Mathematics 4024 Quick Revision Notes — every chapter

1

Arithematics

Types of number · Order of operations and negative numbers · Fractions · Decimals and ordering · Halfway values and differences · Recurring decimals to fractions

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2

Indices

The laws of indices · Zero, negative and fractional powers · Indices in algebra · Equations with the unknown in the power

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3

Standard Form

What standard form is · Ordering numbers in standard form · Calculating without a calculator · Using a calculator and real problems

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4

Significant Figures

Rounding to decimal places · Rounding to significant figures · Estimating a calculation · Choosing a sensible accuracy

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5

Functions

Function notation · Inverse functions · Composite functions · Domain, range and asymptotes

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6

Factorization

Common factors · Difference of two squares · Quadratics x² + bx + c · Quadratics ax² + bx + c · Four terms: grouping · Solving by factorising

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7

Statistics

Averages and range · Grouped data · Charts and diagrams · Histograms · Cumulative frequency, quartiles and IQR · Scatter diagrams

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8

2D Trigonometry

Pythagoras' theorem · Sin, cos and tan (SOH CAH TOA) · Elevation, depression and bearings · Sine rule and cosine rule · Area of any triangle

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9

Mensuration

Units · Area and perimeter of 2D shapes · Circles, arcs, sectors and segments · Prisms, cuboids and cylinders · Pyramids, cones and spheres · Working backwards

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10

Time

12- and 24-hour clocks · Time intervals and decimal hours · Timetables and time zones

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11

Kinematics

Speed, distance and time · Distance–time graphs · Speed–time graphs · Conversion graphs and rates

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12

Circles

Circle words · Right angles in circles · Angles at the centre and circumference · Alternate segment theorem · Writing reasons

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13

Simultaneous

Elimination · Substitution · Forming simultaneous equations · One linear and one non-linear equation

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14

Co-Ordinate Geometry

Coordinates and straight-line graphs · Gradient · Length and midpoint · The equation y = mx + c · Parallel and perpendicular lines

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15

Number Sequences

Term-to-term rules · Linear sequences: the nth term · Special sequences · Quadratic sequences · Cubic and exponential sequences · Patterns of shapes

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16

Graphical Solutions

Solving equations from a graph · Finding the line to draw · Simultaneous equations on a graph · Gradient of a curve

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17

Linear Inequalities And Shading

Symbols and number lines · Solving inequalities · Regions on a graph

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18

Symmetry

Line symmetry · Rotational symmetry · Symmetry of triangles and quadrilaterals · Symmetry in solids

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19

Polygons

Basic angle facts · Angles and parallel lines · Angles in polygons · Giving reasons

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20

Daily Maths

Percentages · Reverse percentages · Simple and compound interest · Ratio and proportion · Rates, currency and units · Pie charts

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21

Proportionality

Direct proportion · Inverse proportion · The effect of a change

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22

Limits Of Accuracy

Bounds of a rounded value · Bounds of calculations · Giving an answer to a suitable accuracy

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23

Hcf Lcm

Prime factorisation · HCF and LCM · Word problems · Square roots, cube roots and the smallest n

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24

Graphs Of Functions

Shapes of graphs · Tables of values and plotting · Key features · Reading from a graph

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25

Algebra

Expressions and substitution · Expanding brackets · Solving linear equations · Forming expressions and equations · Changing the subject · Algebraic fractions · Quadratic equations

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