National certificate mathematics /
Abbott P.
National certificate mathematics / P. Abbott and H. Marshall - London : The english universities press, 1960. - xii, 380 p. : ill. ; 20 cm. - The technical college series .
Content
INDICES AND LOGARITHMS
The index notation
Laws of indices
Fractional and negative indices
Meaning of a logarithm
Laws of logarithms
LOGARITHMS TO OTHER BASES THAN
Meaning
General relation between logarithms of a number to two different bases
Naperian logarithms
Relation to common logarithms
QUADRATIC EQUATIONS
Methods of solution
Imaginary roots
Simultaneous quadratics
MENSURATION 1
Areas of plane rectilinear figures
Formula for area of triangle
Regular polygons
Irregular rectilinear figures
Areas of irregular curved figures by trapezoidal, mid-ordinate and simpson's rules
Volumes of irregular solids
MENSURATION II
The circle
Intersecting chords and their properties
Area of sector and of segment
Angular velocity
MENSURATION III
Area and volume of prism and cylinder
Volume of frustum
Area and volume of pyramid and cone
Area and volume of frustum
Area and volume of sphere
PROGRESSIONS
Meaning of a series
Arithmetic series
Geometric series
Sum of n terms
Approach to infinity
Sum to infinity
THE TRIGONOMETRICAL RATIOS
Sines of angles up to 360
Negative angles
The sine graph
Cosines of angles up to 360
The cosine graph
Tangents of angles up to 360
Well-known identities
Trigonometrical functions
SOLUTION OF TRIANGLES
Sine rule
The ambiguous case
Cosine rule
THE ADDITION FORMULA
Expansions of sin (A +B), cos (A+B)
Ratios of multiple and sub-multiple angles
Trigonometrical equations
THE PLOTTING OF MORE DIFFICULT GRAPHS
Recapitulation of previous work
Graphs of cubic expressions
Alternative methods
The graphs of y = x(x-a) (x-b), y= ax3 + bx2 + cx +d
The graphs of y=3.5x2.8, y=3
DETERMINATION OF LAWS
The linear law
Laws other than linear and their reduction to a straight line
THE BINOMIAL THEOREM
Meaning of binomial expression
Simple expansions of (a + b)
Expansion of (a + b)n
FUNCTIONS-RATE OF INCREASE - DIFFERENTIATION
Meaning of function
Dependent and independent variables
Functional notation
Gradient and slope
Gradient of straight line
Gradient of a curve
Velocity at a point
Differentiation from first principles
Differential coefficient
Differentiation of simple functions
Differentiation of y = axn
Differentiation of a sum
Velocity and acceleration by differentiation
MAXIMA AND MINIMA
The sign of the differential coefficient
Stationary values
Turning points
Maximum and minimum points
Application to practical problems
Include Bibliography and index
340048077
Mathematics
510 / ABB
National certificate mathematics / P. Abbott and H. Marshall - London : The english universities press, 1960. - xii, 380 p. : ill. ; 20 cm. - The technical college series .
Content
INDICES AND LOGARITHMS
The index notation
Laws of indices
Fractional and negative indices
Meaning of a logarithm
Laws of logarithms
LOGARITHMS TO OTHER BASES THAN
Meaning
General relation between logarithms of a number to two different bases
Naperian logarithms
Relation to common logarithms
QUADRATIC EQUATIONS
Methods of solution
Imaginary roots
Simultaneous quadratics
MENSURATION 1
Areas of plane rectilinear figures
Formula for area of triangle
Regular polygons
Irregular rectilinear figures
Areas of irregular curved figures by trapezoidal, mid-ordinate and simpson's rules
Volumes of irregular solids
MENSURATION II
The circle
Intersecting chords and their properties
Area of sector and of segment
Angular velocity
MENSURATION III
Area and volume of prism and cylinder
Volume of frustum
Area and volume of pyramid and cone
Area and volume of frustum
Area and volume of sphere
PROGRESSIONS
Meaning of a series
Arithmetic series
Geometric series
Sum of n terms
Approach to infinity
Sum to infinity
THE TRIGONOMETRICAL RATIOS
Sines of angles up to 360
Negative angles
The sine graph
Cosines of angles up to 360
The cosine graph
Tangents of angles up to 360
Well-known identities
Trigonometrical functions
SOLUTION OF TRIANGLES
Sine rule
The ambiguous case
Cosine rule
THE ADDITION FORMULA
Expansions of sin (A +B), cos (A+B)
Ratios of multiple and sub-multiple angles
Trigonometrical equations
THE PLOTTING OF MORE DIFFICULT GRAPHS
Recapitulation of previous work
Graphs of cubic expressions
Alternative methods
The graphs of y = x(x-a) (x-b), y= ax3 + bx2 + cx +d
The graphs of y=3.5x2.8, y=3
DETERMINATION OF LAWS
The linear law
Laws other than linear and their reduction to a straight line
THE BINOMIAL THEOREM
Meaning of binomial expression
Simple expansions of (a + b)
Expansion of (a + b)n
FUNCTIONS-RATE OF INCREASE - DIFFERENTIATION
Meaning of function
Dependent and independent variables
Functional notation
Gradient and slope
Gradient of straight line
Gradient of a curve
Velocity at a point
Differentiation from first principles
Differential coefficient
Differentiation of simple functions
Differentiation of y = axn
Differentiation of a sum
Velocity and acceleration by differentiation
MAXIMA AND MINIMA
The sign of the differential coefficient
Stationary values
Turning points
Maximum and minimum points
Application to practical problems
Include Bibliography and index
340048077
Mathematics
510 / ABB