Student Workbook – Revision Guide e –books

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Each one of the eight (8) workbooks contain a Revision Guide and Exam style questions (Paper 1 and Paper 2) for reinforcement of concepts learned. It supplement textbooks and teaching notes.

Workbook - Revision Guide 1

Number and algebra

• Number systems
• Approximation: decimal places; significant figures.
• Percentage errors
• Estimation
• Expressing numbers in scientific notation
• SI (Système International) and other basic units of measurement
• Arithmetic Sequences and Series
• Geometric Sequences and Series
• Quadratic equations, factorization

Workbook Revision Guide 2

LOGIC

• Venn diagrams
• Compound statements: implication; equivalence ; negation ; conjunction ;
• disjunction ; exclusive disjunction .
• Translation between verbal statements, symbolic form and Venn diagrams.
• Truth tables
• concepts of logical contradiction and tautology.
• Definition of implication: converse; inverse; contrapositive.
• Logical equivalence.

Workbook Revision Guide 3

PROBABILITY

• Probability of an event
  P(A)=
• Probability of a complementary event,
  P(A')=1-P(A)
• Venn diagrams; tree diagrams; tables of outcomes. Solution of problems using "with replacement" and "without replacement".
• Combined events:
  P(A B)=P(A) + P(B) - P(A B)
• Mutually exclusive events:
  P(A B)=P(A) + P(B)
• Independent events:
  P(A B)=P(A) P(B)
• Conditional probability:
  P(A|B)=

Workbook Revision Guide 4

FUNCTIONS

• Domain and range. Mapping diagrams.
• Linear functions and their graphs, for example,
  f: xmx + c
• The graph of the quadratic function: f(x) = αx² + bx +c
• Properties of symmetry; vertex; intercepts.
• The exponential expression:
  α^b; b
• Graphs and properties of exponential functions
  f(x)=a^x;, f(x)=a^λx;
  f(x)=ka^λx + c; k, a, c, λ
• Growth and decay; basic concepts of asymptotic behaviour.
• Graphs and properties of the sine and cosine functions:
  f(x)=a sin bx + c;
  f(x)=a cos bx + c; a, b, c
• Amplitude and period.
• Accurate graph drawing.
• Use of a GDC to sketch and analyse some simple, unfamiliar functions.
• Use of a GDC to solve equations involving simple combinations of some simple, unfamiliar functions.

Workbook Revision Guide 5

GEOMETRY AND TRIGONOMETRY

• Coordinates in two dimensions: points; lines; midpoints.
• Distances between points.
• Equation of a line in two dimensions:
  the forms y = mx + c
  & ax + by + d =0
• Gradient; intercepts. Points of intersection of lines; parallel lines; perpendicular lines.
• Right-angled trigonometry. Use of the ratios of sine, cosine and tangent.
• The sine rule:
  ==
• The cosine rule
  a² = b² + c² – 2bc cos A;
  cosA=
• Area of a triangle:
  ab sinC
• Construction of labelled diagrams from verbal statements.
• Geometry of three-dimensional shapes: cuboid; prism; pyramid; cylinder; sphere; hemisphere; cone.
• Lengths of lines joining vertices with vertices, vertices with midpoints and midpoints with midpoints; sizes of angles between two lines and between lines and planes.

Workbook Revision Guide 6

STATISTICS

• Classification of data as discrete or continuous.
• Simple discrete data: frequency tables; frequency polygons.
• Grouped discrete or continuous data: frequency tables; mid-interval values; upper and lower boundaries.
• Frequency histograms.
• Stem and leaf diagrams (stem plots).
• Cumulative frequency tables for grouped discrete data and for grouped continuous data; cumulative frequency curves.
• Box and whisker plots (box plots).
• Percentiles; quartiles.
• Measures of central tendency.
• For simple discrete data: mean; median; mode.
• For grouped discrete and continuous data: approximate mean; modal group; 50^th percentile.
• Measures of dispersion: range; interquartile range; standard deviation.
• Scatter diagrams; line of best fit, by eye, passing through the mean point.
• Bivariate data: the concept of correlation.
• Pearson’s product–moment correlation coefficient:use of the formula
  r=
• Interpretation of positive, zero and negative correlations.
• The regression line for y on x: use of the formula
  y -=
• Use of the regression line for prediction purposes.
• The x² test for independence: formulation of null and alternative hypotheses; significance levels; contingency tables; expected frequencies; use of the formula
  X calc²=; degrees of freedom; use of tables for critical values; p-values.

Workbook Revision Guide 7

CALCULUS

• Gradient of the line through two points. Tangent to a curve.
• The principle that
  f(x)=axⁿ f'(x) = anx^n-1
  f"(x) = an(n-1) x^n-2
• The derivative of functions of the form
  f(x) = axⁿ + bx^n-1 + ..., n
• Gradients of curves for given values of x.
• Values of x where f' (x) is given.
• Equation of the tangent at a given point.
• Increasing and decreasing functions.
• Graphical interpretation of
  f' (x) >0, f' (x) = 0, f' (x) < 0
• Values of x where the gradient of a curve is 0 (zero): solution of
  f'(x) = 0
• Local maximum and minimum points

Workbook Revision Guide 8

Financial Mathematics

• Currency conversions.
• Simple interest: use of the formula
  I = where C = capital, r = % rate, n = number of time periods, I = interest
• Compound interest: use of the formula
  I = C x (1 + )ⁿ - C
• Depreciation.
• Construction and use of tables: loan and repayment schemes; investment and saving schemes; inflation.

DEMO SOON