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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: 26Estimated time: 45 minutes

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Question 1out of 26

Which sum differentiation rule is correct?

(f + g)' = f + g

(f + g)' = f' + g'

(f + g)' = 0

(f + g)' = f'g'

Question 2out of 26

The derivative is f′(x) = 2(x − (2)). Where is f increasing?

x < 2

x ≥ 2

x = 2

x > 2

Question 3out of 26

What type of variable is precisely measured human height?

A constant

Qualitative nominal variable

Qualitative ordinal variable

Quantitative continuous variable

Question 4out of 26

What shape is an axial section of a right cone?

An isosceles triangle with base equal to the diameter

A circle

A rectangle

A scalene triangle in every case

Question 5out of 26

How are solutions in a stated interval selected from a general trigonometric solution?

Convert all values to positive

Ignore interval endpoints

List one arbitrary period

Keep only general-solution values that belong to the stated interval

Question 6out of 26

Some school students were surveyed. What are the surveyed group and all school students called?

Both are populations

The terms are interchangeable

The surveyed students are the sample; all school students are the population

Both are samples

Question 7out of 26

What does “axial section” mean?

An axial section passes through the axis of rotation

It is defined by volume

It never meets the axis

It is always parallel to the axis

Question 8out of 26

Find the distance between the parallel planes 5x + 12y = 0 and 5x + 12y + 91 = 0.

The distance between the parallel planes Ax + By + Cz + D₁ = 0 and Ax + By + Cz + D₂ = 0 is |D₂ − D₁| / √(A² + B² + C²).

Question 9out of 26

Velocity is v(t) = 8t + (-1). Find acceleration.

8 m/s²

-2 m/s²

5 m/s²

12 m/s²

3 m/s²

Question 10out of 26

For f(x) = 6x² + (8)x, solve f′(x) = 56.

-3

-6

Question 11out of 26

What is a logical sequence of stages in a statistical study?

Question, data collection, analysis, interpretation and conclusion

Collect unrelated data

Graph only

Conclusion before data

Question 12out of 26

How is the derivative sign related to increasing and decreasing?

Only f values determine monotonicity

f increases where f′ < 0

The signs have no meaning

f increases where f′ > 0 and decreases where f′ < 0

Question 13out of 26

What shape is an axial section of a cylinder?

An equilateral triangle

A square of side r only

A circle of radius h

A rectangle with sides 2r and h

Question 14out of 26

An oblique segment of length 5 has an orthogonal projection of length 3 on a plane. Find the sine of the angle α between the segment and the plane.

4/5

4/3

3/5

3/4

The oblique segment, its orthogonal projection and the perpendicular to the plane form a right triangle. First find the perpendicular length using the Pythagorean theorem. The sine of the angle between the segment and the plane is the perpendicular length divided by the oblique length.

Question 15out of 26

Given f(x) = (5x + 2)². Find f′(0).

Use the chain rule: ((kx + b)ⁿ)′ = n(kx + b)ⁿ⁻¹ · k. First differentiate the function, then substitute the given value of x. Do not forget the factor k obtained by differentiating the inner function.

Question 16out of 26

The correlation coefficient is r = 0.90. What is the direction?

Negative

Zero

Positive

Question 17out of 26

Compare correlations r₁ = 0.60 and r₂ = 0.70. Which is stronger?

They are equal

The first is stronger

The second correlation is stronger

Signs alone determine strength

Question 18out of 26

What should be considered when deciding whether a linear model is suitable?

Any line is suitable

Use slope alone

Consider R², residuals, context and whether extrapolation is justified

Ignore residuals

Question 19out of 26

When is a line perpendicular to a plane?

It is parallel to the plane

It lies in the plane

It is perpendicular to two intersecting lines in the plane

It is perpendicular to one arbitrary line only

Question 20out of 26

A pyramid diagonal section has base 22 cm and height 5 cm. Find its area.

55 cm²

62 cm²

41 cm²

16 cm²

37 cm²

Question 21out of 26

A box has 8 red and 6 blue balls. Two are drawn without replacement. Find the probability both are red.

7/13

8/14

6/14

4/13

Question 22out of 26

What is the geometric meaning of a derivative at a point?

The x-intercept only

The instantaneous rate of change and the tangent slope

The area under the graph

Only the function value

Question 23out of 26

Independent events A and B have probabilities 40% and 20%. Find P(A and B) as a decimal.

0.35

0.08

0.3

0.26

0.48

Question 24out of 26

How are “and” and “or” interpreted in probability?

The words have no mathematical role

Both always mean multiplication

“And” usually follows one path and multiplies; incompatible “or” branches add

Both words always mean addition

Question 25out of 26

For f(x) = 4x² + (5)x, find the tangent slope at x = -5.

-35

-78

-42

-19

-76

Question 26out of 26

Model A has R² = 0.25. After adding another predictor, model B has R² = 0.55. By what percentage did the part of variation unexplained by model A decrease?

30 %

45 %

40 %

55 %

First find the variation unexplained by model A: 1 − R²(A). Then find its decrease: R²(B) − R²(A). The relative decrease is (R²(B) − R²(A)) / (1 − R²(A)) · 100%. Do not confuse percent with percentage points.

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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.

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