BSEH Secondary Mathematics - Basic study plan

Classify polynomials by degree and number of terms, and evaluate them at given values without a calculator.

Solve linear equations in one variable, including those with fractional coefficients and parentheses, and check each solution by substitution.

Graph linear equations in two variables by building a table of at least three ordered pairs and verifying the line passes through them.

Convert between the standard form and slope-intercept form of a line, and read off slope and intercepts from each.

Solve pairs of linear equations in two variables by substitution and by elimination, and decide which method is faster for a given system.

Set up and solve at least five word problems (age, digit, fraction, work, and mixture types) as systems of two equations.

Factor quadratic expressions by splitting the middle term, and state the conditions under which the method applies.

Solve quadratic equations by factorization, completing the square, and the quadratic formula, and confirm all three give the same roots.

Compute the discriminant of a quadratic and use its sign to classify roots as real and distinct, real and equal, or not real.

Derive the relationship between roots and coefficients (sum and product) and use it to build an equation from given roots.

Generate the first five terms of an arithmetic progression from a first term and common difference, and find the nth term using the general formula.

Derive and apply the sum formula for the first n terms of an arithmetic progression, including problems asking for a specific term count.

Solve word problems where the unknown is the number of terms, the common difference, or a sum.

Prove that the square root of a prime number is irrational using the contradiction method, and reproduce the proof unaided.

Convert terminating and repeating decimals into fractions in lowest terms, and identify which rational numbers have terminating decimal expansions.

Place irrational numbers on the number line using geometric construction, and compare two surds without a calculator.

Plot points in all four quadrants, compute the distance between two points, and find the coordinates of a point dividing a segment in a given ratio.

State and apply the basic proportionality theorem and its converse to find unknown lengths in divided triangles.

Identify similar triangles using the AA, SSS, and SAS similarity criteria, and write the correspondence of vertices correctly.

Use the ratio of areas of similar triangles to solve problems relating side ratios to area ratios.

Apply the Pythagorean theorem and its converse, and use the result on the relationship between the sides and altitude of a right triangle.

Apply the tangent-radius perpendicularity result, the equal-tangent-lengths result, and the angle in a semicircle result to find unknown angles.

State and use the alternate segment theorem and the cyclic quadrilateral angle result in multi-step angle chases.

Construct a tangent to a circle from an external point and bisect a given angle and segment using ruler and compass only, writing the construction steps.

Compute the six trigonometric ratios for 0, 30, 45, 60, and 90 degrees from memory and evaluate compound expressions using them.

Prove simple trigonometric identities by converting everything to sine and cosine.

Solve height-and-distance problems involving one and two angles of elevation or depression, drawing the diagram before computing.

Compute the surface area and volume of combinations of solids such as a cone on a cylinder or a hemisphere on a cylinder.

Convert between units consistently and handle problems where a solid is melted and recast into another shape using volume conservation.

Find the area of a sector and the length of an arc given a central angle, and use these in composite figure problems.

Compute mean, median, and mode for grouped data, including the median and mode from a cumulative frequency table.

Draw a cumulative frequency curve and read the median from it, and convert a frequency table into a histogram.

Compute classical probability for single and two-stage experiments, including dice, cards, and balls from a bag.

Full-length mock paper under exam timing, then classify every error by domain and by error type (concept, calculation, misreading).