Millions saw the apple fall, but Newton asked why.
To escape the earth's gravitational pull, a rocket has to produce 3.5 million kilograms of thrust!Find out more
Maths is sometimes called the science of patterns.
The Fibonacci Spiral gets wider by a factor of φ for every quarter turn it makes.Find out more
Sometimes the questions are complicated, and the answers are simple.
Kevin's Classroom will teach you the recipes required to solve any problem!Find out more
We provide in depth video tutoring for Grade 10, 11, 12, and University students in the following subjects:
Once students have mastered the basic foundation tools of maths, they then need to learn to recognize which of these tools to use for each sum.
Mathematics is like a language: First we learn to make words and spell them, then we learn grammar and how to put those words together correctly. In maths we do the same: spelling and vocabulary are the different branches of maths, and grammar is the rules we apply to those branches of maths.
The reason that many people cannot communicate as well mathematically as they can in their language is that we are exposed to language from birth and practise it everyday, but we do not do this with math! It is my belief that we should encourage our children to use maths from a very early age. Measuring, counting, drawing shapes, using rulers and tape measures and blocks and all of the things that kids used to play with before electronics took over. Seeing a shape on screen is not the same as holding it in your own hands.
Number systems, algebraic expressions, squaring binomials, products resulting in difference of two squares, product of a trinomial and a binomial, products resulting in sum or difference of two cubes, factorisation, grouping, the difference of 2 squares, perfect square trinomials, factorising trinomials, sum or difference of 2 cubes, simplifying algebraic fractions using factors, multiplication and division of fractions, addition and subtraction of fractions, exponential notation, laws of exponents, rational exponents, negative exponents, exponential equations, linear equations, equations with fractions, literal equations (changing the subject of the formula) quadratic equations with one unknown, simultaneous linear equations, linear inequalities.
Patterns and sequences, patterns with a linear general term, arithmetic sequences, number patterns.
The relationship between two variables, domain and range, function notation, functions and graphs, sketch graphs, restricted domains, finding the equations of straight lines, investigating functions, average gradient, the effect of translations on the graph,sketch graphs, determining the equation of the graph, trigonometric functions, trigonometric graphs.
Mathematical modelling (word sums)
What is trigonometry, notation and terminology, naming the sides of triagnles, trigonometric ratios, calculations in trigonometry, finding the ratio given the angle, finding the angle given the ratio, reciprocals of trigonometric ratios, solving right angled triangles, the cartesian plane, negative angles, special angles, trigonometric graphs, angles of elevation and depression, bearings.
The distance between 2 points, the coordinates of the midpoints of a line segment, the gradient of a line, volumes and surface areas of polyhedrons.
Intersecting and parallel lines, polygons, triangles, quadrilaterals, paralellograms, rectangles, squares, rhombuses, kites, midpoint theorem, proofs requiring construction, equivalent statements volume and surface areas of solids which are not polyhedrons, spheres and hemispheres, multiplying one or more dimensions by a factor k.
Simple and compound Interest, the simple interest formula, calculating interest rates, loan repayments, inflation, population growth, exchange rates, time lines.
Outcomes and Events, compound events, sample spaces, events, intersection and union of sets, calculating probabilities, mutually exclusive and complementary events.
Finding average measures of central tendency, mean, median, mode, types of data, frequency tables, grouped data, finding measures of dispersion or spread around the median, the interquartile range, box and whisker diagrams.
Algebra: equations with fractions, k-method, inequalities, complex roots, absolute values. Differentiation: Trigonometry, radian measure, functions, limit theory, differentiation. Integration: anti-differentiation, integration, the integral, Riemann sums and the definite integral, integration to find area under a curve.
Addition and subtraction of fractions, simplification of surds, simple equations involving surds, equations with rational exponents, factorising, quadratic equations, simultaneous equations, completing the square, The quadratic formula, inequalities
Linear and quadratic sequences.
Analytical formulas, the equation of a straight line, the angle of inclination of a straight line.
The parabola, the hyperbola, the exponential function, graphs, trigonometric functions
Identities, reduction formulas, trigonometric equations, sine, cosine and area rule
Lines, triangles, circles, theorems.
Appreciation and depreciation, time lines, basic interest.
Dependent and independent events, Venn diagrams, tree diagrams, contingency tables.
Histograms and frequency polygons, ogives, variance and standard deviation, symmetrical and skewed data.
Algebra: fractions, factorising cubics, partial fractions, polynomial inequalities, completing the square and quadratic formula, complex numbers.
Polynomials, polynomial division, the remainder theorem, the factor theorem, solving third degree equations.
Sequences, arithmetic sequences, geometric sequences, series, geometric series, sigma notations, infinite geometric series, sum to infinity of a geometric series.
Functions, domain and range, inverse of a function, exponential functions and their graph, logarithmic functions, simple logarithmic equations, laws of logarithms, using logarithms to solve exponential equations, the graph of logarithmic functions, Increasing and decreasing functions, concavity and points of inflection, calculations from the graphs differentiation in calculating minimum and maximum values, rates of change, calculus of motion.
General solution to equations, solving more complex trigonometric equations, angles in trigonometric identities, compund angle identities, deriving other compund angle formulae, double angle identities, using double angles to prove identities, simplifying and evaluating expressions using the compound angle and double angle identities, solving trigonometric equations using compound and double angle identities.
Circles, The equations of a circle with centre the origin and radius r, the equations of the circle with centre a;b and the radius r, the equation of a tangent to the circle.
Summary of Circle Theorems, Areas of triangles, Proportional division Theorem, Similar polygons, similar triangles, the theorem of Pythagoras, converse of theorems.
Terminology, timelines, annuities, the formula for future value annuities, loans and loan repayments using the formula for a geometric series, loans and loan repayments using present value formula, calculation time period, fixed payment loans, pyramid schemes.
Counting the different options, using the fundamental counting principal in probability problems.
Regression and correlation, bivariate data, the line of best fit, the least squares regression line.
There is a perception that physics is very complicated and that it uses advanced maths. In fact, the maths in high school physics is very basic.
Physics is the study of things around us and how the various everyday things we encounter affect us. We learn how we can understand them and use them in our best interests.
The nice thing about physics is that firstly we can actually see the effect of physics in our everyday life- things like friction, gravity and electrical circuits for example. So it comes to life if we look at each situation and ask a few simple questions…actually its all about those few questions and knowing which ones to ask!
The second nice aspect is that generally each section is independent. Therefore you can play to your strengths when writing tests and exams. So if mechanics is your strong point you can be assured of a good score there.
Vectors and scalars, motion in one dimension, reference frame and position, distance and displacement, speed, velocity and acceleration, motion graphs, energy.
Transverse pulses on a string or spring, superposition of pulses, wave properties, wave period and frequency, wave speed, longitudinal waves, amplitude, wavelength, frequency, period and wave speed, transverse waves, sound, pitch, loudness and quality of sound, ultrasound, electromagnetic radiation, the electromagnetic spectrum, the photon.
Magnetism, electrostatics,electric circuits, magnets, charge, potential difference and EMF, current, resistance, resistors in series, resistors in parallel, measurement of voltage and current.
Vectors in two dimensions, the resultant of vectors, the resolution of a vector into 2 perpendicular components, Newton’s Laws and the application of Newton’s Laws, Newton’s law of Universal Gravitation, different kinds of forces, force diagrams and free-body diagrams, the relationship between force and acceleration.
Geometrical optics, reflection and refraction, Snell’s Law, critical angles, total internal reflection, two dimensional and three dimensional wave fronts.
Electrostatics, Coulomb’s Law, electric field, electromagnetism, magnetic field associated with current carrying wires, electric circuits, Ohm’s law, electrical energy.
Newton’s equations of motion, Newtons second law, conservation of momentum, impulse, vertical projectile motion in one dimension, work, energy and power, work-energy theorem, conservation of energy, graphs of displacement vs time, velocity vs time and acceleration vs time, , the photo-electric effect, the cut-off frequency, dual nature of light, work function, emission and absorption spectra.
The Doppler effect, the Doppler equation, the Doppler effect and light, applications of the Doppler effect , the photo-electric effect, the cut-off frequency, dual nature of light, work function, emission and absorption spectra.
Electric circuits, internal resistance, power in electric circuits, series and parallel, resistors, Ohms Law, electrodynamics, AC and DC, electric motors, electrical machines
I see chemistry as being similar to cooking: you take ingredients, mix them together and either heat them or cool them to end up with a new product.
Insert a chemistry blurb here --
Classification of matter, states of matter and Kinetic Molecular Theory, The atom, Atomic Mass and diameter, relative atomic mass, structure of the atom, isotopes, electron configuration, The Periodic Table, Chemical bonding, particles making up substances, homogenous and heterogenous mixtures, conductors and insulators, magnetic and non magnetic materials, elements and compounds, names and formulae of substances
Physical and chemical change, representing chemical change, reactions in aqueous solutions, quantitive aspects of chemical change, chemical bonding, valence electrons and electron dot diagrams, atoms and compounds, conservation of atom and mass, balanced chemical equations, law of constant composition, ions in aqueous solutions, electrolytes and extent of ionization as measured by conductivity, atomic mass and mole concept, molecular and formula masses, determining of composition and substance, molar volume of gases, concentration of solutions, basic stoichiometric calculations.
Atomic combinations, molecular structure, chemical bonds, molecular shape, valence pair shell electron pair repulsion theory, electro negativity, polarity, bond energy, bond length, inter molecular forces, the effect of inter molecular forces on physical properties, the chemistry of water, ideal gases and thermal properties, kinetic theory of gases and motion of particles, Boyle’s Law, the general gas equation , ideal gases vs real gases.
Quantitative aspects of chemical change, molar volume of gases, concentration of solutions, stoichiometric calculations, volume relationships in gaseous reactions, energy and chemical change, energy changes in reactions related to bond energy changes, exothermic and endothermic reactions, activation energy, types of reactions, acid-base reactions, Redox reactions, oxidation numbers.
Organic molecules, formulae and functional groups, homologous series, plastics and polymers, addition, reactions, substitution, IUPAC naming, Isomersion, physical properties, elimination, optical phenomena and properties of materials
Rate and extent of reaction, factors, mechanisms of reaction, Kc, Measuring rates of reaction, mechanisms of catalysis, Le Chateliers principal, chemical equilibrium, acids and bases, Acid and Base reactions, Kw, Titrations, Hydrolysis, electro chemical reactions, Oxidation numbers, standard electrode potential, galvanic cells, standard reduction potentials, Chemical Industry