Year 10 Mathematics Advanced

TERM 3, 2025

Equations B

Students will solve monic quadratic equations by factorisation. They will solve simple cubic equations and solve linear inequalities, including graphing their solution on a number line.

Equations C

Students will learn to solve complex linear equations including those involving algebraic fractions. They will solve quadratic equations using factorisation, completing the square and the quadratic formula and verify solutions using substitution. Following this they will learn to solve quadratic equations arising from substitution into existing formulas and solve word problems involving quadratic equations. Finally, students will be shown how to solve equations reducible to quadratics, how to rearrange literal equations to change the subject and solve linear simultaneous equations both algebraically and graphically, analysing the results contextually.

Non-Linear Relationships B

Students will learn how to graph parabolas, identify their representative equations and translate parabolas vertically whilst identify their representative equations. They will graph exponential curves and identify their representative equations, describe the properties of simple exponential curves and identify their representative equations. Following this students will identify and match the equations with the graphs of both linear and non-linear relationships. Finally, student will learn how to identify and match the equations with the graphs of both linear and non-linear relationships and to solve a pair of simultaneous equations involving one non-linear equation using graphing applications.

Non-Linear Relationships C

Students will graph parabolas and describe their features and transformations. They will graph exponentials, hyperbolas and circles, whilst being able to describe their features and transformations. Following this they will learn to distinguish between different types of graphs by examining their algebraic and graphical representations and solve problems. Finally, students will learn to graph and compare polynomial curves and describe their features and transformations.

Indices B

Students will apply index laws to manipulate algebraic expressions involving negative-integer indices. They will also apply index laws to simplify algebraic products and quotients involving negative-integer indices.

Indices C

Students will define and describe real, rational and irrational numbers, convert between a recurring decimal and its fractional form and identify and apply surd notation. They will then expand and simplify expressions with surds using arithmetic operations and rationalise denominators of expressions involving surds. By the end of the topic students will also learn to identify, describe and apply the relationship between surd notation and fractional indices, and evaluate numerical expressions with fractional indices and surds using digital tools.