

5

6

7


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N5 Chapter 4 – Simultaneous Equations

1. Constructing Straight Line Graphs

Remember even scale and label axis

2. Solving equations Graphically

3. Solve Simple Sim. Equations by Elimination

4x y 4

3x y 0

4. Solve Harder Sim. Equations by Elimination

2x 3y 6

3x 2y 10

5. Using Sim. Equations in Real-Life


this topic.

Topic Mark : %

1

2

3

4

5

6


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4+ Chapter 20 - Similarity

1. Similar Figures

15 cm

3 cm

7 cm2cm

yz

6 cm

1.4 cm

ESF

RSF

Enlargement Scale Factor 15

53

ESF

Reduction Scale Factor 3 1

15 5RSF

2. Similar Triangles

8cm812cm

5cm

7.5cm

ESF =

RSF =

122

3

3

2

3. Parallel Lines

1

2

3


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4. Area of Similar Figures.

4cm

2cm

12cm

6cm

Small Area = 4 x 2 = 8cm2

Large Area = 12 x 6 = 72cm2

Large Area = (3)2 x 8 = 9 x 8 = 72cm2

Scale factor = ESF = 4

12= 3

5. Volume of Similar Figures.


this topic.

Topic Mark : %

3

4

5

2

2

( )

( )

large small

small large

OR

Area ESF Area

Area RSF Area


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N5 Chapter 5 – Pythagoras Theorem

1. Revision of Simple Pythagoras Theorem

Longest side squared

=

Two shorter sides squared and added together

Normally written as c2 = a2 + b2

2. Converse of Pythagoras Theorem

For any right-angle triangle c2 = a2 + b2

Converse, if c2 = a2 + b2 triangle MUST be right-angled

3. Pythagoras Theorem in 3D

Pythagoras twice !


this topic.

Topic Mark : %

1

2

3

4


Pupil Signature___________________________________________________


N5 Chapter 6 – Straight Line

1. Equation give gradient and y-intercept

y mx c

m = gradient

c = y - intercept

2. Equation given any two point 1 1(x ,y ) and 2 2(x ,y )

3. Straight Line in Real – Life

4. Determining the gradient given two points

2 1

2 1

y ym

x x

5. Straight Line of the form

y b m(x a) (a,b)

6. General form of Straight

ax by c 0


this topic.

Topic Mark : %

1

2

3

4

5

6

7


Pupil Signature___________________________________________________


N5 Chapter 10 - Formulae

1. Changing the Subject ( Balancing Method )

2. Harder Changing the Subject

3. Understanding Formulae


this topic.

Topic Mark : %

1

2

3


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4+ Chapter 18 - Angles in Circles

1. Isosceles Triangles

2. Angles in a Semi-Circle

3. Tangent Line

4. Tangent Kite

Topic Mark : %

1

2

3

4


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N5 Chapter 12 – Functions & Graphs

1. Functions

f(x) is simply the y-coordinate

Typical function notation is 2f(x) x 3x 4

2. Composite Function

A function made up of basic functions.

3. Graphs of some special Functions

Straight Line Function Quadratic Function


this topic.

Topic Mark : %

1

2

3

4


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N5 Chapter 14 – Quadratic Function Part 1

1. Solving Quadratics

graphically

2. Recap Factorising Trinomials

3. Solving Quadratics by factorising

4. Solving Harder Quadratics by factorising

5. Sketching a Parabola using factorisation.

1

2

3

4

5


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6. Intersection point between a Line and Parabola


this topic.

Topic Mark : %

6

7


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N5 Chapter 19 – Quadratic Function Part 2

1. Completing the Square

2. Quadratic Graph (Complete the Square format)

3. Quadratics of the form 2axy

1

2

3


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4. Quadratic Formula

5. Discriminant


this topic.

Topic Mark : %

5

6

7


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N5 Chapter 16 – Trigonometry Graphs

1. Basic Trig. Graphs

Sine Graph Cosine Graph

2. Graphs of the form oxay sin

3. Graphs of the form obxay sin

4. Graphs of the form cbxay o sin

1

2

3

4


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5. Phase angle obxay )sin(


this topic.

Topic Mark : %

5

6


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N5 Chapter 20 – Trigonometry Equations

1. Trig Function and Circle connection

2. Solving Trig Equations

3. Negative Cosine

1

2

3


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4. Special Trig. Relationships

1cossin 22 xx x

xx

cos

sintan


this topic.

Topic Mark : %

4


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Unit 3 – Relationships Assessment Details

Outcome 1.1 1.2 1.3 1.4 1.5 #2.1 #2.2

Content Linear

Equations

Quadratic

Graphs

Quadratic

Equations Geometry Trig Reasoning Reasoning

Marks

Available 11 9 6 9 8 2 2

Threshold 6 5 3 5 4 1 1

Your

Score

Overall Mark ( Circle as appropriate ) Pass Failed


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N5 Numeracy - Bridging Units

N5 Numeracy Bridging Unit

Assessment Details

Outcome 1.3 #2.3

Content Measurement Probability

Marks

Available 2 3

Threshold 1 2

Your

Score


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FINAL SQA EXAM

END OF NATIONAL 5 COURSE


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My Achievements

Skill Activity Date & Teacher Signature

st ninian’s high school - mathsrevision · maths national 5 course ... 3. removing double...

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