Whiteboard Templates for Maths HW Graph Paper Number… Algebra Statistical Charts Calculator Area & Volume Geometry… Trigonometry Probability Functions… Navigation Icons Parent Menu Home Page Last Viewed External Link Animation Levels MDT Resource Medium Grid 3 Draft Version 17.2 Created :25-1-2017

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Graph Paper Divided Board Plan Graphing Functions Medium Grid Large Grid Small Grid Split Screen Divided Board Plan Whiteboard 6 Frames 4 Frames Key Words How to… Steps Graphing Functions Prior Knowledge Given Couples Substitution Trigonometric Functions & Calculus

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Graphing a Function using a given Table Function: Domain: 3

Evaluating Outputs and Graphing a Function Function: Domain: 3

Trigonometric Functions Sin(A) Cos(A)

Graphing a Sine Function Function: Domain: sin(x) 1

Graphing a Cosine Function Function: Domain: 1

Algebra Solving Equations Using Arrays Algebra Tiles Quadratic Roots Linear Patterns Quadratic Pattern Binomial Theorem

Algebra Tiles 1 x x2 x -x2 -x -1 -x

Roots of a Quadratic Equation Roots of the quadratic equation ax2 + bx + c = 0 p.20

The Binomial Theorem p.20

Solving Equations & Inequalities Inequality Double inequality

Solving Equations 2

Solving Inequalities 1

Solving Double Inequalities 1

Growing Visual Linear Patterns Supporting Student Workbook on Linear Patterns Available Online Click on the Pattern www.projectmaths.ie

Linear Patterns

How many dots are there?

How many dots are there?

How many dots are there?

How many dots are there?

IMAGINE A SQUARE WITH 10 DOTS AT EACH SIDE How many dots are there? IMAGINE A SQUARE WITH 10 DOTS AT EACH SIDE

Pattern 1 1st Difference 3

Pattern 2 1st Difference 3

Pattern 3 1st Difference 3

Pattern 4 1st Difference 3

Pattern 5 1st Difference 3

Pattern 6 1st Difference 3

Pattern 7 1st Difference 3

Pattern 8 1st Difference 3

Pattern 9 1st Difference 3

Pattern 10 John wants to save up for a school tour which will happen at the end of the school year. He speaks to his parents about it and they agree that he can get a part-time job to help him afford the trip. His parents give him €100 to start him off and each week he saves €20 of his wages. 1st Difference 3

Quadratic Factors Trial & Error Using Arrays Quadratic Array Two Quadratic Arrays Quadratic Factors Quadratic Factors Trial & Error Cubic Array Two Cubic Arrays

Quadratic Array for Multiplication and Division Question: Answer:

Quadratic Arrays for Multiplication and Division

Quadratic Factorisation using the Guide Method Question: Guide Number Product Factors Sum Answer:

Quadratic Factorisation using the Guide Method Question: Guide Number Product Factors Sum Answer:

Cubic Array for Multiplication and Division Question: Answer:

Cubic Arrays for Multiplication and Division

Growing Visual Quadratic Patterns Supporting the Student Workbook on Quadratic Patterns available on our website Click on the pattern to go to that page. Pattern 5 Pattern 10 Pattern 1 Pattern 6 Pattern 11 Pattern 2 Pattern 7 Pattern 12 Pattern 3 Pattern 8 Pattern 13 Pattern 4 Pattern 9 Pattern 14

Quadtatic Pattern Next, Near, Far, Any? 4 Stage No. (n) No. of squares (s) 1st Difference 2nd Difference 4

Pattern 1 1st Difference 2nd Difference 3

Pattern 2 1st Difference 2nd Difference 3

Pattern 3 1st Difference 2nd Difference 3

Pattern 4 1st Difference 2nd Difference 3

Pattern 5 1st Difference 2nd Difference 3

Pattern 6 1st Difference 2nd Difference 3

Pattern 7 1st Difference 2nd Difference 3

Pattern 8 1st Difference 2nd Difference 3

Pattern 9 1st Difference 2nd Difference 3

Pattern 10 1st Difference 2nd Difference 3

Pattern 11 1st Difference 2nd Difference 3

Pattern 12 1st Difference 2nd Difference 3

Pattern 13 1st Difference 2nd Difference 3

Pattern 14 A tiling company specialises in multi-colour tile patterns. A small guest house is interested in the pattern below for its square shaped reception area. How many tile will be needed in total if the reception area needs 36 green tiles in the centre pattern? 1st Difference 2nd Difference 3

Back-to-Back Stemplot Statistical Charts Line Plot Bar Chart Histogram Pie Chart Stemplot Back-to-Back Stemplot Scatter Graph

Line Plot Title: 1

Bar Chart Title: 1

Histogram Title: 1

Stemplot Title: Key: 1

Back to Back Stemplot Title: Key: Key: 1

Scatter Graph Title: 1

Pie Chart Title: 1

Number Number Lines Fractions Order of Operations Venn Diagrams Number Systems Complex No. Indices Logarithms Sequences… Financial Maths

Venn Diagrams 1 Set 2 Sets 3 Sets

Venn Diagram with 1 Set 1

Venn Diagram with 2 Sets 1

Venn Diagram with 3 Sets 1

Number Line 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 1 2 3 4 5 6 7 8 9 10 11 12 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 3

Using the Calculator

Complex Numbers Argand Diagrams Rectangular Form Polar Form Number Systems De Moivre

Complex Numbers: Argand Diagram Im Re

Argand Diagram: Complex Numbers in Polar Form Im Re

Complex Numbers: De Moivre’s Theorem

Order of Operations BEMDAS BIMDAS BIRDMAS

Order of Operations - BEMDAS left to right A S

Order of Operations - BIDMAS M D left to right A S

Order of Operations - BIRDMAS left to right A S

Inferential Statistics Probability Empirical Rule Probability Tables Bernoulli Trials Inferential Statistics Ordinary Level Higher Level

The Empirical Rule for Normal Distribution 1

Normal Distribution Tables standardising formula p.34 p.36-37

Bernoulli Trials p.33

Inferential Statistics LC Ordinary Level – Sample Proportions Margin of Error Confidence Interval Hypothesis Test HL

Margin of Error of the Proportion (OL) Ordinary Level Approximation for the 95% level of confidence margin of error: n Sample size This formula is not in Formulae and Tables. It is an approximation relating to the product of the 95% level of confidence z-value (p.37) and the standard error of the proportion (p.34)

95% Confidence Interval of the Proportion (OL) Population proportion Sample proportion n Sample size This formula is not in Formulae and Tables.

Hypothesis Test on a Population Proportion (OL) State the Hypotheses Analyse sample data Interpret the results Step 1 – State the Hypotheses State the null hypothesis (H0) and the alternative hypothesis (H1). p Population proportion p0 Hypothesised value of the population proportion H0 is a statement of no change. We express it as a statement of equality. Note: Stating the alternative hypothesis as “not being equal” means that it could be either “less than” or “greater than” a value. This results in a two-tailed hypothesis test.

Hypothesis Test on a Population Proportion (OL) State the Hypothesis Analyse sample data Interpret the results Step 2 – Analyse the sample data using a confidence interval Construct the 95% confidence interval State if p0 is inside or outside the confidence interval Step 3 - Interpret the results If p0 is outside the interval it would indicate that p ≠ p0 so the result is significant and we reject H0. If p0 is inside the interval we fail to reject H0. Clearly state your conclusion.

Inferential Statistics LC Higher Level Proportions Margin of Error Sample Size? Confidence Interval Hypothesis Tests Means CI for Population Mean CI for Sample Mean Hypothesis Tests OL

95% Margin of Error for a Population Proportion (HL) Higher Level 95% level of confidence margin of error: p Population proportion Sample proportion n Sample size Standard error of the proportion (p.34) This formula is not given in Formulae and Tables. 1.96 is the z-value relating to a 95% level of confidence (p.37).

Sample Size for a required Margin of Error (HL) Use the approximation for the 95% level of confidence margin of error for a Population Proportion: n Sample size Margin of error for 95% L.o.C This formula is not in Formulae and Tables. It is an approximation relating to the product of the 95% level of confidence z-value (p.37) and the standard error of the proportion (p.34)

95% Confidence Interval for a Population Proportion - HL This formula is not in Formulae and Tables. It is a confidence interval based on the standard deviation of σ “p hat.” p Population proportion Sample proportion n Sample size Standard error of the proportion (p.34)

Hypothesis Test on a Population Proportion - HL State the Hypotheses Analyse sample data Interpret the results Step 1 – State the Hypotheses State the null hypothesis (H0) and the alternative hypothesis (H1). p Population proportion p0 Hypothesised value of the population proportion H0 is a statement of no change. We express it as a statement of equality. Note: Stating the alternative hypothesis as “not being equal” means that it could be either “less than” or “greater than” a value. This results in a two-tailed hypothesis test.

Hypothesis Test on a Population Proportion - HL State the Hypothesis Analyse sample data Interpret the results Step 2 Analyse the sample data using either a: Confidence interval Z-value P-value

Hypothesis Test on a Population Proportion - HL State the Hypothesis Analyse sample data Interpret the results Step 2 – Analyse the sample data using a confidence interval Construct the required confidence interval for a proportion p.34 State if p0 is inside or outside the confidence interval Step 3 - Interpret the results If p0 is outside the interval it would indicate that p ≠ p0 so the result is significant and we reject H0. If p0 is inside the interval we fail to reject H0. Clearly state your conclusion.

Hypothesis Test on a Population Proportion - HL State the Hypothesis Analyse sample data Interpret the results Step 2 – Analyse the sample data using a z-value We can standardise our p0 value using: This formula is not in Formulae and Tables. It is derived from an understanding of the standardising formula (p.34) and the standard error of the proportion (p.34). Step 3 - Interpret the results If |z|>1.96 it would indicate that p ≠ p0 at a 5% level of significance so we reject H0. If |z|<1.96 we fail to reject H0. Clearly state your conclusion. 1

Hypothesis Test on a Population Proportion - HL State the Hypothesis Analyse sample data Interpret the results Step 2 – Analyse the sample data using a p-value Samples are normally distributed around p so we can standardise p0 using: Find P(Z ≤ |zp|) (p.36-37) Our p-value = 2(1 - P(Z ≤ |zp|) This formula is not in Formulae and Tables. It is derived from an understanding of the standardising formula (p.34) and the standard error of the proportion (p.34). Step 3 - Interpret the results If p-value < 0.05 it would indicate that p ≠ p0 at a 5% level of significance so we reject H0. If p-value > 0.05 we fail to reject H0. Clearly state your conclusion 4

95% Confidence Interval for a Population Mean - HL µ Population mean Sample mean n Sample size σ Standard deviation If σ is unknown use s This formula is not given in Formulae and Tables. 1.96 is the z-value relating to a 95% level of confidence (p.37). The margin of error is the product of the z-value multiplier and the standard error of the mean (p.34): 2

95% Confidence Interval for a Sample Mean - HL µ Population mean Sample mean n Sample size σ Standard deviation If σ is unknown use s This formula is not given in Formulae and Tables. 1.96 is the z-value relating to a 95% level of confidence (p.37). The margin of error is the product of the z-value multiplier and the standard error of the mean (p.34): 2

Hypothesis Test for a Sample Mean - HL State the Hypothesis Analyse sample data Interpret the results Step 1 – State the Hypotheses State the null hypothesis (H0) and the alternative hypothesis (H1). H0:µ = µ0 H1: µ ≠ µ0 µ Population mean µ0 Hypothesised value of the population mean H0 is a statement of no change. We express it as a statement of equality. Note: Stating the alternative hypothesis as “not being equal” means that it could be either “less than” or “greater than” a value. This results in a two-tailed hypothesis test. 1

Hypothesis Test for a Mean - HL State the Hypothesis Analyse sample data Interpret the results Step 2 Analyse the sample data using either a: Z-value P-value

Hypothesis Test for a Mean HL State the Hypothesis Analyse sample data Interpret the results Step 2 – Analyse the sample data using a z-value Use the one-sample z-test (p.35): If σ is unknown use s Step 3 - Interpret the results If |z|>1.96 it would indicate that µ ≠ µ0 at a 5% level of significance so we reject H0. If |z|<1.96 we fail to reject H0. Clearly state your conclusion. 1

Hypothesis Test for a Mean - HL State the Hypothesis Analyse sample data Interpret the results Step 2 – Analyse the sample data using a p-value Apply the one-sample z-test (p.35) : If σ is unknown use s Find P(Z ≤ |z|) (p.36-37) Our p-value = 2(1 - P(Z ≤ |z|) Step 3 - Interpret the results If p-value < 0.05 it would indicate that p ≠ p0 at a 5% level of significance so we reject H0. If p-value > 0.05 we fail to reject H0. Clearly state your conclusion. 2

Financial Maths Compound Interest Depreciation Sum of Present Values (t1 = 0) Sum of Present Values (t1 ≠ 0) Sum of Future Values Amortisation

Financial Maths: Compound Interest F = final value, P = principal Present value P = present value, F = final value p.30 p.30 Present Future 1

Financial Maths: Depreciation - Reducing balance method F = later value, P = initial value p.30 Present Future 1

Series of equal withdrawals from fixed amount (Sum of Present Values) where: a is the first term r is the common ratio Present value P = present value, F = final value p.30 p.22 Immediate first withdrawal Present Future 4

Series of equal withdrawals from fixed amount (Sum of Present Values) P = present value, F = final value where: a is the first term r is the common ratio p.30 p.22 Delayed first withdrawal Present Future 4

Series of equal installments (Sum of Future Values) where: a is the first term r is the common ratio Compound interest F = final value, P = principal p.30 p.22 Present Future 4

Financial Maths: Amortisation Amortisation – mortgages and loans (equal repayments at equal intervals) A = annual repayment amount P = principal p.31

Functions Calculus Mapping Functions Table and Mapping Table (and Graph) Mapping Diagrams Graph given Table Comparing Functions Composite Functions Types of Functions Calculus Differentiation Integration

Function Machine with Mapping Diagram 1

Function Machine with Table and Mapping Diagram 1

Functions: Table and Graph Function: Domain: Table Function machine 4

Mapping Diagrams 3

Investigating Functions with a Mapping Diagram and Graph Function: Domain: 4

Graphing a Function from a Table Function: Domain: 4

Comparing Functions - Simultaneous Functions Domain: 4

Composite Functions Function: Function: Function machines Mapping Diagram Table 2

Differential Calculus p.25

Integral Calculus p.26

Fraction Wall – Comparing Fractions 5

Length, Area and Volume Parallelogram Trapezium Circle/Disc Arc/Sector Triangle Cylinder Cone Sphere Frustum of Cone Prism Pyramid Trapezoidal Rule

Length & Area: Parallelogram

Length and Area of a Trapezium

Length of a Circle and Area of a Disc p.8

Length of an Arc and Area of a Sector p.9

Length and Area of a Triangle p.9

Surface Area and Volume of a Cylinder p.10

Surface Area and Volume of a Cone p.11

Surface Area and Volume of a Sphere

Surface Area and Volume of a Frustum of Cone p.12

Surface Area and Volume of a Prism

Surface Area and Volume of a Pyramid

Area Approximations: Trapezoidal Rule

Trigonometry Pythagoras Trig Ratios Sine Rule Cosine Rule Area of a Triangle Identities… Unit Circle Angle Ratios Compound Angle Double Angle Product & Sums Trig. Functions

Pythagoras’ Theorem p.16

Trigonometric Ratios p.16

The Sine Rule p.16 sine rule

The Cosine Rule p.16 cosine rule

Area of a Triangle p.16 area

Compound Angle Formulae

Double Angle Formulae p.14

Trigonometric Products and Sums/Differences

Trigonometry: Identities & Definitions p.13 sec2 A = 1 + tan2 A

Trigonometry: The Unit Circle p.13

Trigonometric Ratios of certain angles p.13

Geometry Synthetic Geometry Co-ord. Geometry

Synthetic Geometry Theorems Constructions Enlargements Axial Symmetry Central Symmetry Rotations

Geometry Theorems Theorem ____: 1. Diagram: 4. To Prove: 5. Proof: 2. Given: 3. Construction:

Geometry Construction

Construct: The perpendicular bisector of [AB] Geometry Construction Construct: The perpendicular bisector of [AB] A B

Geometry: Enlargements Centre of Enlargement Centre of Enlargement 3

Geometry Transformations: Axial Symmetry Axis of symmetry Axis of symmetry Axis of symmetry 3

Geometry Transformations: Central Symmetry Centre of Symmetry Point of Reflection 1

Geometry Transformations: Rotations Point of Rotation 3

Co-ordinate Geometry of the Line Line Formulae Area of Triangle Distance to line, Angle & Division Co-ordinate Geometry of the Circle Centre (h, k) Centre (-g, -f)

Co-ordinate Geometry of the Line p.18 1

Co-ordinate Geometry: Area of a Triangle p.18 1

Co-ordinate Geometry of the Line (LCHL) p.19 1

Co-ordinate Geometry: Circle p.19 1

Co-ordinate Geometry: Circle p.19 1

Number Systems Venn Diagram p.23 C R Q Z N Z\N Q\Z R\Q C\R 3

Indices p.21

Logarithms p.21

Sequences and Series Arithmetic Geometric

Arithmetic Sequence and Series p.22 In the following Tn is the nth term, and Sn is the sum of the first n terms where a is the first term and d is the common difference.

Geometric Sequence and Series p.22 In the following Tn is the nth term, and Sn is the sum of the first n terms where a is the first term and r is the common ratio.

Homework Assignment and Notes Date: Notes: Maths Homework: Due: