LESMAHAGOW HIGH SCHOOL Mathematics Department. National 5. Relationships Scheme of Work

Size: px

Start display at page:

Download "LESMAHAGOW HIGH SCHOOL Mathematics Department. National 5. Relationships Scheme of Work"

Hilary Simmons
6 years ago
Views:

1 LESMAHAGOW HIGH SCHOOL Mathematics Department National 5 Relationships Scheme Work

2 Relationships Main Resource (Supplementary resource Int 2 Credit Book 1/2) Applying algebraic skills to linear equations Determining the equation a straight line when given the gradient Use the formula y b = m(x a) or equivalent to find the equation a straight line, given one point and the gradient the line. Use the functional notation f x Identify the gradient and y-intercept from y = mx + c Identify the gradient and y-intercept from various forms the equation a straight line. EXTN Use graphing packages to investigate the equation a straight line including parallel lines, lines with zero gradients and gradients that are undefined. Use a variety contexts such as science, finance, commerce, experimental data, population statistics, life expectancy etc. Discuss the importance functional notation as an alternative mathematical language to Leibniz notation. 1.1 B2 Ex H2.6 Page 2-4 Working with linear equations and inequations Coefficients are a member?? Solutions are a member??? Real-life limitations should be considered for inequations. For example, maximum safe load for a concrete beam a given cross section area 1.2 B1 Ex 12.1 B1 Ex 12.5 Page Working with simultaneous equations Construct from text Graphical solution Algebraic solution Investigate real-life situations such as hiring a car, mobile phone charges, health and fitness. Intersection paths moving objects described by equations. 1. B1 Ex 15.2 B1 Ex 15. B1 Ex 15.4 B1 Ex 15.5 Page 8-41 Use graphing packages is encouraged to enable more complex realistic contexts to be investigated. 2 Changing the subject a formula Linear equation Equation involving a simple square or square root. EXTN Contexts using formulae from science, technology, health and wellbeing and finance. s = ut at! 1.4 B2 Ex 2.5 EXTN B2 Ex 2.6 Page 41 E = 1 2 mv!

3 Applying algebraic skills to graphs quadratic relationships 2-4 Recognise and determine the equations a quadratic function form its graph Sketching a quadratic graph Equations the form y = kx! and y = x + p! + q; k, p, q?? Equations the form y = x m x n and y = x + p! + q Use graphics stware may be beneficial. Graphing packages can be used to investigate the graphs quadratic functions including zooming in on noninteger solutions roots. 2.1 B2 Ex 9.1 Page B2 Ex 6.1 B2 Ex 6.2 B2 Ex 6. B2 Ex 6.4 Page Identifying features a quadratic function Identify the nature, coordinates the turning point and the equation the axis symmetry a quadratic the form y = k x + p! + q where k = 1 or 1 Examples quadratic functions should include real-life contexts such as projectile motion. 2. B2 Ex 6.5 Applying algebraic skills to quadratic equations 8 Working with quadratic equations Factorised Graphically Quadratic formula The discriminant Roots Emphasis should be made on the connection between these aspects quadratic equations. Factorised 2x + x 5 = B2 Ex 6.1 B2 Ex 6.2 B2 Ex 6. B2 Ex 6.4 B2 Ex 9.4 Page 46 Page 48 Page 49 The solution 2x! 7x 15 = 0 is an integration skills with those the EF Unit. TJ online notes on the Discriminant. Applying geometric skills to lengths, angles and similarity Applying the theorem Pythagoras Using Pythagoras theorem in complex situations including converse and space diagonals. Link to D coordinates Contexts such as construction, engineering, home improvement, graphic.1 B1 Ex 2.4 B1 Ex 2.5 B1 Ex 2.6 Page 51

4 design can be used. Distance between two points on a coordinate diagram. -4 Applying the properties shapes to determine an angle involving at least two steps Quadrilaterals, triangles, polygons and circles Relationship in a circle between the chord and perpendicular bisector EXTN Use geometry stware packages may be beneficial.2 B1 Ex 10.6 B1 Ex 10.7 B1 Ex 10.8 B1 Ex 10.9 Page 55 5 Using similarity Interrelationship scale length, area and volume Link to surds and indices (e.g. volume to length or length to volume). It is important to develop confidence on handling the closely relate ideas similarity, proportion and ratio. Emphasis should be placed on geometric cases, scale plans and engineering diagrams; angles stay the same, distances scale in simple proportion, areas in square proportion and volumes in cubic proportion.. B2 Ex 5.1 B2 Ex 5.2 B2 Ex 5. B2 Ex 5.4 B2 Ex 5.5 Page 57 Real-life contexts and problem solving approaches such as cost in proportion to volume could be used. Applying trigonometric skills to graphs and identities Working with the graphs trigonometric functions Working with trigonometric relationships in degrees Basic graphs Amplitude Vertical translation Multiple angle Phase angle EXTN Sine, cosine and tangent angles 0 60 Period Related angles Solve basic equations Trigonometric identities EXTN Use graphing packages is encouraged where possible. Real-life contexts should be used including applications in wave theory. Introduce the quadrant diagram linked to graphs as a possible method finding further solutions to trigonometric equations. Use the graphs sine and cosine to increase understanding and use symmetry in these graphs to find further solutions. Consider including stware displays 4.1 B2 Ex 7.1 B2 Ex 7.2 B2 Ex 7. B2 Ex 7.4 B2 Ex 7.5 B2 Ex 7.6 B2 Ex B1 Ex 11.1 B1 Ex 11.2 B1 Ex 11. B1 Ex 11.4 B1 Ex 11.5 B1 Ex 11.6 B1 Ex 11.7 Page 59 Page 61 Page 62 Page 64

5 cos! x + sin! x = 1, tanx = sinx cosx involving addition (superposition/inference) two waves (e.g. same wave length, different phase or same phase at origin, slightly different wavelengths). B2 Ex 11.1 B2 Ex 11.2 B2 Ex 11. Extn Reasoning skills Interpreting a situation where mathematics can be used and identifying the strategy needed Can be attached to a skill Outcome 1 to require analysis the situation. This should be a mathematical or real-life context problem in which some analysis is required. The learner should be required to choose an appropriate strategy and employ mathematics to the situation. Explaining a solution and/or relating it to context Can be attached to a skill Outcome 1 to require explanation the solution The learner should be required to give meaning to the determined solution in everyday language.

TeeJay Publishers. SQA - National 5. National 5 Course Planner Using TeeJay's Books IC1 and IC2

TeeJay Publishers. SQA - National 5. National 5 Course Planner Using TeeJay's Books IC1 and IC2 TeeJay Publishers Draft SQA - National 5 National 5 Course Planner Using TeeJay's Books IC1 and IC2 This Course Planner for National 5, based on TeeJay s Int-2-Credit Books 1 & 2, comes in two parts :-