SHS Core Mathematics practice questions
513 questions across 18 topics of the new NaCCA curriculum, each with a written explanation.
Core Mathematics is the subject every SHS student sits, and the one where practice counts for most. Year 1 covers number sets, fractions and percentages, algebraic expressions and factorisation, linear equations, relations and functions, angles and the Pythagorean theorem, perimeter, area and volume, vectors and trigonometry, probability, and organising and presenting data. Year 2 continues with sequences and series, equations and inequalities, ratios, rates and proportions, rigid motion, surface areas and volumes, and further work with data and probability experiments.
- Year 1
- 9 topics
- Year 2
- 9 topics
- Questions
- 513
Question mix across the subject: 154 recall, 192 applying skills and concepts, 132 strategic thinking and 35 extended thinking.
Year 1 topics(9)
- Algebraic Expressions and Factorisation27 questionsNumber patterns and algebraic expressions, the four operations on algebraic expressions, factorisation, perfect squares and the difference of two squares, and operations on simple algebraic fractions.Try sample questions
- Angles & The Pythagorean Theorem27 questionsDrawing and measuring angles, parallel/perpendicular lines and transversals, the exterior angle theorem, angle sums of polygons, and identifying and applying the Pythagorean theorem to right triangles.Try sample questions
- Data Organisation, Analysis and Presentation25 questionsClassifying data (primary/secondary, qualitative/quantitative), collecting data, organising and presenting it with frequency tables and graphs, and summarising it with measures of central tendency.Try sample questions
- Fractions and Percentages27 questionsThe concept and types of fractions, operations on fractions, connections between fractions/decimals/percentages, and applying percentages to profit, loss, percentage change and simple interest.Try sample questions
- Linear Equations, Relations and Functions26 questionsChange of subject of a formula, solving linear equations and inequalities in one and two variables, relations and functions (including mappings), and the gradient, equation and distance between two points on a straight line.Try sample questions
- Number Sets27 questionsThe real number system and its subsets (natural, whole, integer, rational, irrational), the closure/commutative/associative/distributive/identity/inverse properties, and two- and three-set problems including De Morgan's law.Try sample questions
- Perimeter, Area and Volume27 questionsSI and imperial referents for measurement, and finding the perimeter and area of regular, composite and irregular 2-D shapes and the volume of prisms.Try sample questions
- Probability of Independent Events26 questionsSample spaces of simple and compound experiments, and finding and expressing the probability of two independent events as fractions, decimals, percentages or ratios.Try sample questions
- Vectors and Trigonometry25 questionsRepresenting vectors geometrically and algebraically, and the three basic trigonometric ratios (sine, cosine, tangent) of acute angles including the special angles 30°, 45° and 60°.Try sample questions
Year 2 topics(9)
- Data Collection, Organisation and Representation35 questionsDesigning data collection instruments (questionnaires, interview and observation guides, surveys), representing data with cumulative frequency curves (ogives), waffle charts and box plots, and analysing it with measures of dispersion.Try sample questions
- Equations and Inequalities25 questionsSolving simultaneous linear equations in two variables using the elimination, substitution and graphical methods, and applying them to real-life problems.Try sample questions
- Number Sets (Advanced)34 questionsSurds (pure, mixed, compound), rationalisation, the laws of indices and logarithms, and modular arithmetic, with their applications in banking, population growth and calendar/duty-roster systems.Try sample questions
- Patterns and Relations Involving Sequences and Series34 questionsArithmetic and geometric sequences and series, their nth terms and sums, and patterns and relationships between them.Try sample questions
- Ratios, Rates and Proportions35 questionsProportional reasoning involving ratios, rates and direct/inverse proportion, applied to real-life problems such as speed, density and scale.Try sample questions
- Rigid Motion27 questionsTranslation, reflection, rotation and enlargement of shapes on the Cartesian plane, and their properties and real-world applications.Try sample questions
- Surface Areas and Volumes29 questionsFinding the surface area and volume of prisms, pyramids, cylinders, cones and spheres, and solving real-world measurement problems involving them.Try sample questions
- Vectors and Trigonometry (Advanced)29 questionsPosition vectors, vector addition/subtraction/scalar multiplication, resultant vectors via the cosine rule, inverse trigonometric ratios, and angles of elevation and depression.Try sample questions
- Working with Data & Probability Experiments28 questionsAdvanced statistical and probability reasoning, including probability experiments and their application to real-life decision-making.Try sample questions
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