TeeJay Int 2-Credit Book IC2 Course Structure and Organisational Notes TJ May 2007 Page Number 1
TeeJay s IC2 book is a continuation of book IC1. It is the updated Credit Book for use in fourth (or late third) year and following on from book IC1, covered in S2/3, will complete the Credit course in tremendous depth, particularly in its algebraic content. With the growing trend in the presentation of pupils for National Qualifications, both textbooks were produced to follow the order of the Intermediate 2 course. i.e. Maths 1, Maths 2 then Maths 3, with revision for NAB s and practice NAB s built in. Book IC2 concentrates on Maths 3, together with KU and RE revision examples and papers for S Grade and revision examples and papers for NQ Intermediate 2. Two chapters of the Higher Course are included in the textbook to allow the Higher course to commence earlier in S4. The index lists the topics in two colours, the material in blue forms the basis of the Intermediate 2 course and these topics could form the basis as a free-standing Int 2 course (but only for students who had previously followed a General or Int 1 course) the material in red along with that in blue, cover the entire content of the Standard Grade Credit course. It is recommended that if pupils intend to sit Higher at some stage, they should follow the entire contents of the textbook, since the bare bones of the Intermediate 2 course do not in any way lay a sound foundation for progressing to Higher. The book is intended to be taken home by the students (hence the stitch-binding), but should be covered by a stiff plastic sleeve for added protection. Homework will be of the form... finish the exercise at home... There are 4 cumulative home exercises (of the old ink-exercise form), and the answers to these are not given in the book. There is a revision exercise at the end of Mathematics 3 with a specimen NAB. (set at minimum competency level C) Pages 3-6 give the course outline for MATHEMATICS 3 along with consolidation of and practice in sitting NAB 3. Pages 7 & 8 give guidance for Basic Revision, Non Calculator & Calculator Questions, and a Specimen Paper for Credit & Int. 2. Page 9 contains the course outline for the two HIGHER CHAPTERS - Recurrence Relations & Equation of a Straight Line. MIA & Heinemann :- It should be possible for most schools to store a half dozen MIA Books 3B and 4B (also MIA Higher or Heinemann Higher) in each classroom. TeeJay has provided a list of pages and exercises from these books which should provide additional practice for those pupils working at an advanced pace. TJ May 2007 Page Number 2
Topic Exer Pgs I/C MATHEMATICS 3 Ext n /Assessment Ch 0 - Revision 1-9 I/C Good revision exercise. Could be used as consolidation / remediation Maths 1 & Maths 2 after Book IC1 (Maths 1 & Maths 2) has been assessed. Ch 1 - Patterns 1.1 10 C Linear Patterns of the form y = mx. Complete table & find formula. 1.2 11-12 C Linear Patterns of the form y = mx + c. Correction Value to be found. 1.3 13-14 C Trickier patterns. Square Numbers / Triangular Numbers. MIA 3B page 58 15 REMEMBER, REMEMBER Assessment after Ch 2 Ch 2 - Algebraic 2.1 16-17 I/C Algebraic Fractions - simplify. e.g. cancelling MIA 4B page 141 Operations 2.2 18 I/C Algebraic Fractions - factorise. 3 types of factorising (done before) MIA 4B pages 141-142 2.3 19-20 I/C Algebraic Fractions - + /. Look for common denominator. MIA 4B pages 144-145 2.4 21 I/C Algebraic Fractions - x /. Watch how division changes to multn! MIA 4B pages 142-143 2.5 22-23 I/C Change subject of formula. Basic, change side etc. cross multn. MIA 4B page 149 2.6 24-25 I/C Change subject of formula (harder). Brackets; Square roots etc MIA 4B pages 149-150 26 REMEMBER, REMEMBER Assessment Date :-... TeeJay Assessment 1 Ch 3 - Money Matters 3.1 27-28 C Wages & Salaries. Time and Half; Double Time etc. MIA 3B pages 44-45 (not mentioned in Int2 3.2 29 C Gross Pay, Deductions, Net Pay. Meaning of annual. MIA 3B pages 161-162 course) 3.3 30 C Income Tax. incl. - Taxable Income. MIA 3B pages 166-167 3.4 31-32 C V.A.T. (usually 17 5%). Calculator reqd. MIA 3B pages 48-49 3.5 33 C Hire Purchase. incl. - finding how much each payment was. MIA 3B page 52 3.6 34 C Insurance. House, Contents, Life. MIA 3B pages 168-169 3.7 35 C Foreign Exchange. to foreign currency (x) and back ( )! MIA 3B pages 53-54 36 REMEMBER, REMEMBER Assessment Date :-... TeeJay Assessment 2 Home Exercise 1 37 C Consolidates Chapters 1-3. To be tackled at home. Given one Practice Makes Perfect 1 week to complete. (If desired, of the old ink exercise type). Covers Chapters 1-3 Answers not in book. TJ May 2007 Page Number 3
Topic Exer Pgs I/C MATHEMATICS 1 Ext n /Assessment Non-Calc Practice 1 38 I/C Practice in basic number work. Ch 4 - Functions 4.1 39-41 C Number Machines. Find ƒ( 3). Also working back to find p given ƒ(p). MIA 4B pages 18-19 & Graphs 4.2 42-44 C Quadratic Function. f (x) = ax 2 + bx + c The Parabola. MIA 4B pages 21-22 (not mentioned in Int2 course) 4.3 45 C Hyperbolic Function. a f (x ) = x MIA 4B pages 25-26 46 REMEMBER, REMEMBER Assessment after Ch 5 Ch 5 - Similar Figures 5.1 47-49 C Similarity. Find enlarge/reduction Scale factor. MIA 3B pages 16-23 select 5.2 50-51 C Similar Triangles. Corresponding sides equal... MIA 3B pages 25-26 5.3 52-53 C Similar Triangles and Parallel Lines. Proof of similarity in triangle. MIA 3B page 27 5.4 54-55 C Ratio - Similar Areas. Find Area Scale Factor first. MIA 4B pages 159-160 5.5 56-57 C Ratio - Similar Volumes. Find Volume Scale Factor first. MIA 3B pages 161-162 58 REMEMBER, REMEMBER Assessment Date :-... TeeJay Assessment 3 Ch 6 - Quadratic 6.1 59 I/C Sketching Parabolas within range of values for x. MIA 4B pages 21-22 Function 1 6.2 60 I/C Solve Quad Eqns. graphically. Zeros Roots. MIA 4B page 71 6.3 61 I/C Factorisation - revision. Revise all three types! MIA 4B pages 72-73 6.4 62-64 I/C Solve Quad Eqns. by factorisation. (x + 3)(x 5) = 0 etc. MIA 4B pages 74 and 76. p 81 also 6.5 65 C Sketch parabolas by factorising. Roots, Turning Pts. Line of Symm. MIA 4B page 75 6.6 66 C Intersection of line & parabola. Set 1 function = to the other. MIA 4B pages 79-80 67 REMEMBER, REMEMBER Assessment Date :-... TeeJay Assessment 4 Home Exercise 2 68 C Consolidates Chapters 1-6 To be tackled at home. Given one Practice Makes Perfect 2 week to complete. (If desired, of the old ink exercise type). Covers Chapters 1-6 Non-Calc Practice 2 69 I/C Practice in basic number work. TJ May 2007 Page Number 4
Topic Exer Pgs I/C MATHEMATICS 1 Ext n /Assessment Ch 7 - Trig Graphs 7.1 70-71 I/C Recognise / Draw Sine Graph. Mention Period 360. MIA 4B page 62 7.2 72-73 I/C Recognise / Draw Cosine Graph. Mention Period 360. MIA 4B pagee 62 7.3 74 I/C Recognise / Draw Tangent Graph. Mention Period 180. MIA 4B page 63 7.4 75-76 I/C y = asinx y = acosx. Amplitude. MIA 4B pages 63-64 7.5 77-78 I/C y = sinax y = cosax. Periodicity. MIA 4B pages 63-64 7.6 79-81 I/C y = sinax + b y = cosax + b. MIA 4B page 65 7.7 82 I/C y = sin(x a) y = cos(x a). Phase Angle. (Not in C - good for H) 83 REMEMBER, REMEMBER Assessment after Ch 8 Ch 8 - Surds & Indices 8.1 84 I/C A Surd? Explanation. MIA 4B page 121 8.2 85-86 I/C Simplify surds. + x. Rationalise the denominator MIA 4B pages 121-122 8.3 87 I/C Indices - Revision of powers. MIA 4B pages 112-113 8.4 88-89 I/C Rules of Indices - multiplying, dividing, powers of powers. MIA 4B page 114 89-90 I/C a0 = 1 and negative powers. MIA 4B pages 114-115 8.5 91 I/C Fractional indices and roots. MIA 4B pages 116-117 92 REMEMBER, REMEMBER Assessment Date :-... TeeJay Assessment 5 Ch 9 - Quadratic 9.1 93-94 I/C Completed Square form - Min TP. (Mainly Int 2). Function 2 9.2 95 I/C Completed Square form - Max TP. (Mainly Int 2). 9.3 96 I/C Quadratics of form y = kx 2. (Mainly Int 2). 9.4 97-98 I/C The Quadratic Formula. When to use it! MIA 4B pages 77-78 99 REMEMBER, REMEMBER Assessment after Ch 10 Home Exercise 3 100 C Consolidates Chapters 1-9 To be tackled at home. Given one Practice Makes Perfect 3 week to complete. (If desired, of the old ink exercise type). Covers Chapters 1-9 Non-Calc Practice 3 101 I/C Practice in basic number work. TJ May 2007 Page Number 5
Topic Exer Pgs I/C MATHEMATICS 1 Ext n /Assessment Ch 10 - Proportion 10.1 102 C Direct Proportion - Reminder. MIA 4B pages 87-88 (Variation) 10.2 103 C Indirect Proportion. the faster you go, the less time it takes. MIA (not mentioned in Int2 course) 10.3 104-105 C The language of Variation. Straight forward variation using α. MIA 4B pages 89-90 10.4 106 C Harder Variation involving powers and roots. Read Qu s carefully! MIA 4B pages 90-91 and late p93 10.5 107-108 C Inverse Variation. α 1/... MIA 4B page 93 10.6 108-109 C Joint Variation. P α MN/T MIA 4B pages 94-95 10.7 110-111 C Direct & Inverse Variation Graphs. Learn shape of both. MIA 4B pages 56-57 10.8 112-113 C Effect of Change. One quantity is say, halved, what happens to other? MIA 4B pages 86 and 92 114 REMEMBER, REMEMBER Assessment Date :-... TeeJay Assessment 6 Ch 11 - Trig Equations 11.1 115-118 I/C Solving Trig Eqns. Using the 4 quadrants A S T C. MIA 4B pages 59-61 and p 66 11.2 119 I/C Sine & Cos Rule with negatives. MIA 4B page 127 & page 132 Select! 11.3 120-121 I/C Trig Identities. incl. some useful Trig Formula. eg. tana = sina cosa 122 REMEMBER, REMEMBER Assessment after Ch 12 MIA 4B page 67 Ch 12 - Iteration 12.1 123-124 C Iterative method to solve quadratic eqns. MIA 4B pages 83 (not mentioned in Int2 12.2 125-126 C Iterative method to solve non-quadratic eqns. MIA 4B pages 83 course) 126 REMEMBER, REMEMBER Assessment Date :-... TeeJay Assessment 7 Home Exercise 4 127 C Consolidates Chapters 1-12 To be tackled at home. Given one Practice Makes Perfect 4 week to complete. (If desired, of the old ink exercise type). Covers Chapters 1-12 Non-Calc Practice 4 128 I/C Final practice in basic number work. This completes Maths 3 of the Basic Intermediate 2 course. It is recommended that pupils practice for and sit NAB 3 for Int 2. Revision for NAB 3 129-131 I(/C) This revision section is set at minimum competency level C. Practice Nab 3 132 This mirrors the NAB s as produced by the SQA. NAB 3 TJ May 2007 Page Number 6
Basic Revision Topic Page I/C Basic Revision Topic Page I/C Rounding (dec. pl. & sig. figs.) 135 I/C Scientific Notation (to SN and back again) 135 I/C Fraction Work (+ x ) 135 C Percentage Work (incl. examples on finding original price) 135 I/C Ratio Work (Cancelling & sharing) 135 C Time, Distance, Speed (Use triangle formulae) 136 C Equations (incl. eqns with fractions) 136 C Circle Work 1 (Perimeter, area, diameter, radius) 136 C Pythagoras Theorem (incl. Converse proof) 137 C Inequalities (Watch for sign changing) 137 C Rotational Symmetry (180 Rotation) (& reflection) 138 C Angle Work (Isosceles triangle, supplementary, par. lines) 138 C Algebra (Expanding brackets) 139 I/C Patterns (Complete table & find formula) 139 C Arcs & Sectors (Arcs, sectors & segments) 140 I/C Volumes (Prism, cone, sphere, cylinder) 140 I/C Factorisation (All 3 types) 141 I/C Surface Area (Nets & SA of cylinder & prism) 141 I/C Function Notation (Find ƒ(x) etc) 141 C Trigonometry (RAT) SOHCAHTOA 142 C Angles in Circles (Using tangents and Pythagoras) 142 I/C Gradients & Lines (grad formula, y-intercept and Eqn) 143 I/C Simultaneous Equations (incl. wordy Qu.) 143 I/C Similar Figures (incl. similar areas and similar volumes) 144 C Iteration (Calculate root to 1 dec. pl.) 144 C Algebraic Fractions (Common denominator & factors) 145 I/C Appreciation/Depreciation (Monthly/yearly inc/dec) 145 I/C Probability (Use rule for probability) 145 I/C Quadratic Equations & Parabolas (Factorise & Formula) 146 I/C Trig. (Sin/Cos Rule) (Choose which to use - & bearings) 147 I/C Change of Subject of Formula 147 C Variation (Direct, Inverse, Joint & effect changes) 148 I/C Surds & Indices (Simplify, use rules & rationalise den) 148 I/C Integer Work (Watch double negative) 148 I/C Trig Graphs (Recognise trig graphs) 149 I/C Trig Equations (Use of 4 Quadrants) 149 I/C Trig Identities (Useful formulae to attempt proofs) 149 I/C Statistical Graphs (Dot/Box plot, Stem & Leaf etc..) 150-151 I/C Statistical Analysis (Median, Quartiles, Standard Dev) 152 I/C TJ May 2007 Page Number 7
Non Calculator Exam Questions Page I/C Calculator Exam Questions Page I/C Bodmas... 154 C Fractions... 154 C Functions & Substitution... 154 I/C Expressions... 154 I/C Equations... 155 I/C Inequalities... 155 C Ratio... 155 C Percentages... 155 I/C Gradients & Lines... 156 I/C Factorisation... 156 I/C Change of Subject of Formula... 156 I/C Trig Graphs... 157 I/C Circles... 157 I/C Simultaneous Equations... 157 I/C Number Patterns... 158 C Probability... 158 I/C Statistical Diagrams... 159 I/C Parabolic Curves... 160 I/C Surds... 160 I/C Indices... 160 I/C Percentages... 162 I/C Time Distance Speed... 162 C Pythagoras... 163 C Scientific Notation... 164 C Straight Line... 164-165 I/C Volume... 166-167 I/C Brackets/Factors... 168 I/C Arcs & Sectors... 169 I/C SOHCAHTOA... 170 I/C Formulae & Inequalities... 171 C Angles... 172 I/C Simultaneous Equations... 173 I/C Statistics... 174-175 I/C Sin/Cos Rule, Area of Triangle... 176-177 I/C Money Topics... 178 I/C Similar Figures... 179 C Quadratics... 180 I/C Trig Graphs... 181 I/C Variation... 182 C Trig Equations... 183 I/C Iteration... 184 C Specimen Exam Papers Credit Paper 1 Pgs 186-188 Paper 2 Pgs 189-191 Int. 2 Paper 1 Pgs 192/193 Paper 2 Pgs 194-196 TJ May 2007 Page Number 8
Topic Exer Pgs HIGHER Ext n /Assessment Ch H1 - H1.1 198 General Term of a Sequence - find 1st few terms and nth term in a sequence Hein Pgs 70-71 MIA Pgs 85-86 Recurrence Relations H1.2 199 Intro to the Recurrence Relation U n+1 = 5U n 6, when U 0 is 2 Hein Pgs 71-72 MIA Pgs 85-86 H1.3 200-201 Developing an Explicit Formula from a Rec Rel. Set up Rec Rels. H1.4 202-204 Linear Rec Rel. Tending towards a Limit using a calculator. Hein Pgs 73-76 MIA Pgs 86-88 H1.5 205-206 Finding the Limit of a Rec Rel using a Formula or otherwise. Hein Pgs 78-79 MIA Pg 91 H1.6 207 Finding a Rec Rel when you know some terms. Use of simultaneous eqns. Hein Pgs 79-80 MIA Pg 92 208 REMEMBER, REMEMBER Assessment Date :-... TeeJay Higher Assessment 1 y y 2 1 Ch H2 - H2.1 209-210 Gradient of a Line. Intro of the Gradient Formula m = x x Equation of a 2 1 + colliear Hein Pgs 1-4 MIA Pgs 4-6 Straight Line H2.2 211 Angle between a line and the x-axis. m = tan θ Hein Pgs 2/3 & 7 MIA Pgs 4-6 H2.3 212-213 Revision y = mx + c. Mention lines parallel - means equal gradients. Hein Pgs 8-9 MIA Pg 8-9 H2.4 214 The Distance Formula (or use Pythagoras). MIA Pgs 2-3 H2.5 215 Ax + By + C = 0. Finding gradient & y-intercept Hein Pg 10 MIA Pg 10 H2.6 216-217 y b = m(x a). Eqn of line when you are not given a point on y-axis. Hein Pgs 11-12 MIA Pgs 11-13 H2.7 217-218 Perpendicular Lines. m 1 x m 2 = 1. Watch for Special Lines x =... y =... Hein Pgs 6-7 MIA Pg 7 H2.8 219-222 Medians, Altitudes, Perpendicular Bisectors - Know the difference between! Hein Pgs 12-20 MIA Pgs 12-17 223 REMEMBER, REMEMBER Assessment Date :-... TeeJay Higher Assessment 2 TJ May 2007 Page Number 9