YAKILI | upper sixth pure Mathematics with statistics

Course / Course Details

upper sixth pure Mathematics with statistics

Uppersixth Arts

By - High School Mathematics
0 students
166 Hours 40 Min
(0)

Course Curriculum

16 chapters
268 lectures
134 quizzes
166 Hours 40 Min total length

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1 Introduction to circle theorems.m4v

5 Min

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3 Introduction to circle theorems.m4v [Quiz]

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4 Introduction to Circles and Parts of Circles.m4v

5 Min

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6 Introduction to Circles and Parts of Circles.m4v [Quiz]

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7 The Circumference of a Circle

5 Min

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9 The Circumference of a Circle_1 edited.m4v [Quiz]

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10 Equations of the circle - Given centre and radius

5 Min

11 Given coordinates of the ends of a diameter

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13 Passing through three given points.

5 Min

14 Intersection of a straight line with a circle

5 Min

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16 Equation of a tangent to a circle

5 Min

17 Length of a tangent from external point to a circle

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19 Intersecting circles

5 Min

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21 Condition for two circles to touch

5 Min

22 Orthogonal circles

5 Min

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24 Radical axis of two circles.

5 Min

25 The equation of a circle through the points of intersection of two given circles and a given point

5 Min

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1 Introduction to the Complex Number System

5 Min

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3 The imaginary number i and its algebra

5 Min

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5 Complex Numbers

5 Min

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7 Complex conjugate

5 Min

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9 The Argand Diagram

5 Min

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11 Geometrical representation of a complex numbers

5 Min

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13 Addition and subtraction of complex numbers

5 Min

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15 Product and Quotient of Complex Numbers

5 Min

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17 Multiplication and Division in Polar form

5 Min

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19 simple equations and expansions

5 Min

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21 Modulus-Argument (Polar) form of a complex Number

5 Min

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23 Modulus and Argument of a Complex Number.

5 Min

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25 Complex roots of a polynomial equation

5 Min

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27 Square root of complex Numbers:

5 Min

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29 Equality of Complex Numbers

5 Min

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31 Geometrical representation of sums, products and quotients of complex numbers

5 Min

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33 The nth roots of unity -Cube roots of a complex number

5 Min

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1 Subtraction of Vectors.m4v

5 Min

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3 Subtraction of Vectors [Quiz]

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4 Multiplication of a vector by a matrix

5 Min

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6 Multiplication of a vector by a matrix [Quiz]

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7 The unit vector in the direction of a given vector.m4v

5 Min

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9 The unit vector in the direction of a given vector.m4v [Quiz]

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10 Equations of planes

5 Min

11 Different forms of the equation of a plane

5 Min

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13 Lines and planes

5 Min

14 Intersection of a line and a plane

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16 Angle between two planes

5 Min

17 Intersection of two planes

5 Min

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19 Perpendicular distance of a point from a plane

5 Min

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1 Definite integral

5 Min

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3 Simple applications of integration to calculate:  area of plane  volumes of solids of revolution,  centroidsand centres of mass

5 Min

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5 Approximations to definite integrals using the trapezium rule

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1 Solution of simple first order differential equations (involving polynomial, trigonometric, exponential and logarithmic functions) with variables that can be separated

5 Min

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1 Determination of an interval

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3 Graphical method of solving equations

5 Min

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5 The Newton - Raphson process

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7 Any other iterative process, including the interval bisection or midpoint method and the method of Linear interpolation or Chord method.

5 Min

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1 Types of data.

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3 Tabular and graphical representation of data

5 Min

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5 Measure of central tendency

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7 Measure of dispersion

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9 Combined mean and combined variance for two or more samples

5 Min

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11 Weighted means (e.g. index numbers)

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1 Scatter diagram

5 Min

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3 Regression function *Linear correlation and regression lines

5 Min

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5 Least square regression lines

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7 covariance

5 Min

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9 Regression coefficient

5 Min

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11 calculating the equation of the least square regression lines

5 Min

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13 The product –moment correlation coefficient, r

5 Min

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15 Relationship between regression coefficient and r

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17 Minimum sum of squares of residuals

5 Min

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19 Spearman’s coefficient of Rank correlation and its significance and limitations

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21 Kendall’s Rank correlation coefficient, its use and limitations

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1 Probability terminology

5 Min

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3 Empirical or experimental method of obtaining probabilities (tossing coins and dice, drawing cards...).

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5 Possibility space and probability space for such experiments

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7 Classical definition of probability

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9 Probability of an event

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11 Probability laws - Limit law (probability scale)

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13 Complementary events

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15 The occurrence of only one of two events

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17 Mutually exclusive events

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19 Exhaustive events

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21 Conditional probability

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23 Independent events and their applications

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25 Probability Trees

5 Min

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27 Use of permutations and combinations to calculate probability Bayes’ theorem

5 Min

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1 Elementary notions of discrete probability distributions.

5 Min

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3 The probability mass function (p.m.f) or probability density function (p.d.f) and the probability distribution.

5 Min

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5 The expectation of a random variable E(X)

5 Min

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7 The expectation of any function of X, E[g(x)]

5 Min

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9 The properties of the expectation.

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11 The variance Var(X) of X and its properties

5 Min

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13 The cumulative distribution function of a discrete random variable

5 Min

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15 The mode and median of a discrete random variable

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17 Moment generating functions

5 Min

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1 The binomial distribution -mean and variance

5 Min

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3 cumulative binomial probability tables

5 Min

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5 The recurrence formula and calculation of the mode

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7 The uniform distribution and derivation of its expectation and variance

5 Min

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9 The geometric distribution

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11 mean and variance

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13 The Poisson distribution

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15 mean and variance

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17 Unit interval

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19 use of the poisson distribution as an approximation of the binomial distribution

5 Min

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21 cumulative Poisson probability table

5 Min

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23 Distribution of two independent Poisson variables

5 Min

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25 Relationship between probability distributions and frequency distributions

5 Min

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1 The Probability density function of a continuous random variable

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3 Expectation, variance and mode of a continuous discrete random variable

5 Min

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5 The cumulative distribution function

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7 The median and the other quartiles

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1 The exponential distribution including its mean an variance

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3 The uniform or rectangular distribution

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5 mean and variance.

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7 The normal distribution

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9 probability density function

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11 Expectation and variance

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13 The standard normal variable and the use of the standard normal table to find probabilities for normally distributed variable

5 Min

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15 The use of the normal distribution as:  an approximation of the binomial with application of continuity correction  an approximation of the Poisson distribution with the application of cont

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1 Sampling with or without replacement from a finite population

5 Min

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3 Sampling distribution of statistics

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5 Random sampling and random number tables

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7 Sampling of attributes

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9 Sampling from an infinite population

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11 The sample mean

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13 The distribution of the sample mean

5 Min

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15 The central limit theorem

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17 Sampling methods

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19 Estimation of population parameters

5 Min

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21 Point estimation-unbiased estimator

5 Min

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23 Most efficient estimator for the population parameters( mean and variance)

5 Min

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25 Pooled estimation of population mean and population variance

5 Min

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27 Interval estimation (confidence intervals)

5 Min

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29 Confidence interval for the population mean, population variance known

5 Min

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31 Confidence interval for the population mean, population variance unknown

5 Min

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33 Confidence interval for the difference between two populations.

5 Min

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1 The role of the null and alternative hypotheses in significance testing

5 Min

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3 Significance testing of a hypothetical value for probability and for the mean of Poisson distribution

5 Min

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5 Significance testing for a population mean and the difference between two means using large scale(using central limit theorem)

5 Min

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Instructor

High School Mathematics

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