IB Mathematics: Solving, Factoring, and Graphing Techniques

Find the value of an expression

Using appropriate numerical or algebraic methods, typically requires exact form or simplified rational/surd result.

Solve

Find all possible solutions of an equation or inequality, showing all stages of reasoning. Solutions may be exact (with surds or algebraic expressions) or approximate when specified.

Factorise

Express an algebraic expression as a product of simpler expressions. In IB, this includes use of factor theorem, grouping, difference of squares, etc.

Roots (of an equation)

The values of the variable for which the equation equals zero, expressed as exact values, whether rational, surd, or complex.

Sketch

Draw a graph showing the general shape and key features such as intercepts, asymptotes, turning points - without using a calculator.

Plot

Mark given points accurately on coordinate axes using specified scale, usually followed by 'join with a smooth curve where appropriate.'

Make A the subject of …

Rearrange the given formula to isolate A on one side, leaving A = …. This tests algebraic manipulation skills.

Index form

Express numbers or expressions in the form a^n, where a is the base and n is the index (exponent). Important for applying the laws of exponents.

Surd

An expression involving a root that cannot be simplified to a rational number. IB prefers exact forms (e.g. √2) and rationalising denominators.

y-intercept

The value of y where the graph crosses the y-axis (x = 0), often identified in the form y = mx + c → intercept = c.

Intersection

The point(s) where two graphs meet. In coordinate geometry, these are the simultaneous solutions to the equations of the two graphs.

Bisect

Divide a line segment or angle into two equal parts. In constructions or geometric proofs, this means each resulting part is congruent.