Math-textbook-pdf

e-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersity Glossary

Review Multiply out Multiplying out the terms inside a bracket by the Pie chart A circular chart which uses slices or sectors of the
term multiplying the bracket. ( is includes multiplying one circle to show the data.
Review bracket by another.) See also expansion.
Mutually exclusive Events that cannot happen at the same time. Plane symmetry A flat surface that cuts a solid into two halves
Review so that one half is the mirror image of the other.
N
Point of contact e point at which a tangent to a circle and
Natural number Any whole number from 1 to infinity, chord meet.
sometimes called “counting numbers”. 0 is not included.
Negative correlation A trend, in bivariate data, where, as one Polygon A plane (two-dimensional) shape with three or
value increases, the other value decreases. more sides.
Net e plane shape formed from the faces of a solid when
it is “unfolded”. Positive correlation A trend in bivariate data where as one value
Net income Income from earnings after deductions and tax increase, so does the other.
have been subtracted.
No correlation No apparent linear relationship between tow Possible outcomes e possible results from an event.
sets of data.
nth term e value in the nth position in a sequence. Power Another word for exponent or index, indicating how
Numerator e number on the top of a fraction. many times a base number is multiplied by itself.
Numerical data Data that is in the form of numbers.
Primary data Data collected by the person who is going to use it.
O
Prime factor A prime number that divides exactly into another
Object e original position of a point before a transformation. number with no remainder.
Obtuse An angle greater than 90° but less than 180°.
Opposite A “shorter” side of a right-angled triangle that is Prime number A whole number greater than 1 which has only
“opposite” an angle other than the right-angle. two factors: the number itself and 1.
Order of rotational symmetry e number of times a shape fits
onto itself in one rotation. Principal e initial amount of money invested or borrowed.
Outcome e possible results of an “experiment”.
Probability A measure of how likely an event is to happen
P
Probability scale e range of values from zero to one.
Parabola e graph of a quadratic relationship.
Parallel Lines that “never meet”. e shortest distance between a Possibility diagram A list or diagram that shows all the equally
pair of parallel lines remains the same. likely outcomes of an “experiment”.
Percentage A fraction with a denominator of 100.
Percentage decrease e amount that something has decreased Profit When goods are sold for more than they were bought, the
as a percentage of the original value. profit is the selling price − cost price.
Percentage increase e amount that something has increased
as a percentage of the original value. Projection e image of a line on a plane such that the angle
Percentiles e value of data at a specified position (the data between the angle and the image is the smallest possible.
must be arranged in increasing order).
Perimeter e distance around the edges of a plane shape. Q
Periodic Repeats at regular intervals.
Perpendicular At right angles to. When the angle between two Quadratic equation An equation that contains a quadratic
lines is 90°, the lines are perpendicular to each other. expression.
Perpendicular bisector A line that cuts exactly through the Quadratic expression An expression where one term has a
middle of another line, making an angle of 90° with it. variable squared (and no variable with a higher power).
Pictogram A diagram that uses symbols or small pictures to Quadrilateral Polygons with four sides.
represent data. Qualitative Another name for categorical data.
Quantitative Another name for numerical data.
Quartiles e values one quarter and three quarters through a
set of data when arranged in ascending order.

R

Radius (plural Radii) a straight line from the centre to the
circumference of a circle or sphere
Range A measure of the spread of data. e largest value − the
smallest value.
Rate A comparison of two different quantities.
Ratio A comparison of amounts in a particular order.
Rational number A number that can be expressed as a fraction
in its lowest terms.

Glossary 691

Copyright Material - Review Only - Not for Redistribution

Cambridge IGCSE Mathematics e-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersity

ReviewReciprocal e fraction obtained when the values of the Sequence A set whose elements have been listed in a particular
numerator and denominator are interchanged. (See also order, with some connection between the elements.
Reviewhyperbola.)
Set A list or collection of objects that share a characteristic.
ReviewRecurring decimals A decimal that continues forever, repeating
itself at regular intervals. Set builder notation A means of describing the elements of a set
without having to write them all down.
Reflection A transformation that creates an image by reflecting
points in a given line. Similar Plane objects that have the same shape and proportion
but are different in size.
Reflex An angle greater than 180° but less than 360°.
Simple interest Interest that is calculated only on the original
Region A region in a plane that satisfies a set linear amount borrowed or invested.
inequalities.
Simplest Form An equivalent fraction where the numerator and
Relative frequency e experimental probability of an event denominator are the smallest allowable whole numbers. Also
happening. called lowest terms.

Reverse percentage Finding the original value of an item before Simultaneous At the same time (or in the same position).
a percentage change has been applied.
Sine ratio For a given angle (other than the right-angle)
Right-angle An angle that is exactly 90°. in a right-angled triangle, the sine ratio is the length of the
side opposite to the angle divided by the hypotenuse of
Rotation A transformation that creates an image by rotating the triangle.
points by a given angle about a fixed point.
Sine rule In any triangle, the ratio of the sine of an angle to the
Rotational symmetry Symmetry by turning a shape about a length of the side opposite the angle is always the same.
fixed point so that it looks the same in different positions.
Slant Height In a cone, the slant height is the shortest
S distance from a point on the circumference of the base to
the apex.
Salary Earnings based on a fixed yearly amount, usually paid in
monthly instalments. Solid A three-dimensional object.

Sample space A list or diagram that shows the possible Solution e value obtained from solving an equation.
outcomes of two or more events.
Speed A rate that compares distance travelled in a given time.
Scalar A quantity that has size (magnitude) but not direction.
Spread A measure such as range or interquartile range.
Scale A ratio that indicates how much smaller (or larger) a
drawing is from the original object. Square e product obtained when a number is multiplied
by itself.
Scale drawing A representation of an object, either bigger or
smaller than the original, whose corresponding sides remain in Square root A number that, multiplied by itself gives a square.
the same proportion.
Standard Form A shorthand method of writing very large or
Scale factor of areas e multiplying factor for the area of a very small numbers.
shape that is enlarged from an original. ( is is the square of the
multiplying factor for sides.) Subject e variable written by itself (usually to the left of
the “=” sign).
Scale factor of lengths e multiplying factor for the sides of a
shape that is enlarged from an original. Subset A set whose elements are all also members of another
(usually larger) set.
Scale factor of volumes e multiplying factor for the volume of
a shape that is enlarged from an original. ( is is the cube of the Substitute To replace one value with another (usually a letter
multiplying factor for sides.) with a number).

Scatter diagram A diagram that plots pairs of bivariate data Substitution e replacement of a letter in a formula or
to help determine if there is any correlation between them. expression with a number.

Secondary data Data used for statistical purposes that has Subtended An angle formed at the meeting of two given lines.
not been collected by the person performing the statistical
analysis. Surface Area e total area of the faces of a three-dimensional
solid.
Sector Part of a circle defined by the angle that two radii make at
the centre of the circle. Symbol A short way of writing mathematical information, such
as “=” which means is equal to.
Selling price e price that a trader sells goods for.
Symmetrical A shape that has a property of symmetry.
Semi-circle Half of a circle.
Symmetry Having the same shape in different positions either
through reflection in a line or rotation about a point.

692 Glossary

Copyright Material - Review Only - Not for Redistribution

e-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersity Glossary

Review T U

Review Tangent A straight line that just touches a curve at Union A set that contains all the elements of two or more sets
one point. but without any repeats.
Unitary method A method for solving proportion problems.
Tangent ratio For a given angle (other than the right-angle) Universal set For a given problem, all the elements that could
in a right-angled triangle, the tangent ratio is the length of the possibly be included.
side opposite to the angle divided by the side adjacent to Unknown angle An angle whose value is to be calculated.
the angle. Unknown side A side whose length is to be calculated.
Upper bound e largest value that a number (given to a
Tax threshold e amount of money that can be earned before specified accuracy) could be.
any tax becomes payable. Upper quartile e value of data at the 75th percentile.

Term Part of an expression or the individual numbers, letters, V
objects etc in a sequence.
Variable A letter in a formula or equation that can have
Terminating decimals A decimal that does not continue different values.
forever. Vector A quantity that has direction as well as size.
Venn diagram A pictorial method for illustrating the elements
Term-to-term rule e rule that tells you how to generate the and interconnections of sets.
next term in a sequence. Vertically opposite A pair of equal angles formed when two
straight lines cross.
Theoretical probability e chance of an event happening, Vertices e points where two or more edges of a plane
calculated if it is known that the possible outcomes are equally shape meet.
likely. Volume e amount of space contained inside a solid object.
Vulgar Fraction Another name for “common” fractions that
Transformation A change in the position of a point or line have a numerator and denominator.
following a given rule.
W
Translation A transformation that creates an image of a point
by “sliding” it along a plane. Wages Pay based on the number of hours worked, usually
paid weekly.
Trend e general direction of the line of best fit for
bivariate data.

Trial An “experiment” to determine the value of an
outcome.

Triangle A polygon with three sides.

Turning point A point on a graph where it changes direction.
Usually a maximum or minimum point.

Two-way table A table that summarises the data from two or
more sets of data.

Review

Glossary 693

Copyright Material - Review Only - Not for Redistribution

Cambridge IGCSE Mathematics e-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersity

ReviewIndex obtuse, 47 C
and parallel lines, 53–54
Review2-D shapes, 135–148 reflex, 47 calculator use, 17–18
3-D objects, 148–150 right, 47, 227 inverse functions, 346, 349
Review3-D trigonometry, 375–377 round a point, 51 setting in degrees mode, 340
straight, 47 for sine and cosine ratios, 349
A subtended, 472 standard form calculations,
supplementary, 51 118–119
acceleration, 522–524 triangle theorems, 55–56 for tangent ratios, 342
acute angles, 47 vertically opposite, 51
addition apex, 154 capacity, units of, 283
arc of a circle, 145, 472 Cartesian plane see regions
algebraic fractions, 329–330 area, 134
fractions, 105–106 circles, 140, 141–142 in a plane
of like terms, 29–30 sector of a circle, 145 categorical data, 74
of vectors, 576 of similar shapes, 237–239 centre of rotation, 463
adjacent side, 341 units of, 136, 283 charts, 86
algebra, 23 average(s), 254–255
indices, 35–43 average speed, 515–516 see also graphs
simplifying expressions, axis of symmetry, 416, 466 bar charts, 89–92
choosing, 96–97
29–32 B histograms, 485–492
substitution, 26–28 pictograms, 86–88
working with brackets, 33–35 bar charts, 89–92 pie charts, 92–95
writing expressions, 24–26 base, 35 chord of a circle, 64
algebraic fractions, 326–331 bearings, 339–340 and symmetry, 467–468
alternate angles, 54 bias, 162 circles, 64–65, 140
angle sum binomials, squaring, 219 arcs and sectors, 145–148
of a polygon, 62–63 bisection area, 141–145
of a quadrilateral, 60–61 angles, 65–66 circumference, 140
of a triangle, 57 lines, 65 radius, 64
angles, 46–47 bivariate data, 384–390 symmetry in, 467–470
see also trigonometry BODMAS, 15 theorems, 470–474
acute, 47 borrowing & investing, 401 circumference, 140
alternate, 54 class intervals, 485
bisecting, 65–66 compound interest, 405–407 equal, 485–488
circle theorems, 472–475 hire purchase, 403–404 unequal, 488–492
co-interior, 54 simple interest, 401–402 co-interior angles, 54
complementary, 51 boundaries, rules about, 316–317 coefficient, 29
corresponding, 53, 232 brackets, 15–16 collection of data, 74, 75–76
of depression, 337–338 expansion of, 123–125, column vectors, 557
drawing, 50 combined events, 596, 597
of elevation, 337–338 216–217 probability of, 598–599
exterior, 62 multiplying out, 215 commission, 395
finding unknown, 52–53 working with, 33–35 common denominator, 105,
included, 246 buying and selling, 409–413
interior, 62 310, 329
measuring, 47–49

694 Index

Copyright Material - Review Only - Not for Redistribution

e-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersity Index

Review common factor, 128 currency conversions, 294–297 divisibility tests, 10
compasses (pair of), using, 65–66 curves division
Review complement of a set, 187
complementary angles, 51 cumulative frequency, 494–498 algebraic fractions, 328–329
Review completed square form, quadratics, cyclic quadrilaterals, 473 in expressions, 31–32
cylinder, surface area & volume, fractions, 106–107
331
composite functions, 549–550 151–152 E
composite numbers, 6
compound bar charts, 91 D earnings, 395
compound interest, 405–407 calculations of, 396–398
conditional probability, data, 74 deductions from, 398–401
collection methods, 75–76
604–605 displaying using charts, 86–97 elements of a set, 185
cones, surface area & volume, 154 organisation of, 76–86 elimination method, simultaneous
congruence, 244–247 types of, 74–75
constant term, 207, 216 equations, 306–307
constraints, 301, 319 decagon, 61 empty set, 186
constructions, 65–67 deceleration, 522 enlargement, 557, 566–568
continuous data, 75, 262, 485 decimals equal vectors, 574
conversion equations, 24
converting percentages to,
currency, 297 109–110 cubic, 432
graphs, 294–296 exponential, 42, 437
metric system units, 283 fractions with, 107–108 functions, 536–542
correlation, 383–385 irrational numbers, 182 linear, 125–127
corresponding angles, 53, 232 recurring, 182 quadratic, 222–223, 322–324,
corresponding sides, 231–232 rounding, 18–19
cosine ratio, 349 terminating, 182 416–418
cosine rule, 368–369 deductions, 398 reciprocal, 424
combining with sine rule, 369–370 denominator, 103 setting up to solve problems,
cost price, 409 dependent variable, 384
calculating, 410–411 diagrams 537–539
percentage profit & loss, 410 possibility, 165–167 simultaneous linear, 303–310,
cube of a number, 10 scatter, 384–387
cube roots, 10–11 tree, 597–603 429–431
cubic curves Venn, 189–191 solving higher order, 434–435
plotting, 432–434 diameter, 64 straight line, 200–202,
solving higher order equations, difference between two squares,
207–211
434–435 221–222 equidistant, 467
cubic equations, 432 direct proportion, 525–526 equilateral triangle, 56
cuboids equivalent form, percentages,
in algebraic terms, 528–529
nets, 149–150 directed numbers, 13 109–110
plane of symmetry, 464 equivalent fractions, 103–104
surface area & volume, 150–151 comparing and ordering, 14 equivalent ratios, 509–510
cumulative frequency, 492 discount, 412–413 estimated mean, 263
curves, 494–498 discrete data, 75, 262 estimation, 119–120
percentiles, 500–501 distance-time graphs, 517–520 events, 161
quartiles, 498–500 Distance-Time-Speed triangle,
tables, 492–493 combined, 596, 597, 598–599
515–516 independent & mutually exclusive,
distance travelled
167–168, 597
Distance-Time-Speed triangle, not happening, probability
515–516
of, 164
speed-time graphs, 522–524 exact form answers, 355
exchange rate, 297

Index 695

Copyright Material - Review Only - Not for Redistribution

Cambridge IGCSE Mathematics e-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersity

Reviewexpansion ratios written as, 507 grouped frequency tables, 79–80, 486
of brackets, 124–123 standard form, 114–119 grouping symbols, 15
Review of double brackets, 216–217 frequency, 485
of expressions, 33–35 frequency density, 488–489 H
Review frequency tables, 78–80
experimental probability, 161 averages & ranges, 258–260 HCF (highest common factor), 6, 9
exponent, 35 cumulative, 492–493 heptagon, 61
exponential equations, 42, 437 functions, 546 hexagon, 61
exponential graphs, 437–439 composite, 549–550 highest common factor (HCF), 6
exponential notation, 114–119 inverse, 550–552
expressions, algebraic, 24 notation, 546–547 using prime factors to find, 9
hire purchase, 403–404
expanding, 33–35 G histograms, 485
factorising, 128–129
simplifying, 29–33 geometrical drawings, 65–70 equal class intervals, 485–488
substituting values in, 26–28 gradient, 202–206 unequal class intervals, 488–492
writing, 24–26 horizontal lines, 202–203
exterior angles, polygons, 62–63 of a curve, 441–443 hyperbolas, 424–426
extrapolation, 388 in distance-time graphs, 519 hypotenuse, 212, 341
extreme values, 255–256 in speed-time graphs, 522
graphical solutions I
F higher order equations, 434–435
to quadratic equations, 428–430 image, 558
face (of a solid), 150 to simultaneous equations, imperial measurements, 294
factorisation, 128–129 303–305 included angle, 246
to simultaneous linear & included side, 246
quadratic expressions, 219–221, independent events, 167–169, 597
324–326 non-linear equations, 429–431 index/indices, 25
graphs
factors, 5–6 fractional, 41–43
divisibility tests, 10 see also charts laws of, 37–39
prime factors, 8–9 choosing most appropriate, 96–97 negative, 39–40
using to solve quadratic equations, conversion, 294–296 notation, 35–36
222–223 cubic, 432–435 inequalities
of directly proportional linear programming, 319–321
favourable combinations, 598 in one variable: linear, 310–314
favourable outcomes, 162–163 relationships, 525 in two variables: regions on a
FOIL (First, Outside, Inside, Last), 217 distance-time, 517–521
foreign currency, 297– of equations with combinations of plane, 314–319
formulae, 23, 536 integers, 2
terms, 435–437 intercepts, x and y, 212–213
cosine rule, 368 exponential, 437–439 interest, 401
quadratic, 322–323 kinematic, 517–524
sine rule, 364–365 line graphs, 95 compound, 405–407
transformation of, 129–131, quadratic, 416–420 simple, 401–403
reciprocal, 424–426 interest rate, 401
543–546 recognising which to draw, 440 interior angles, polygons, 62
fraction bars, 15 scatter diagrams, 383–386 interquartile range, 265–267, 498,
fractional indices, 41–43 speed-time, 522–524
fractions, 101 straight-line, 200–216 499–500
greatest and least values, 319–321 intersection
algebraic, 326–331 gross income, 398
equivalent, 103–104 grouped data, 262, 485 of two lines, 303, 429–431
estimation, 119–120 of two sets, 188
operations of, 104–108 inverse functions, 550–552
percentages, 109–114 calculator use, 346, 349

696 Index

Copyright Material - Review Only - Not for Redistribution

e-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersity Index

Review inverse proportion, 527–528 M negative indices, 39–40
in algebraic terms, 529–530 negative sign, directed
Review magnitude, vectors, 570, 579
investment, 401–406 mark up (of cost price), 410 numbers, 13
Review irrational numbers, 140, 182–185 mass, units of, 283 negatives in inequalities, 313
irregular polygons, 64 maximum, 416 net income, 398
isosceles triangles, 55 mean, 254 nets of solids, 148–149
no correlation, 384, 385
K estimated, 263, 264–265 non-unit fractions, indices with, 42
frequency table data, 261 nonagon, 61
kinematic graphs, 517 grouped data, 262–265 ‘nose to tail’ rule, vectors, 576, 577
distance-time, 517–522 measurement, 282 notation
speed-time, 522–524 conversion graphs, 294–296
money, 297 functions, 546–547
kite, 60, 135 time, 285–289 indices, 35–36
units, 283–285 vectors, 571
L upper and lower bounds, 289–294 nth term, 175–176
median, 255 number lines, 310–311
laws of indices, 37–39 estimating, 493–494 numbers, 2
LCM (lowest common multiple), frequency table data, directed numbers, 13–14
factors, 5–6
4–5, 9 261–262, 492 irrational, 182
length, units of, 283 median class, grouped data, 263 linking with symbols, 3
letters, representing unknown metric measurements, 283 multiples, 3–5
midpoint of a line segment, 215–216 order of operations, 15–18
values, 24–26 minimum, 416 powers and roots, 10–12
‘like terms’, 29–30 mixed numbers, 104 prime factors, 8–9
line of best fit, 385–386 modal class, 263, 486 prime numbers, 6–8
line graphs, 95 mode, 254 rational, 182–185
line segment, 214 rounding, 18–19
frequency table data, 261 numerator, 103
length of, 214 money management, 394 numerical data, 75
midpoint of, 215
line symmetry, 461–463 borrowing and investment, O
circles, 467 401–406
linear equations, 125–127 object, 557
linear inequalities, 310 buying and selling, 409–413 obtuse angles, 47, 56
number lines, 310–311 currency conversions, 294–295 octagons, 61
solving algebraically, earning money, 395–400 ogives, 494
multiples, 3–5 operations, order of, 15–18
312–314 multiplication opposite side, 341
linear programming, 319–321 algebraic fractions, 328–329 order of operations, 15–18
lines, 46 in expressions, 31–32 order of rotational symmetry, 463
fractions, 104 organisation of data, 76
see also straight lines of vector by a scalar, 574–576
bisecting, 65 multiplying out brackets, 215 frequency tables, 78–80
constructing, 65–66 mutually exclusive events, 167–168, tally tables, 76–78
graphs, 95 two-way tables, 83–86
parallel, 46 597 outcomes, probability, 162
perpendicular, 46 tree diagrams, 597–598
loss, 409 N
lower bound, 289–294
lower quartile, 265–266 natural numbers, 2
lowest common multiple (LCM), 4–5 negative correlation, 384, 385
using prime factors to find, 9
lowest terms, 103

Index 697

Copyright Material - Review Only - Not for Redistribution

Cambridge IGCSE Mathematics e-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersity

ReviewP principal, 401 quantitative data, 75
prisms, surface area & volume, quartiles, 265–267, 498–500
Reviewpair of compasses, using, 65–66
parabolas, 416–420 151–152 R
Reviewparallel lines, 46 probability, 161
radius, 64
and angles, 53–55 calculating from tree diagrams, range, 258–259
parallelograms, 59 598–603
estimated, 262, 263
area and perimeter, 135 combined events, 597, 598–599 grouped continuous data, 262–265
patterns, generating sequences from, conditional, 604–605 interquartile, 265–267, 498–499
of event not happening, 164 rates, 506–507
179–181 experimental, 161 ratio method, 511
pentagons, 61 independent events, 167–169, rational numbers, 182–186
per annum, meaning of, 401 ratios, 506, 507
percentage increases/decreases, 597 dividing quantities into, 510–511
mutually exclusive events, equivalent, 509–510
111–112 expressing in form of 1:n or n:1, 512
percentage loss, 410 167–168, 597 increasing/decreasing quantities,
percentage profit, 410 possibility diagrams, 165–166
percentages, 109–114 theoretical, 162–164 532
percentiles, 265, 500–501 probability scale, 161 and scale, 512–516
perimeter, 134 profit, 409 and similar shapes, 236–244
projection, 375–376 trigonometric, 336–349
of a sector, 145 proportion writing in simplest form, 507–508
circumference, 140 direct, 525–526, 528–529 reciprocal, 40, 106
polygons, 135 inverse, 527–528, 529 reciprocal equations, 424
periodicity, 366 unitary method, 526 reciprocal graphs, 424–426
perpendicular bisector, 67, 467 protractors, using, 47–50 rectangle, 59
perpendicular lines, 46 pyramids, surface area & area & perimeter, 135
pi (π), 140 recurring decimals, 182–186, 355
pictograms, 86–88 volume, 154 reflection, 557, 558–561
pie charts, 92–95 Pythagoras’ theorem, 227–230 reflex angles, 47
plane symmetry, 464–465 applications of, 230–231 regions in a plane, 314–315
plotting a straight line, 200–202 greatest & least values, 319–321
points, 46 Q rules about boundaries, 316–317
polygons, 61–63 regular polygons, 61, 135
area & perimeter, 135–140 quadrant of a circle, 145 reverse percentages, 113–114
symmetry in, 462, 463–464 quadratic equations, 222 revolution, 47
positive correlation, 384, 385, 387 rhombus, 60
position vectors, 580 using factors to solve, 222–223 area & perimeter, 135
possibility diagrams, 165–167 using quadratic formula to solve, right angle, 47, 227
possible outcomes, 597 circle theorems, 472–473
powers, 11–12 322–324 right-angled triangles, 56, 226
see also index/indices quadratic expressions, 216–217 checking for, 228–230
raising, 38 finding unknown side using tan,
symbol for, 15 completing the square, 321–322
zero, 38 difference between two squares, 342–346
primary data, 75 investigation, 341–342
prime factors, 8–9 221–222 labels for sides, 341
prime numbers, 2 factorising, 219–221, 324–326 Pythagoras’ theorem, 227
finding, 6–8 squaring a binomial, 219
quadratic formula, 322–324
quadratic graphs, 416–420
quadrilaterals, 59–61
area of, 135
cyclic, 473
qualitative data, 74

698 Index

Copyright Material - Review Only - Not for Redistribution

e-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersity Index

Review roots, 11–12 shapes difference between two, 221
sign for, 15 circles, 64–65, 140–144 formulae containing, 544
Review perimeters & areas, 135–148 squares (shape), 59
rotation, 557, 561–563 polygons, 61–64, 135–140 area & perimeter, 135
Review rotational symmetry, 463 quadrilaterals, 59–61 constructing, 68
similar, 236–237 standard form, 114–119
centre of, 463 transformation of, 556–570 statistical investigation, 74
circles, 467 triangles, 55–59 straight angles, 47
order of, 463 straight lines
three dimensions, 466 similar shapes, 236–237 equation of, 207–211
two dimensions, 463–464 similar solids, 240–241 gradient of, 202–206
rounded measurements, similar triangles, 231–235 length of segment, 214
simple interest, 401–403 midpoint of segment, 215
289–291 simplest form, 103 plotting, 200–202
rounding of numbers, 18–19 simplifying expressions, 29–32 x and y intercepts, 212–213
rulers, using, 65–66 subject of a formula, 129, 543
algebraic fractions, 326–328 changing, 129–130, 543–544
S simultaneous, 303 subsets, 188–189
simultaneous inequalities, 318–323 substitution, 24
salary, 395 simultaneous linear equations simultaneous equations, 305
sample space, 597 of values in formula, 26–28,
scalars, 570 algebraic solution, 305–307
scale, 512–513 graphical solution, 303–305 544
manipulation, 307209 subtended angle, 472
drawings, 336–338 sine ratio, 349 subtraction
problems, solving, 513–515 sine rule, 364–365
scale drawings, 336–338 ambiguous case of, 365–366 algebraic fractions, 329–330
scale factor, 237 combining with cosine rule, fractions, 105–106
of areas, 237, 240 of like terms, 29–30
of enlargement, 566 369–37-0 of vectors, 577–578
of lengths, 240 slant height, 154 supplementary angles, 51
of volumes, 240 solids (3-D objects), 148 surds, 355
scalene triangles, 55 surface area, 150
scatter diagrams, 384–387 nets of, 148–149 cones, 154
secondary data, 75 similar, 240–243 cuboids, 150–151
sectors of a circle, 145–146 surface area & volume, 150–157 cylinders, 151–152
segments of a circle, 64 symmetry in, 464–466 prisms, 151
angle theorem, 472 solution, 126 pyramids, 154
selling and buying, 409–413 speed of similar solids, 240
selling price, 409 calculating average, 515–516 spheres, 155
calculating, 410 in distance-time graphs, 519–520 symbols
semi-circle, 64, 145 speed-time graphs, 522–524 grouping, 15
90 degree angle in, 460 spheres using to link numbers, 3
sequences, 175–180 planes of symmetry, 464 symmetry, 459
set builder notation, 192–193 surface area & volume, 155 properties of circles, 467–470
sets, 185–186 spread see range in three dimensions (solids),
complement of, 187 square of a binomial, 219
set builder notation, 192–193 square of a number, 10 464–466
subsets, 188–189 square roots, 10 in two dimensional shapes,
unions & intersections, 188 formulae containing, 544
universal, 187 square(s), power, 10 461–464
Venn diagrams, 189–190 of binomials, 219

Index 699

Copyright Material - Review Only - Not for Redistribution

Cambridge IGCSE Mathematics e-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersitCyoPprye-ssC-aRmebrviidegweCUonipvyersity

ReviewT tree diagrams universal set, 187
probability calculations from, upper bound, 289–294
Reviewtables 598–603 upper quartile, 265–266
cumulative frequency, 492–493 using to show outcomes, 597–598
frequency, 78–80, 258–260 V
tally, 76–78 trends, 385
two-way, 83–86 trials, probability, 161 variables, 24, 129
triangles, 55–59 vectors, 570–582
tally tables, 76–78 velocity, 520
tangent ratio, 342 see also right-angled triangles Venn diagrams, 189–191
area & perimeter, 135 vertical lines, 202–203
calculating angles, 346–349 area using trigonometry, 372–374 vertically opposite angles, 51
finding unknown side, 342–346 congruent, 244–247 vertices, 149
tangent to a curve, 441–443 constructing, 66–67 volume, 150
and symmetry of circles, 467, 468 labelling of sides and angles, 364
tax threshold, 400 similar, 231–235 cones, 154, 278
terminating decimals, 182 trigonometry, 340–342 cuboids, 150–151
terms, 24, 174 sine and cosine ratios, cylinders, 151–152
in a sequence, 175–176 prisms, 151–152
theoretical probability, 162–164 349–355 pyramids, 154
three-dimensional objects, 148–150, solving problems using, of similar solids, 240
spheres, 155
240–244 355–358 units of, 283
symmetry of, 464–466 tangent ratio, 342–349 vulgar fractions, 103
time calculations, 285–289 in three dimensions, 375–377
trading, 409–413 trinomials, 326 W
transformations, 558 turning point, 416
combining, 584–585 two-dimensional shapes, 135–148 wages, 395
enlargement, 566–568 symmetry of, 461–464
reflection, 558–561 two-way tables, 83–86 X
rotation, 561–563
simple plane, 557–559 U x-intercept, 212–213
translation, 564–566
translation, 558, 564–566 union of two sets, 188 Y
using vectors to describe, 572–574 unitary method, 510, 526
trapezium, 60 units, 283–285 y-intercept, 207–210
area & perimeter, 135
of area, 136 Z
speed-time graphs, 523–524
zero power, 38

Review

700 Index

Copyright Material - Review Only - Not for Redistribution

Review Review Review
e-ssC-amRebvriidegweCUonpivyersiCtyoPprye-ssC-amRebvriidegweCUonpivyersiCtyoPprye-ssC-amRebvriidegweCUonpivyersiCtyoPprye-ssC-amRebvriidegweCUonpivyersity
Copyright Material - Review Only - Not for Redistribution

Review Review Review
e-ssC-amRebvriidegweCUonpivyersiCtyoPprye-ssC-amRebvriidegweCUonpivyersiCtyoPprye-ssC-amRebvriidegweCUonpivyersiCtyoPprye-ssC-amRebvriidegweCUonpivyersity
Copyright Material - Review Only - Not for Redistribution

Review Review Review
e-ssC-amRebvriidegweCUonpivyersiCtyoPprye-ssC-amRebvriidegweCUonpivyersiCtyoPprye-ssC-amRebvriidegweCUonpivyersiCtyoPprye-ssC-amRebvriidegweCUonpivyersity
Copyright Material - Review Only - Not for Redistribution

Review Review Review
e-ssC-amRebvriidegweCUonpivyersiCtyoPprye-ssC-amRebvriidegweCUonpivyersiCtyoPprye-ssC-amRebvriidegweCUonpivyersiCtyoPprye-ssC-amRebvriidegweCUonpivyersity
Copyright Material - Review Only - Not for Redistribution