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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.

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Question Nr. 1out of 25

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

Ignore residuals

Use slope alone

Any line is suitable

Consider R², residuals, context and whether extrapolation is justified

Question Nr. 2out of 25

A cone has radius 5 cm and slant height 6 cm. Using π ≈ 3.14, find lateral area.

175.85 cm²

13.1 cm²

94.2 cm²

118.39 cm²

128.51 cm²

Question Nr. 3out of 25

Differentiate f(x) = 2x^6.

12x^5

6x^1

2x^5

12x^6

Question Nr. 4out of 25

How do surface area and volume scale when all lengths are multiplied by k?

Surface area changes by k² and volume by k³

Both change by k²

Volume changes by k only

Both change by k

Question Nr. 5out of 25

What does a cross-section of a solid mean?

Every face of a solid

The intersection of a solid with a plane

The volume of a solid

The shadow of a solid only

Question Nr. 6out of 25

Which formula describes the tangent line at x = a?

y = f'(a)

y − a = f(a)(x − f'(a))

y − f(a) = f'(a)(x − a)

y = f(a)x

Question Nr. 7out of 25

A right prism has base 5 cm × 12 cm and height 9 cm. Find its diagonal-section area.

117 cm²

52 cm²

84 cm²

165 cm²

21 cm²

Question Nr. 8out of 25

Event A has probability 80%. Find its complement probability.

20 %

32 %

16 %

97 %

47 %

Question Nr. 9out of 25

What is a dihedral angle?

Any angle between two lines

The angle between two half-planes with a common edge

The angle at a triangle vertex

A full rotation only

Question Nr. 10out of 25

A box has 8 red and 3 blue balls. Two are drawn without replacement. Find the probability both are red.

3/11

7/10

8/11

28/55

Question Nr. 11out of 25

Observed y = 7, predicted ŷ = 25. Find residual y − ŷ.

-1

-28

-54

-35

-18

Question Nr. 12out of 25

What relative positions can a line and a plane have?

It can only be perpendicular

It always has two intersections

It always lies in the plane

It may lie in the plane, intersect it once, or be parallel to it

Question Nr. 13out of 25

For f(x) = 1x² + (14)x, find the critical x where f′(x) = 0.

-7

-3

-12

Question Nr. 14out of 25

A right prism has rectangular base sides 16 cm and 30 cm and height 9 cm. Find its diagonal-section area.

217 cm²

103 cm²

306 cm²

70 cm²

176 cm²

Question Nr. 15out of 25

On [-3, 5], f(x) = 4(x − (0))². Find the maximum value.

107

100

Question Nr. 16out of 25

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

Graph only

Collect unrelated data

Question, data collection, analysis, interpretation and conclusion

Conclusion before data

Question Nr. 17out of 25

For f(x) = 6x² + (5)x + (3), calculate f′(-3).

-55

-31

Question Nr. 18out of 25

Is every point where f′(x) = 0 necessarily an extremum?

It is a candidate; the derivative sign or other analysis is needed

The function must equal zero there

It is always a maximum

It is never an extremum

Question Nr. 19out of 25

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

x ≤ -2

x < -2

x > -2

x = -2

Question Nr. 20out of 25

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

Only the function value

The instantaneous rate of change and the tangent slope

The x-intercept only

The area under the graph

Question Nr. 21out of 25

Which statement is a criterion for a line parallel to a plane?

One common point proves parallelism

Every line is parallel to every plane

A line in the plane is outside it

A line parallel to a line in the plane and not lying in the plane is parallel to the plane

Question Nr. 22out of 25

For f(x) = 5x² + (-8)x, solve f′(x) = 22.

-8

-3

Question Nr. 23out of 25

A cylinder has radius 2 cm and height 6 cm. Using π ≈ 3.14, find total surface area.

162.51 cm²

61.1 cm²

69.36 cm²

100.48 cm²

115.9 cm²

Question Nr. 24out of 25

Why must endpoints also be checked on a closed interval?

Because an absolute optimum on a closed interval may occur at an endpoint

The derivative is undefined at every endpoint

Only endpoints can be extrema

Endpoints never matter

Question Nr. 25out of 25

How are the volumes of a prism and pyramid with equal base and height related?

Only surface areas differ

The volumes are equal

A pyramid with the same base and height has one third of the prism volume

The pyramid is three times larger

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