# 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) = αx
^{2}+ 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

a^{2}= b^{2}+ c^{2}– 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 x
^{2}test for independence: formulation of null and alternative hypotheses; significance levels; contingency tables; expected frequencies; use of the formula

X calc^{2}=; 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)=ax^{n}f'(x) = anx^{n-1}

f"(x) = an(n-1) x^{n-2} - The derivative of functions of the form

f(x) = ax^{n}+ 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