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Student Workbook – Revision Guide e –books


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:
    αb; b
  • Graphs and properties of exponential functions
    f(x)=ax;, f(x)=aλx;
    f(x)=kaλx + 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; 50th 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) = anxn-1
    f"(x) = an(n-1) xn-2
  • The derivative of functions of the form
    f(x) = axn + bxn-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