High School Pure Mathematics | Grade 10 - Grade 12

Explore algebraic fractions and learn to simplify by factoring common factors and canceling terms in numerators and denominators through examples.

Explore solving for x across quadratic, linear, exponential, and surd equations, using the quadratic formula, simplifying surds, and checking solutions with worked examples.

Explore quadratic patterns by identifying second differences and deriving the general formula t_n = a n^2 + b n + c for quadratic sequences.

Identify general solutions to trigonometric equations by analyzing signs across quadrants, leveraging reference angles and the functions' periods to generate all valid x in degrees.

Learn how to simplify and add or subtract fractions in algebra, using a common denominator, with step-by-step examples.

Explore algebraic fractions and learn to simplify by factoring out common factors and canceling terms. The lecture guides you through several worked examples, illustrating factorization and cancellation to simplify expressions.

Explore analytical geometry concepts by calculating gradients, distances via the distance formula, and midpoints, then apply these to solve problems and verify right angles and equal distances.

Explore exponential functions with a financial example, identify the domain, x-intercept, y-intercept, and asymptote, and determine when the function increases.

Explore hyperbola and straight line graphs by plotting points from y = a/x + q, finding line intercepts, and locating their intersections at (2,2) and (-1,-4).

Learn the general method for sketching cubic curves, locating turning points and intercepts, and using derivatives to identify x- and y-intercepts for accurate curve sketches.

Learn to sketch a curve by identifying intercepts and turning points, then determine the point of inflection using the first and second derivatives of the function.

Learn how to use the power rule to find derivatives and apply derivative rules through concrete examples.

Learn to find derivatives from first principles using the limit as h approaches zero, with worked examples on x^2 and 2x^2-4.

Explore how angles of elevation and depression, 70° and 42°, along with a 30 m distance determine a tower’s height using a triangle and alternate angles.

Factor quadratics by the product–sum method and grouping, choosing two numbers that multiply to ac and add to b, then extract a common factor to get binomial factors.

Find the equation of a quadratic with a turning point using the form a(x-p)^2+q. Determine a from another point, then locate the x-intercepts.

Convert circle equations to standard form by completing the square, identifying the center (h, k) and radius r, and apply to examples with centers (2, 7) and (-1, 4).

Learn how to find the product of polynomials by expanding and combining like terms, using examples to illustrate the steps.

Explain the geometric sequence through example terms like 2, 6, 18, identifying the common ratio and applying the geometric sequence formula to find subsequent terms.

Apply the theorem of pythagoras and soh cahtoa to solve right triangle problems, identify opposite, adjacent, and hypotenuse, and compute missing sides from given data.

Graph the parabola defined by 2x^2 - 4, determine its y-intercept, x-intercepts (where y=0), and vertex at (0,-4) with a minimum value of -4.

Learn to plot a hyperbola and a straight-line graph, find intercepts and asymptotes, and solve for intersection points to understand their graphs.

Graph linear and quadratic functions by building data sets, finding x and y intercepts, and locating intersections on a shared graph.

Learn to graph an exponential function, identify the y-intercept and intercepts, and derive the inverse by swapping variables to obtain a logarithm base 2 of x.

Learn to analyze ungrouped data by sorting values, finding the range, and computing quartiles (Q1, median, Q3) and the interquartile range, illustrated with a box and whisker diagram.

learn to compute the mean, variance, and standard deviation from a data set using standard formulas, and apply these concepts to interpret data.

Explore computing variance and standard deviation through concrete examples, using algebraic steps, fraction simplification, and understanding numerator and denominator relationships.

Learn to convert infinite recurring decimals to fractions by letting x equal the repeating decimal, multiplying to move the repeating block, and subtracting to obtain 2/9 and 25/99.

Learn how to solve simultaneous linear equations using elimination, substitution, and equating methods, including matching coefficients, substituting values, and verifying solutions.

Master trigonometric identities through sign analysis across quadrants, learn to simplify expressions using identities, and apply these techniques to evaluate trigonometric functions.

Explore graphing hyperbolic functions by identifying asymptotes and x-intercepts through a practical example, illustrating how these functions shape their curves.

Explore exponential functions through a financial example, learning to identify y-intercepts and asymptotes, analyze domain and range, and determine when the graph increases.

Learn arithmetic sequences and the role of the common difference, determine terms, and apply linear patterns through worked examples and step-by-step reasoning.

Learn to prove trigonometric identities by simplifying the left-hand side to match the right-hand side through algebraic manipulation, using sine squared terms.

Learn simple, intelligent methods for simplifying surds by factoring out common factors, grouping terms, and applying division to simplify expressions.

Learn to solve simultaneous equations using substitution, turning the system into a quadratic, then substitute back to find x and y, with an example worked step by step.

Learn how to analyze statistics for grouped data by constructing a frequency table, calculating cumulative frequencies, and locating Q1, Q2 (the median), and Q3 within class intervals.

Learn to find mean, mode, and median for ungrouped data by arranging values and applying the formulas. The example yields mean 6, mode 3, and median 5.

Draw graphs of trigonometric functions across 0 to 360 degrees using a table of values, and analyze tangent with undefined points, asymptotes, period, and range.

Learn straight lines and gradient on a graph by using two points to find the gradient and derive the equation of the line with y = mx + c.

Discover how to find variance and standard deviation using a table, compute the mean, apply squared deviations, sum them, and derive the standard deviation.

Apply the Pythagoras theorem to triangles to find an unknown side when two sides are known, using x squared and y squared through practical examples.