CONTENTS
PART ONE
THE C.X.C. BASIC PROFICIENCY SYLLABUS
(CORE SYLLABUS)
PAGE
2.30 The set of odd numbers 21
1. SETS 1 2 2.31 The set of odd or even numbers 21
2.32 The highest common factor (H.C.F.) 22
1.1 Defining a set 2 2.33 The lowest-common multiple (L.C.M.) 22
1.2 Elements. Number of elements in a set 2 2.34 The sequence of numbers 23
1.3 Finite and infinite sets 3 2.35 Number bases 24
1.4 The null empty set 3 The decimal system 25
2.36
1.5 The universal set 3 2.37 The binary system 25
1.6 Subsets 4 2.38 Converting from decimal to bicimal 27
1.7 The number of subsets 4 2.39 Converting from bicimal to decimal 28
1.8 Equal sets 5 2.40 Adding binary numbers 29
1.9 Equivalent sets. One-to-one correspondence 5 2.41 Subtracting binary numbers 30
1.10 Venn diagrams 5 2.42 Multiplying binary numbers 30
1.11 The complement 5 2.43 Numbers to base five 31
1.12 The intersection of two sets 6 Converting from decimal to base five 32
2.44
1.13 The union of two sets 6 2.45 Converting from base five to decimal 32
1.14 Subsets \ 7 2.46 Adding base five numbers 33
1.15 Disjoint sets 7 2.47 Subtracting base five numbers 33
1.16 The number of elements in two sets 9 2.48 Multiplying base five numbers 33
2.49 Octal numbers 34
2. NUMBER THEORY 11 2.50 Converting from decimal to octal 34
2.51 Converting from octal to decimal 35
2.1 The set of natural numbers 11 2.52 Adding octal numbers 36
2.2 The set of whole numbers 11 2.53 Subtracting octal numbers 36
2.3 The set of integers 11 2.54 Multiplying octal numbers 36
2.4 The set of rational numbers 11 2.55 Other number cases 37
2.5 The set of irrational numbers 12
2.6 The set of real numbers 12 3. COMPUTATION 39
2.7 Basic arithmetic operations 12
2.8 Some meanings of zero 13
3.1 The order of arithmetic operations 39
2.9 The identity for addition 13 prob with whole numbers
mbers 39
3.2
2.10 The identity for multiplication 13 Word problems
roblems - whole numbers 40
34
2.11 The Inverse for numbers under addition 13
3.4 Operations
with fractions 43
2.12 The inverse for numbers under multiplicationl3 3.5 Wordproblems - fracti
fractions 46
2.13 Multiplication by zero 13
M 3.6 Operations with mixed numbers 47
2.13 by zero 13
3.7 Mixed operations - fractions 49
14
2.15
2.16
2.17
The law of closure -
The commutative law f
The associative law.'
t 14
14
3.8
3.9
Operations with decimals
Decimal numbers
51
53
3.10 Word problems - decimals 55
2.18 The distributive law 14
3.11 Mixed operations - decimals 57
2.19 The powers of numbers' 3.12 Approximations: Nearest whole number 59
2.20 Defined arithmetic operations 16
3.13 Approximations: Nearest multiple of ten 59
2.21 The factors of a number 17
3.14 Approximations: Decimal places 61
2.22 The set of square numbers 17
3.15 Recurring decimals 61
2.23 The set of rectangle numbers 18
3.16 Approximations: Significant figures 63
2.24 The set of prime numbers 19
3.17 Standard form or scientific notation 64
2.25 The set of composite numbers 19
3.18 Constructing the range in which the exact
2.26 The set of prime or composite numbers 19
value of a computation must her 65
2.27 The prime factors of a number 19
3.19 Short cuts in computation 68
2.28 The multiples of a number 20
3.20 Ratio 71
2.29 The set of even numbers 21
,3.21 Proportional parts 72 5.18 Depreciation 205
3.22 Direct proportion 75 5.19 C.X.C. Past Paper Questions 209
3.23 The ready reckoner 76
3.24 Inverse proportion 78
3.25
6. ALGEBRA 1 214
The percentage of a quantity 79
3.26 Expressing one quantity as a percentage
6.1 Introduction 214
of another 80 6.2 Using symbols to represent numbers 214
3.27 The arithmetic mean or average 82 6.3 Substituting numerals for symbols in 215
3.28 The square of a number 83
algebraic expressions
3.29 The square root of a number 88 6.4 Addition and subtraction of algebraic terms 218
3.30 The reciprocal of a number 92 6.5 Multiplication and division of algebraic terms 229
3.31 C.X.C. Past Paper Questions 94 6.6 The distributive law 223
6.7 Binary operations 226
4. MEASUREMENT 95 6.8 Factorization 227
6.9 Factorizing using the distributive law 227
4.1 The metric system 95 6.10 The highest common factor (H.C.F.) 228
4.2 The metric systemunit of length 95 6.11 Factorizing using the highest common
4.3 The metric system unit for area 97 factor 229
4.4 The metric system unit for volume 98 6.12 Factorizing by grouping 230
4.5 The metric system unit of capacity 100 6.13 Addition and subtraction of algebraic
4.6 The metric system unit of mass 101 fractions 232
4.7 The systeme international d' unit6s 102 6.14 Multiplication and division of algebraic
4.8 Areas and perimeters of simple plane fractions 234
figures 104 6.15 Equations 235
4.9 Areas and perimeters of complex 6.16 Solution of linear equations in one unknown 236
compound figures 123 6.17 Inequations 240
4.10 Volumes, densities and surface areas 6.18 Solution of linear inequations in one unknown 241
of simple right solids 127 6.19 Simultaneous equations 244
4.11 The volume and surface area of a sphere 142 6.20 Solution of simultaneous linear equations 244
412 Time 145 6.21 Word problems - linear equations 248
4.13 Average speed 147 6.22 Word problems - linear inequations 252
4.14 Converting units of speed 149 6.23 Word problems- simultaneous linear
4.15 The estimated margin of error for a given equations . 254
measurement 150 6.24 Positive integral indices 258
4.16 Measurement on maps and scale drawings 152 6.25 Multiplication 258
4.17 C.X.C. Past Paper Questions 156 6.26 Division 258
6.27 Power to a power 259
5. . CONSUMER ARITHMETIC 160 6.28 Zero index 259
6.29 Negative indices 259
5.1 Salary 160 6.30 Fractional (rational) indices 260
5.2 Basic wage 161' 6.31 The laws of indices 261
5.3 " Overtime wage. Gross wage 163 6.32 Solution of equations where the unknown
5.4 Commission. Gross wage 165 quantity is in the index 265
5.5 Income tax 166 6.33 Standard form or scientific notation 266
5.6 Percentage profit and percentage loss 170 6.34 Logarithms . 269
5.7 Percentage change 172 6.35 Anti-logarithms 269
5.8 Discount 174 6.36 Logarithmic theory 271
5.9 Sales tax- vat 175 6.37 Solution of equations using logarithms 273
5.10 Hire purchase 176 6.38 C.X.C. Past Paper Questions 274
5.11 • ' Mortgage 180
5.12 ' Rates. Land and building taxes 181 7. RELATIONS, FUNCTIONS AND
5.13 Electricity bills 186 GRAPHS 1 276
5.14 Telephone bills 190
5.15 Foreign exchange 193 7.1 The Cartesian plane 276
5.'6 Simple interest 197 7.2 Scales 276
5.17 Compound interest 201 7.3 Drawing diagrams 278
11
,7.4 Simple linear graphs 280 8.22 Choosing a measure of central tendency 376
7.5 Inequalities 282 8.23 Measures of dispersion 377
7.6 Representing inequalities on a number line 284 8.24 The range 377
7.7 Representing inequalities on a graph 286 8.25 Interquartile range and semi-interquartile
7.8 Relations 288 range 378
7.9 Functions 290 8.26 Probability 392
7.10 A relation but not a function 291 8.27 Sample space, outcomes and events 382
7.11 Image of x 291 8.28 Equally likely events 383
7.12 The graph of the function f: x -> ax 294 8.29 The impossible event 383
7.13 The graph of the function f: x - arr 295 8.30 The certain event 383
7.14 Direct variation 296 8.31 Probability dealing with one event and its
7.15 Inverse variation 298 complement 383
7.16 The general form of the linear function 300 8.32 Theoretical probability 384
7.17 Graph of the linear function 301 833 C.X.C. Past Paper Questions 386
7.18 The length of a straight line 304
7.19 The mid-point of a straight line 305 9. GEOMETRY 1 390
720 The gradient of a straight line 305
7.21 The equation of a straight line 307 9.1 Introduction 390
7.22 Parallel lines 311 9.2 Point 390
7.23 Perpendicular lines 311 9.3 Line segments 390
7.24 Point of intersection 313 9.4 Lines 390
7.25 Solution of simple equations by the 9.5 Rays 390
method of intersecting graphs 313 9 .6 Angles 391
7.26 Solutions of simultaneous linear equations 9.7 Revolution 391
by the method of intersecting graphs 316 9 .8 Clockwise or anti-clockwise 393
7.27 Graphs of linear inequalities 319 9 .9 Degrees 394
7.28 Solutions of simultaneous linear inequations 322 9.10 Types of angles 396
7.29 General form of the quadratic function 323 9.11 Properties of angles formed by
7.30 Graph of the quadratic function 323 intersecting lines 397
7.31 Solutions of quadratic equations by the 9.12 Measuring angles 406
method of intersecting graphs 326 9.13 Drawing angles 407
7.32 Experimental data 329 9.14 Parallel lines 408
7.33 C.X.C. Past Paper Questions 333 9.15 Perpendicular fines 408
9.16 Constructing a line segment 408
S. STATISTICS 1 336 9.17 Bisecting a line segment 409
9.18 Bisecting an angle 409
8.1 Introduction 336 9.19 Constructing angles of 90', 45' and 22.5' 412
8.2 Proportional bar chart or composite bar chart 336 9.20 Constructing angles of 60', 30' and 15' 413
8.3 Bar charts or column graphs 338 9.21 Bisecting an angle continuously 414
8.4 Chronological bar charts 340
9.22 Planes and polygons 415
8.5 Pie charts 341
9.23 Triangles 416
8.9 Line graphs 345 9.24 Elements of a triangle 416
8.7 Variables 347 9.25 Types of triangles 416
8.8 Frequency tables (ungrouped data) 348
9.26 Angle properties of triangles 417
8.9 Histograms (ungrouped data) 350
J27 Proof of theorems 419
8.10 Frequency polygons (ungrouped data) 353
9.29 Construe s o f a unique tri n g 426
8.11 Frequency tables (grouped data) 356
9.30 Properties of iso
congruent
el triangles 426
8.12 The width of a class interval or class size 357 9.30 Properties of isosceles and equilateral
8.13 Histograms (grouped data) 361
mangles 429
8.14 Frequency polygons (grouped data) 363 9.31 Similar triangles 432
8.15 Measures of central tendency 365 g 32 Properties of similar triangles 433
8.16 The mean 365 9,33 Pythagoras' theorem 435
8.17 The median 368
9.34 Quadrilaterals 439
8.18 The mode 371
T 9.35 Elements of a quadrilateral 439
8.19 e mode ' 374 9.36 Types of quadrilaterals 440
8.20 Types n frequency curves 375 9.37 Angle properties of quadrilaterals 441
8.21 Comparing the three measures of central
9.38 Constructing a unique quadrilateral 444
tendency 376
iii
J. t;
, `
9.39 Polygons 450 10.22 Types of enlarger ncnts 523
9.40 Types of polygons 451 10.23 Properties of enlargements 525
9.41 Angle properties of polygons 451 10.24 Image under>an enlargement 529
9.42 Areas: Triangle, trapezium, parallelogram 10.25 Enlargement on the Cartesian plane 530
and rectangle 455 10.26 Inverse enlargements 532
9.43 Areas: Triangle, rhombus and square 456 10.27 C.X.C. Past Paper Questions 537
9.44 Circles 457
9.45 Properties of circles 457 11. GEOMETRY:TRIGONOMETRY 1 540
9.46 Angle properties of circles 459
9.47 Solids 469 11.1 The notation 540
9.48 Nets: Two dimensional representation of 11.2 The sine of an angle 540
solids 470 11.3 Sin 0 541
9.49 Plans and elevations 473 11.4 Sin-lx or arc sin x 541
9.50 C.X.C. Past Paper Questions . 479 11.5 Finding an unknown side 543
11.6 finding an unknown angle 543
10. GEOMETRY: SYMMETRY AND 11.7 The cosine of an angle 547
TRANSFORMATIONS 1 481 11.8 Cos 0 547
11.9 Cos-ix or arc cos x 548
10.1 Symmetry 481 11.10 Finding an unknown side 549
10.2 Translational symmetry 481 11.11 Finding an unknown angle 550
10.3 Line symmetry or reflective symmetry 484 11.12 The tangent of an angle 554
10.4 Rotational symmetry 487 11.13 Tan 0 554
10.5 Transformations 490 11.14 Tan -lx or arc tan x 555
10.6 Translations 490 11.15 Finding an unknown side 556
10.7 Properties of translations 491 11.16 Finding an unknown angle 557
10.8 Column vectors 493 11.17 Mixed problems 561
10.9 Image under a translation 493 11.18 Complementary angles 562
10.10 Inverse translations 496 11.19 Angles of elevation and depression 563
10.11 Reflections 499 11.20 Bearings 567
10.12 Properties of reflections 499 11.21 C.X.C. Past Paper Questions 571
10.13 Image under a reflection 500
10.14 Inverse reflections C.X.0 Model Examinations - Basic Proficiency
506
10.15 Rotations 510
C.X.C. Model Examinations I to 6
10.16 Properties of rotations 511
Paper I - Basic Proficiency 573
10.17 Image under a rotation 513
10.18 Image under a rotation about the origin 514 C.X.C. Model Examinations 1 to 6
10,19 Inverse rotations 517 Paper 2 - Bask Proficiency 601
10.20 Finding the centre of rotation and the
angle of rotation -518 Three Figure Tables 617
10.21 Enlargement 522
Answers 633
iv
PART ONE
THE C.X.C. BASIC PROFICIENCY SYLLABUS
(CORE SYLLABUS)
PAGE
2.30 The set of odd numbers 21
1. SETS 1 2 2.31 The set of odd or even numbers 21
2.32 The highest common factor (H.C.F.) 22
1.1 Defining a set 2 2.33 The lowest-common multiple (L.C.M.) 22
1.2 Elements. Number of elements in a set 2 2.34 The sequence of numbers 23
1.3 Finite and infinite sets 3 2.35 Number bases 24
1.4 The null empty set 3 The decimal system 25
2.36
1.5 The universal set 3 2.37 The binary system 25
1.6 Subsets 4 2.38 Converting from decimal to bicimal 27
1.7 The number of subsets 4 2.39 Converting from bicimal to decimal 28
1.8 Equal sets 5 2.40 Adding binary numbers 29
1.9 Equivalent sets. One-to-one correspondence 5 2.41 Subtracting binary numbers 30
1.10 Venn diagrams 5 2.42 Multiplying binary numbers 30
1.11 The complement 5 2.43 Numbers to base five 31
1.12 The intersection of two sets 6 Converting from decimal to base five 32
2.44
1.13 The union of two sets 6 2.45 Converting from base five to decimal 32
1.14 Subsets \ 7 2.46 Adding base five numbers 33
1.15 Disjoint sets 7 2.47 Subtracting base five numbers 33
1.16 The number of elements in two sets 9 2.48 Multiplying base five numbers 33
2.49 Octal numbers 34
2. NUMBER THEORY 11 2.50 Converting from decimal to octal 34
2.51 Converting from octal to decimal 35
2.1 The set of natural numbers 11 2.52 Adding octal numbers 36
2.2 The set of whole numbers 11 2.53 Subtracting octal numbers 36
2.3 The set of integers 11 2.54 Multiplying octal numbers 36
2.4 The set of rational numbers 11 2.55 Other number cases 37
2.5 The set of irrational numbers 12
2.6 The set of real numbers 12 3. COMPUTATION 39
2.7 Basic arithmetic operations 12
2.8 Some meanings of zero 13
3.1 The order of arithmetic operations 39
2.9 The identity for addition 13 prob with whole numbers
mbers 39
3.2
2.10 The identity for multiplication 13 Word problems
roblems - whole numbers 40
34
2.11 The Inverse for numbers under addition 13
3.4 Operations
with fractions 43
2.12 The inverse for numbers under multiplicationl3 3.5 Wordproblems - fracti
fractions 46
2.13 Multiplication by zero 13
M 3.6 Operations with mixed numbers 47
2.13 by zero 13
3.7 Mixed operations - fractions 49
14
2.15
2.16
2.17
The law of closure -
The commutative law f
The associative law.'
t 14
14
3.8
3.9
Operations with decimals
Decimal numbers
51
53
3.10 Word problems - decimals 55
2.18 The distributive law 14
3.11 Mixed operations - decimals 57
2.19 The powers of numbers' 3.12 Approximations: Nearest whole number 59
2.20 Defined arithmetic operations 16
3.13 Approximations: Nearest multiple of ten 59
2.21 The factors of a number 17
3.14 Approximations: Decimal places 61
2.22 The set of square numbers 17
3.15 Recurring decimals 61
2.23 The set of rectangle numbers 18
3.16 Approximations: Significant figures 63
2.24 The set of prime numbers 19
3.17 Standard form or scientific notation 64
2.25 The set of composite numbers 19
3.18 Constructing the range in which the exact
2.26 The set of prime or composite numbers 19
value of a computation must her 65
2.27 The prime factors of a number 19
3.19 Short cuts in computation 68
2.28 The multiples of a number 20
3.20 Ratio 71
2.29 The set of even numbers 21
,3.21 Proportional parts 72 5.18 Depreciation 205
3.22 Direct proportion 75 5.19 C.X.C. Past Paper Questions 209
3.23 The ready reckoner 76
3.24 Inverse proportion 78
3.25
6. ALGEBRA 1 214
The percentage of a quantity 79
3.26 Expressing one quantity as a percentage
6.1 Introduction 214
of another 80 6.2 Using symbols to represent numbers 214
3.27 The arithmetic mean or average 82 6.3 Substituting numerals for symbols in 215
3.28 The square of a number 83
algebraic expressions
3.29 The square root of a number 88 6.4 Addition and subtraction of algebraic terms 218
3.30 The reciprocal of a number 92 6.5 Multiplication and division of algebraic terms 229
3.31 C.X.C. Past Paper Questions 94 6.6 The distributive law 223
6.7 Binary operations 226
4. MEASUREMENT 95 6.8 Factorization 227
6.9 Factorizing using the distributive law 227
4.1 The metric system 95 6.10 The highest common factor (H.C.F.) 228
4.2 The metric systemunit of length 95 6.11 Factorizing using the highest common
4.3 The metric system unit for area 97 factor 229
4.4 The metric system unit for volume 98 6.12 Factorizing by grouping 230
4.5 The metric system unit of capacity 100 6.13 Addition and subtraction of algebraic
4.6 The metric system unit of mass 101 fractions 232
4.7 The systeme international d' unit6s 102 6.14 Multiplication and division of algebraic
4.8 Areas and perimeters of simple plane fractions 234
figures 104 6.15 Equations 235
4.9 Areas and perimeters of complex 6.16 Solution of linear equations in one unknown 236
compound figures 123 6.17 Inequations 240
4.10 Volumes, densities and surface areas 6.18 Solution of linear inequations in one unknown 241
of simple right solids 127 6.19 Simultaneous equations 244
4.11 The volume and surface area of a sphere 142 6.20 Solution of simultaneous linear equations 244
412 Time 145 6.21 Word problems - linear equations 248
4.13 Average speed 147 6.22 Word problems - linear inequations 252
4.14 Converting units of speed 149 6.23 Word problems- simultaneous linear
4.15 The estimated margin of error for a given equations . 254
measurement 150 6.24 Positive integral indices 258
4.16 Measurement on maps and scale drawings 152 6.25 Multiplication 258
4.17 C.X.C. Past Paper Questions 156 6.26 Division 258
6.27 Power to a power 259
5. . CONSUMER ARITHMETIC 160 6.28 Zero index 259
6.29 Negative indices 259
5.1 Salary 160 6.30 Fractional (rational) indices 260
5.2 Basic wage 161' 6.31 The laws of indices 261
5.3 " Overtime wage. Gross wage 163 6.32 Solution of equations where the unknown
5.4 Commission. Gross wage 165 quantity is in the index 265
5.5 Income tax 166 6.33 Standard form or scientific notation 266
5.6 Percentage profit and percentage loss 170 6.34 Logarithms . 269
5.7 Percentage change 172 6.35 Anti-logarithms 269
5.8 Discount 174 6.36 Logarithmic theory 271
5.9 Sales tax- vat 175 6.37 Solution of equations using logarithms 273
5.10 Hire purchase 176 6.38 C.X.C. Past Paper Questions 274
5.11 • ' Mortgage 180
5.12 ' Rates. Land and building taxes 181 7. RELATIONS, FUNCTIONS AND
5.13 Electricity bills 186 GRAPHS 1 276
5.14 Telephone bills 190
5.15 Foreign exchange 193 7.1 The Cartesian plane 276
5.'6 Simple interest 197 7.2 Scales 276
5.17 Compound interest 201 7.3 Drawing diagrams 278
11
,7.4 Simple linear graphs 280 8.22 Choosing a measure of central tendency 376
7.5 Inequalities 282 8.23 Measures of dispersion 377
7.6 Representing inequalities on a number line 284 8.24 The range 377
7.7 Representing inequalities on a graph 286 8.25 Interquartile range and semi-interquartile
7.8 Relations 288 range 378
7.9 Functions 290 8.26 Probability 392
7.10 A relation but not a function 291 8.27 Sample space, outcomes and events 382
7.11 Image of x 291 8.28 Equally likely events 383
7.12 The graph of the function f: x -> ax 294 8.29 The impossible event 383
7.13 The graph of the function f: x - arr 295 8.30 The certain event 383
7.14 Direct variation 296 8.31 Probability dealing with one event and its
7.15 Inverse variation 298 complement 383
7.16 The general form of the linear function 300 8.32 Theoretical probability 384
7.17 Graph of the linear function 301 833 C.X.C. Past Paper Questions 386
7.18 The length of a straight line 304
7.19 The mid-point of a straight line 305 9. GEOMETRY 1 390
720 The gradient of a straight line 305
7.21 The equation of a straight line 307 9.1 Introduction 390
7.22 Parallel lines 311 9.2 Point 390
7.23 Perpendicular lines 311 9.3 Line segments 390
7.24 Point of intersection 313 9.4 Lines 390
7.25 Solution of simple equations by the 9.5 Rays 390
method of intersecting graphs 313 9 .6 Angles 391
7.26 Solutions of simultaneous linear equations 9.7 Revolution 391
by the method of intersecting graphs 316 9 .8 Clockwise or anti-clockwise 393
7.27 Graphs of linear inequalities 319 9 .9 Degrees 394
7.28 Solutions of simultaneous linear inequations 322 9.10 Types of angles 396
7.29 General form of the quadratic function 323 9.11 Properties of angles formed by
7.30 Graph of the quadratic function 323 intersecting lines 397
7.31 Solutions of quadratic equations by the 9.12 Measuring angles 406
method of intersecting graphs 326 9.13 Drawing angles 407
7.32 Experimental data 329 9.14 Parallel lines 408
7.33 C.X.C. Past Paper Questions 333 9.15 Perpendicular fines 408
9.16 Constructing a line segment 408
S. STATISTICS 1 336 9.17 Bisecting a line segment 409
9.18 Bisecting an angle 409
8.1 Introduction 336 9.19 Constructing angles of 90', 45' and 22.5' 412
8.2 Proportional bar chart or composite bar chart 336 9.20 Constructing angles of 60', 30' and 15' 413
8.3 Bar charts or column graphs 338 9.21 Bisecting an angle continuously 414
8.4 Chronological bar charts 340
9.22 Planes and polygons 415
8.5 Pie charts 341
9.23 Triangles 416
8.9 Line graphs 345 9.24 Elements of a triangle 416
8.7 Variables 347 9.25 Types of triangles 416
8.8 Frequency tables (ungrouped data) 348
9.26 Angle properties of triangles 417
8.9 Histograms (ungrouped data) 350
J27 Proof of theorems 419
8.10 Frequency polygons (ungrouped data) 353
9.29 Construe s o f a unique tri n g 426
8.11 Frequency tables (grouped data) 356
9.30 Properties of iso
congruent
el triangles 426
8.12 The width of a class interval or class size 357 9.30 Properties of isosceles and equilateral
8.13 Histograms (grouped data) 361
mangles 429
8.14 Frequency polygons (grouped data) 363 9.31 Similar triangles 432
8.15 Measures of central tendency 365 g 32 Properties of similar triangles 433
8.16 The mean 365 9,33 Pythagoras' theorem 435
8.17 The median 368
9.34 Quadrilaterals 439
8.18 The mode 371
T 9.35 Elements of a quadrilateral 439
8.19 e mode ' 374 9.36 Types of quadrilaterals 440
8.20 Types n frequency curves 375 9.37 Angle properties of quadrilaterals 441
8.21 Comparing the three measures of central
9.38 Constructing a unique quadrilateral 444
tendency 376
iii
J. t;
, `
9.39 Polygons 450 10.22 Types of enlarger ncnts 523
9.40 Types of polygons 451 10.23 Properties of enlargements 525
9.41 Angle properties of polygons 451 10.24 Image under>an enlargement 529
9.42 Areas: Triangle, trapezium, parallelogram 10.25 Enlargement on the Cartesian plane 530
and rectangle 455 10.26 Inverse enlargements 532
9.43 Areas: Triangle, rhombus and square 456 10.27 C.X.C. Past Paper Questions 537
9.44 Circles 457
9.45 Properties of circles 457 11. GEOMETRY:TRIGONOMETRY 1 540
9.46 Angle properties of circles 459
9.47 Solids 469 11.1 The notation 540
9.48 Nets: Two dimensional representation of 11.2 The sine of an angle 540
solids 470 11.3 Sin 0 541
9.49 Plans and elevations 473 11.4 Sin-lx or arc sin x 541
9.50 C.X.C. Past Paper Questions . 479 11.5 Finding an unknown side 543
11.6 finding an unknown angle 543
10. GEOMETRY: SYMMETRY AND 11.7 The cosine of an angle 547
TRANSFORMATIONS 1 481 11.8 Cos 0 547
11.9 Cos-ix or arc cos x 548
10.1 Symmetry 481 11.10 Finding an unknown side 549
10.2 Translational symmetry 481 11.11 Finding an unknown angle 550
10.3 Line symmetry or reflective symmetry 484 11.12 The tangent of an angle 554
10.4 Rotational symmetry 487 11.13 Tan 0 554
10.5 Transformations 490 11.14 Tan -lx or arc tan x 555
10.6 Translations 490 11.15 Finding an unknown side 556
10.7 Properties of translations 491 11.16 Finding an unknown angle 557
10.8 Column vectors 493 11.17 Mixed problems 561
10.9 Image under a translation 493 11.18 Complementary angles 562
10.10 Inverse translations 496 11.19 Angles of elevation and depression 563
10.11 Reflections 499 11.20 Bearings 567
10.12 Properties of reflections 499 11.21 C.X.C. Past Paper Questions 571
10.13 Image under a reflection 500
10.14 Inverse reflections C.X.0 Model Examinations - Basic Proficiency
506
10.15 Rotations 510
C.X.C. Model Examinations I to 6
10.16 Properties of rotations 511
Paper I - Basic Proficiency 573
10.17 Image under a rotation 513
10.18 Image under a rotation about the origin 514 C.X.C. Model Examinations 1 to 6
10,19 Inverse rotations 517 Paper 2 - Bask Proficiency 601
10.20 Finding the centre of rotation and the
angle of rotation -518 Three Figure Tables 617
10.21 Enlargement 522
Answers 633
iv
