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Full Grade 12 test
Full Grade 12 mathematics test with mixed topics, dynamically selected questions and a choice of duration. Practise before an assessment or review the whole course at your own pace.
Questions: 11Estimated time: 16 minutes
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Question 1out of 11
An experiment is repeated independently three times. The probability of event A on each trial is 80%. Find the probability that A occurs on all three trials, as a decimal.
Multiply probabilities for independent events occurring together. Convert percentages to decimals first: P(A and B) = (a/100)(b/100). Three independent repeated occurrences have probability (p/100)³.
Question 2out of 11
For acute α with sin α = 0.30, approximate cos α.
Use the fundamental trigonometric identity:
sin² α + cos² α = 1.
- Move sin² α to the other side: cos² α = 1 − sin² α.
- Take the square root: cos α = √(1 − sin² α).
- Because α is acute, its cosine is positive, so use the positive square root.
- Round the result in the same way as the answer choices.
Question 3out of 11
A cone has radius 7 cm and slant height 19 cm. Using π ≈ 3.14, find lateral area.
Cone lateral area is S = πrl, where l is the slant height. Do not add the base area πr² because only lateral area is requested.
Question 4out of 11
What can be stated if f′(a) = 0?
The derivative f′(a) is the instantaneous rate of change and tangent slope. Tangent equation: y − f(a) = f′(a)(x − a). Find f(a) and f′(a) separately. If f′(a) = 0, the tangent is horizontal, but an extremum is not guaranteed.
Question 5out of 11
Independent events A and B have probabilities 40% and 50%. Find P(A and B) as a decimal.
Multiply probabilities for independent events occurring together. Convert percentages to decimals first: P(A and B) = (a/100)(b/100). Three independent repeated occurrences have probability (p/100)³.
Question 6out of 11
A sphere is cut through its centre. The section-circle radius is 7 cm. Find the area of its circumscribed square.
A square circumscribed about the circular section has side length 2r. Its area is S = (2r)² = 4r².
Question 7out of 11
Which formula describes the tangent line at x = a?
The derivative f′(a) is the instantaneous rate of change and tangent slope. Tangent equation: y − f(a) = f′(a)(x − a). Find f(a) and f′(a) separately. If f′(a) = 0, the tangent is horizontal, but an extremum is not guaranteed.
Question 8out of 11
What must first be defined when building an optimisation model?
Define the variable and feasible values from the context. Build the objective function using the constraints. Find candidates, compare relevant values and check the result and units.
Question 9out of 11
Some school students were surveyed. What are the surveyed group and all school students called?
The population is the full group studied and the sample is the observed subset. Precisely measured height is a quantitative continuous variable. Research proceeds through question, collection, analysis, interpretation and conclusion. An outlier can strongly affect the mean, standard deviation and regression line.
Question 10out of 11
Why does strong correlation not necessarily mean causation?
The dependent variable is the response predicted by the model. Assess fit using R², residual patterns, context and prediction range. Correlation alone does not prove causation; a third factor may explain it.
Question 11out of 11
What extremum occurs at the vertex of f(x) = −1x²?
Find the domain and critical points, then the derivative signs on intervals. f′ > 0 means increasing and f′ < 0 decreasing. A change from − to + gives a minimum; + to − a maximum. f′ = 0 alone does not guarantee an extremum. For f′ = 2(x − r), the minimum is at r.
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Full Grade 12 mathematics test
This complete Grade 12 mathematics test helps students review the main school topics in one mixed set of tasks. Questions are selected from different tests for this grade, so each attempt can be different.
Choose your test duration
Choose a 15, 30, 45 or 60 minute test. A longer duration creates a larger task set covering calculation, word problems, geometry and other topics studied in the grade.
Practise before an assessment
A full grade test is useful for independent checking, revision before a class assessment or mathematics exam preparation. Work at your own pace, review the result and try again: dynamic questions help students learn methods instead of memorising previous answers.
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