Assessment and exam practice.

Try this with Essential Mathematics

1. Check the task format, time limit and permitted materials with your school.
2. Start with one timed section or task and record where you spent the most time.
3. Review errors before attempting another section. Separate missing knowledge from timing problems.

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Practice paper focus areas

• Exam 1 — Simpson's rule for an irregular dam surface, including the zero offsets at each end; Right-angled trigonometry for the rise and rafter length of a roof truss; Stratified sampling of a workplace and the explanation of one source of bias
• Exam 2 — Surface area and paint quantity for a cylindrical water tank; Cosine rule applied to a non-right-angled paddock boundary; Stem-and-leaf comparison of two sets of delivery times
• Exam 3 — Composite perimeter and fencing cost for an L-shaped block; Volume, capacity and density of a delivered load of garden soil; Systematic sampling on a production line and the coverage error it can hide
• Exam 4 — Sine rule for a surveyed triangular allotment; Sector area and arc length for a curved garden edge; Self-selected online survey and non-response error
• Exam 5 — Angle of depression from a crane jib to a load on the ground; Surface area and volume of a silo with a conical top using supplied formulae; Census versus sample: cost, time and the quality of the estimate
• Exam 6 — Simpson's rule where the offsets include a zero at one end only; Mass and density of a steel plate and the number of transport loads; Sample size and how closely the sample mean tracks the population mean
• Exam 7 — Pythagoras in three dimensions for a diagonal brace; Area of a composite tiled floor with an allowance for wastage; Measurement error introduced by a poorly calibrated instrument
• Exam 8 — Trapezium approximation compared with Simpson's rule for a block of land; Capacity of a rainwater tank expressed in litres and in kilolitres; Simple random sampling using a random number generator
• Exam 9 — Converting between square metres, hectares and acres; Cosine rule used to find an obtuse angle in a kite frame; Survey question wording and the bias it introduces
• Exam 10 — Arc length and perimeter of a running track with semicircular ends; Surface area of a sphere and of a hemisphere using the supplied formulae; Stratified sample proportions across year levels in a school
• Exam 11 — Angle of elevation to the top of a communications tower; Volume of a triangular prism roof space and its capacity; Combining two samples and the resulting change in the sample mean
• Exam 12 — Estimating an irregular area by decomposition into simple shapes; Density used to find the mass of gravel for a trailer load; Advantages and disadvantages of the four sampling methods
• Exam 13 — Perimeter of a composite shape with a semicircular end; Practical bearing problem solved with the sine rule without the ambiguous case; Non-response error in a postal survey
• Exam 14 — Surface area to be painted on a cylinder that is partly unpainted; Converting cubic centimetres to millilitres for a moulded product; Identifying the dependent and the independent variable in a study
• Exam 15 — Pythagoras and trigonometry combined in an access ramp design; Simpson's rule applied to a swimming-pool surface; Sampling error and how it differs from measurement error
• Exam 16 — Area of a parallelogram and a trapezium in a frame design; Capacity of a cylindrical vat and the number of fills it allows; Designing a survey so that coverage error is avoided
• Exam 17 — Angle between two rafters found with the cosine rule; Surface area of a square-based pyramid using the supplied formula; Choosing a sampling method for a business with distinct departments
• Exam 18 — Composite area with a circular cut-out removed; Mass, volume and density of a concrete footing; Interpreting a stratified calculation that does not give a whole number
• Exam 19 — Finding a diameter by reversing the circumference formula from a measured perimeter; Volume of a composite solid made of a prism and a half-cylinder; Explaining the impact of a biased sample on the conclusion drawn
• Exam 20 — Trigonometric ratios used to find a missing angle in a truss; Area of an irregular garden bed from offsets at equal spacing; Comparing consistency between two years of sales data