AI for Multidisciplinary Professionals

Simplify a numerical or algebraic expression using the positive-index laws.

Simplify an expression containing zero or negative indices.

Interpret and simplify an expression containing fractional indices.

Convert an ordinary number to and from standard form.

Perform arithmetic calculations with numbers written in standard form.

Round a quantity to a specified number of decimal places or significant figures.

Estimate a calculation by rounding its inputs to convenient values.

Evaluate the reasonableness of a numerical answer using sign, magnitude, units, and an estimate.

Simplify a ratio containing integers, fractions, or decimals.

Divide a quantity into parts according to a stated ratio.

Find an unknown quantity in an equivalent-ratio problem.

Solve a direct-proportion problem by determining the constant of proportionality.

Solve an inverse-proportion problem by determining the constant of proportionality.

Express one quantity as a percentage of another.

Calculate the result of a percentage increase or decrease.

Recover an original quantity using a reverse percentage.

Calculate an average rate from a change in quantity and elapsed time.

Calculate average speed from distance and time.

Convert a rate between compatible systems of units.

Use compound units to solve a contextual problem.

Interpret a linear scale on a map or drawing.

Apply an area scale factor to similar maps or drawings.

Calculate compound growth or depreciation over repeated periods.

Solve a multistep financial problem involving interest, instalments, taxation, or currency conversion.

Identify terms, coefficients, constants, and factors in an algebraic expression.

Translate a verbal statement into an algebraic expression.

Evaluate an algebraic expression by substituting signed or fractional values.

Evaluate a multivariable formula with consistent units.

Collect like terms in a linear algebraic expression.

Simplify an expression containing nested brackets.

Derive an algebraic expression for the nth term of a numerical pattern.

Test an nth-term expression against multiple terms of its sequence.

Expand a single bracket by applying the distributive law.

Expand the product of two linear expressions.

Apply the identities for a perfect square and a difference of two squares.

Factorise an expression by extracting its greatest common algebraic factor.

Factorise an expression by grouping pairs of terms.

Factorise a difference of two squares.

Factorise a monic quadratic trinomial.

Factorise a non-monic quadratic trinomial.

Rearrange a formula by reversing a single sequence of operations.

Change the subject of a multivariable formula.

Solve a linear equation with the variable on one side.

Solve a linear equation with the variable on both sides.

Solve a fractional equation that reduces to a linear equation.

Form and solve a linear equation from a contextual problem.

Solve a linear inequality in one variable.

Represent and interpret an inequality solution on a number line.

Solve simultaneous linear equations by substitution.

Solve simultaneous linear equations by elimination.

Find the intersection of two straight-line graphs.

Form simultaneous equations from a contextual problem.

Represent a relationship using ordered pairs, a table, and a Cartesian graph.

Calculate the gradient of a straight line from two points.

Determine the equation of a straight line from its gradient and one point.

Interpret a line’s gradient and intercept in a contextual model.

Determine unknown angles using facts about points, straight lines, and vertically opposite angles.

Determine unknown angles formed by parallel lines and a transversal.

Use the angle sum of a triangle to justify an unknown angle.

Calculate interior and exterior angles of a convex polygon.

Classify a quadrilateral from its side, angle, diagonal, and symmetry properties.

Construct a perpendicular bisector or angle bisector using geometrical instruments.

Construct a triangle or simple polygon from specified measurements.

Write a deductive geometric argument in which every conclusion has a stated reason.

Determine whether two triangles are congruent using a valid congruence test.

Determine whether two triangles are similar using angle or side relationships.

Calculate an unknown length using the linear scale factor of similar figures.

Relate a linear scale factor to the area ratio of similar figures.

Relate a linear scale factor to the volume ratio of similar solids.

Calculate the perimeter or area of a composite plane figure.

Use Pythagoras’ theorem to calculate a missing side or test for a right triangle.

Calculate an unknown side or angle in a right triangle using sine, cosine, or tangent.

Classify a variable as categorical, discrete, or continuous.

Organise raw observations into a frequency table.

Interpret data presented in tables and common statistical diagrams.

Construct a bar graph, pie chart, line graph, dot diagram, or stem-and-leaf diagram for suitable data.

Select an appropriate statistical display for a stated analytical purpose.

Calculate and interpret the mean, median, and mode of ungrouped data.

Calculate range and interquartile range from an ordered dataset.

Identify how sampling or display choices can produce a misleading conclusion.

Express set membership and subset relationships using standard notation.

Calculate unions, intersections, and complements of two sets.

Represent a two-set classification problem using a Venn diagram.

Construct a complete sample space using an organised list, table, or possibility diagram.

Calculate the probability of a single event from equally likely outcomes.

Calculate the probability of a simple combined event from a possibility diagram.

Apply the addition rule to mutually exclusive events.

Apply the multiplication rule to independent events.