L2maths

TGHS Maths

Level 2 Mathematics

This is a full level 2 Mathematics course. Teachers should expect that students taking this course will have passed the Level 1 MCAT. Students need to be equipped to take either Statistics or Calculus at Level 3 (or both). Therefore they should be encouraged to sit all three of the externals offered – withdrawal from a standard is not normally an option.

All tasks and schedules are password protected.

AS 91259 Apply trigonometric relationships in solving problems
Internal 3 credits

Resources

Time Scale (approx.)

Right Angle Triangles

Revision of the work from last year

Theta Ex. 9.01 & 9.02 p144-149

2 lessons

Area of Triangle

Theta Ex. 9.04 p152-153

1 lesson

Sine Rule

Labelling sides/angles

Finding sides

Finding angles

Applications

(students should have seen the derivation of the Sine Rule).

When tackling applications, students should draw a diagram, showing the triangle which they are using.

Theta Ex. 10.02 p. 161-162

Theta Ex. 10.04 p. 164 (though students should have seen the rearrangement).

Theta Ex. 10.05 p. 164-166

5 lessons

Cos Rule

Finding sides

Finding angles

Applications

(students should have seen the derivation of the cosine rule)

Theta Ex. 11.02 p. 173-174

Theta Ex. 11.04 p. 176-177

Theta Ex. 11.06 p. 179-181

5 lessons

Circular Measure

Length of arc

Area of sector

Only need the examples which are in degrees. Area of sector may need some more examples writing. These are explained in terms of fractions of the circumference or area of a full circle.

Theta Ex. 12.02 p. 192-193 Q3, Q4b and Q10b ONLY

Theta Ex. 12.05 p. 199-200 Q1, Q2 and Q3 ONLY

2 lessons

Assessment Preparation

Mixed Trig Examples

Surveying questions

Theta Dimensions Ex. 11.07 p. 183-184

Worksheet: Paddocks

Worksheet: Paddocks (2)

Answers. Also allows production of more worksheets.

4 lessons

Assessment

Practice

Real

A formula resource will be provided.

Practice

Real

5 lessons

Total:

24 lessons (about 5 weeks)

Text book reference: Th = Theta (Orange/Climber)

AS 91257 Apply graphical methods in solving problems
Internal 4 Credits

Graphs
This unit needs supplementing with graphing activities, from eg Desmos.


Function notation & Domain/Range Placing this first allows the teacher to use Range/Domain throughout.	Theta Ex. 4.02 &4.03 p. 52-55	2 lessons
Parabolas Revision of year 11 work. Emphasise transformations.	Theta Ex. 3.01 & Ex. 3.02 p. 38-41	2 lessons
Cubics Transforms of y=x³ and factorized form	Theta Ex. 3.04 p. 46-47	3 lessons
Absolute Value	Theta Ex. 4.04 p. 57	1 lesson
Square Root	Theta Ex. 4.05 p. 61	1 lesson
Rectangular Hyperbola y=^a/x Transformations Equations from Graphs	Theta Ex. 5.01 p. 64-65 Theta Ex. 5.02 p. 72-74 Ex. 5.03 p. 72-74	4 lessons
Exponentials	Theta Ex. 5.05, 5.06, 5.07 and 5.08 p. 79-82	2 lessons
Logarithms	There are no adequate exercises in the Theta text book.	1 lesson
Circles	There are no adequate exercises in teh theta text book.	1 lesson
Practice Assessment	Metal Palm Tree	3 lessons
Real Assessment	Flower Design	2 lessons
Re-assessment	Camping
		22 lessons (about 5 weeks)

AS 91261 Apply algebraic methods in solving problems
External 4 Credits

Algebra

	Resources	Time Scale (approx.)
Review of Y11 Algebra Revision of the work from last year	Theta Chapter 13	5 lessons
Algebraic Fractions	Multiplying Theta Ex. 14.02-14.04 p. 226-227 Adding Theta Ex. 14.05-14.06 p. 228-230	3 lessons
Quadratics	Factorize Quadratics Theta Ex. 15.03-15.06 p. 234-237 Factorize and Simplify Theta Ex. 15.07 p. 238-239	3 lessons
Rearranging Formulas	Theta Ex. 16.03-16.06	2 lessons
Solving Quadratics 'Completing the square' is only needed as a proof of The Formula. Emphasis should be placed on 'The Nature of Roots', as straight solving can be performed with a GC (and they should know how to do this).	Rearrange and Factorize Theta Ex. 17.03 p. 254 Applications Theta Ex. 17.05 p. 256-257 Completing the Square & Proving The Formula Theta Ex. 17.06 p. 259 The Formula Theta Ex. 17.07 & 17.09 p. 260 and p 263 Nature of Roots Theta Ex. 17.10 & 17.11 p. 268-269	8 lessons
Indices The text book material is probably insufficient	Negative Theta Ex. 18.02 & 18.03 p. 272-275 Fractional Indices Theta Ex. 18.04 p. 277 ixed Theta p. 278-279 Bases Theta Ex. 18.06 p. 280	6 lessons
Logarithms Technically, the 1st and 2nd laws of logs are no longer required. Students should still be introduced to them, but emphasis should be placed on the 3rd law, and its application in solving exponetial (index) equations. There is insufficient material in the text book on Index Equivalent Statements, and on Solving Index Equations.	Index Equivalent Statement Theta Ex. 19.01 p. 286 Laws of Logarithms Theta Ex. 19.02 p. 287-288 Solving Index Equations Theta Ex. 19.03 & 19.04 p. 289-293	8 lessons
	Total:	35 lessons (about 7 weeks)

Text book reference: Th = Theta (Orange/Climber)

AS 91269 Apply systems of equations in solving problems
Internal 2 Credits

Systems of Equations

	Resources	Time Scale (approx.)
Non-Linear Simultaneous Equations	Line & Parabola Th. Ex. 29.01 p. 461-472 Line & Circle Th. Ex. 29.02 p. 473-474 Line & Hyperbola Th. Ex. 29.03 p. 475-476 Applications Th. Ex. 29.04 p. 478-479	8 lessons
Practice Assessment	Practice	1 lesson
Real Assessment	Real	2 lessons
	Total:	11 lessons (about 3 weeks)

Text book reference: Th = Theta (Orange/Climber)

AS91267 Apply probability methods in solving problems
External 4 Credits

Probability

	Resources	Time Scale (approx.)
Two Way Tables	Two way table booklet Booklet with answers Worksheet Simple version of booklet (for revision)	3 lessons
Relative Risk	Nulake EAS 2.12 p24-27	2 lessons
And Rule and Or Rule Tree Diagrams	10Ticks L7-8 P1 p17-18 10 Ticks L7-8 P1 p15-16 10Ticks L9-10 P2 p27-28 and p31-32	3 lessons
Describing the Normal Distribution	Teacher notes: Normal Distribution Lesson 1 Th: p338-339 or Th2: p395-396 (Needs more examples writing)	1 lesson
Approximate Areas (68%, 95%, 99%) Using the tables	Teacher notes: Normal Distribution Lessons 2-3 Teacher notes: Normal Distributions Lessons 4-6 Th: p340-344 or Th2: p406-409 Worksheet: Light Bulbs 1 Worksheet: Light Bulbs 2 Worksheet: Light Bulbs 3	5 lessons
Inverse Normal	Th: p361-364 or Th2: p434-436	2 lessons
Finding the mean and s.d using inverse normal (Excellence)	Nulake EAS 2.12 p48 (Needs more examples writing)	1 lesson
End of Unit Assessment	Nulake EAS 2.12 p49-55	2 lessons
	Total:	19 lessons (about 4 weeks)

Text Book Reference: Th = Theta (Edition 1 'sky tower')
Th2= Theta (2nd edition 'climber')

AS91256 Apply Coordinate Geometry Methods in Solving Problems
Internal 2 Credits

Coordinate Geometry

	Resources	Time Scale (approx.)
Midpoints Distance between 2 points Gradient (point-point)	Th: Ex18.01 p213-214 or Th2: Ex1.01 p3 Th: Ex18.02 p215 or Th2: Ex1.02 p4-5 Worksheet: Distance between 2 points worksheet Th Ex18.03 p216-217 or Th2 Ex1.03 p6-7	2 lessons
Revise: y=mx+c	Worksheet needed	1 lesson
Equation (point-gradient) Equation (point-point)	Th: Ex18.07 p221 or Th2: Ex1.07 p11 Th: Ex. 18.08 p222 or Th2: Ex. 1.08 p12	2 lessons
Applications	Th: Ex18.10 p223-224 or Th2: Ex1.10 p13-14	1 lesson
Equation of parallel lines	Th: Ex19.01 p226 or Th2: Ex2.01 p16	1 lesson
Perpendicular lines	Th: Ex19.02 p228 or Th2: Ex2.02 p17	1 lesson
Triangle Properties	Th: Ex19.08 p235-236 or Th2: Ex2.10 p28-29	2 lessons
Distance of point from a line	Worksheet needed	1 lesson
More applications	Th: Ex. 19.09 p236-240 or Th2: Ex. 2.11 p30	1 lesson
Revision	Skills Practice I (Midpoint and point-point equations) The past papers AS90287 (prior to 2012) provide an excellent revision source.	3 lessons
Practice Assessment	The Sailing Race	2 lessons + 1 lesson feedback
Real Assessment	The Loft Conversion Calculations spreadsheet	2 lessons
Re- Assessment	Farmer Fran
	Total:	20 lessons (about 4 weeks)

Text Book Reference:
Th = Theta (Edition 1 'sky tower')
Th2= Theta (2nd edition 'climber')