Year 10 Mathematics

Revisiting fundamental algebraic concepts including operations with variables and basic equation solving.

Applying the distributive law to expand products of binomials and trinomials, including perfect squares.

Identifying and extracting common factors from algebraic expressions and applying grouping techniques.

Mastering techniques for factorizing quadratic expressions of the form ax^2 + bx + c.

Recognizing and factorizing expressions using the difference of two squares and perfect square identities.

Solving single and multi-step linear equations, including those with variables on both sides.

Applying the null factor law to solve quadratic equations after factorization.

Using the quadratic formula to find solutions for any quadratic equation, including those not easily factorized.

Solving linear inequalities and representing their solutions on a number line.

Representing the solution sets of linear inequalities as regions on a coordinate plane.

Solving systems of two linear equations using the substitution method.

Revisiting angle relationships formed by parallel lines and transversals.

Using formal logic and known geometric properties to prove congruency in triangles (SSS, SAS, ASA, RHS).

Proving similarity in triangles using angle-angle (AA), side-side-side (SSS), and side-angle-side (SAS) ratios.

Applying Pythagoras' theorem to find unknown sides in right-angled triangles and solve 2D problems.

Defining sine, cosine, and tangent ratios and using them to find unknown sides in right-angled triangles.

Using inverse trigonometric functions to calculate unknown angles in right-angled triangles.

Solving practical problems involving angles of elevation and depression.

Applying trigonometry to solve navigation problems using true and compass bearings.

Extending Pythagoras' theorem to solve problems in three-dimensional figures.

Applying 2D trigonometric skills to solve problems involving heights and distances in three-dimensional models.

Using the Sine Rule to find unknown sides and angles in non-right-angled triangles.

Using coordinates to calculate the distance between two points on the Cartesian plane.

Calculating the midpoint of a line segment given the coordinates of its endpoints.

Calculating the gradient of a line from two points, an equation, or a graph.

Deriving and using various forms of linear equations (gradient-intercept, point-gradient, general form).

Identifying and constructing equations for parallel and perpendicular lines.

Sketching parabolas by identifying key features: intercepts, turning points, and axis of symmetry.

Investigating the effects of translations, reflections, and dilations on the graph of y = x^2.

Finding the roots of quadratic equations by interpreting the x-intercepts of their graphs.

Investigating the standard equation of a circle centered at the origin and at (h,k).

Sketching circles on the Cartesian plane from their equations and identifying key features.

Exploring the characteristics of exponential growth and decay functions.

Revisiting fundamental concepts of probability, sample space, and events.

Organizing data in two-way tables to calculate probabilities of events.

Representing events and their relationships using Venn diagrams and set notation.

Calculating probabilities of events using the addition and multiplication rules.

Using tree diagrams to list sample spaces and calculate probabilities for events with and without replacement.

Exploring how the occurrence of one event affects the probability of another event.

Determining if two events are independent using probability calculations.

Solving complex probability problems from various real-world scenarios.

Understanding different methods of data collection and sampling techniques.

Classifying data as categorical or numerical, and discrete or continuous.

Creating and interpreting various graphical displays for single variable data (histograms, dot plots, stem-and-leaf plots).

Constructing and interpreting box plots from a five-number summary to visualize data distribution.

Using visual displays and summary statistics to compare two or more data sets.

Examining the relationship between two numerical variables and identifying trends.

Understanding the difference between correlation and causation in bivariate data.

Drawing and using lines of best fit to make predictions and interpret relationships.

Using technology to find the equation of the least squares regression line.

Designing and conducting a statistical investigation, from formulating questions to presenting findings.

Calculating the surface area of various prisms and cylinders.

Calculating the volume of various prisms and cylinders.

Calculating the surface area and volume of pyramids and cones.

Calculating simple interest for investments and loans.

Modeling the growth of investments and the cost of loans over time using compound interest formulas.

Solving practical financial problems involving loans, annuities, and investments.

Using scientific notation and index laws to handle very large and very small numbers accurately.