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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.

Question qty: 35Duration in minutes: 62

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Question Nr. 1out of 35

A cube section parallel to a face is a square of side 2 cm. Find its area.

62 cm²

4 cm²

30 cm²

25 cm²

59 cm²

Question Nr. 2out of 35

A right prism has base 20 cm × 48 cm and height 4 cm. Find its diagonal-section area.

130 cm²

41 cm²

208 cm²

110 cm²

277 cm²

Question Nr. 3out of 35

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

It is never an extremum

The function must equal zero there

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

It is always a maximum

Question Nr. 4out of 35

What general strategy is suitable for a word optimisation problem?

Choose the first critical point automatically

Translate the context into an objective function and constraints, then verify the result

Use every number in one product

Ignore units

Question Nr. 5out of 35

The correlation coefficient is r = 0.40. What is the direction?

Negative

Zero

Positive

Question Nr. 6out of 35

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

Ignore residuals

Any line is suitable

Consider R², residuals, context and whether extrapolation is justified

Use slope alone

Question Nr. 7out of 35

For f(x) = 2x² + (2)x, solve f′(x) = -6.

-2

-9

-3

Question Nr. 8out of 35

A model has R² = 0.81. What percentage of variation does it explain?

53 %

81 %

65 %

24 %

17 %

Question Nr. 9out of 35

Differentiate the constant function f(x) = -9.

-4

-2

-3

Question Nr. 10out of 35

Independent events A and B have probabilities 50% and 75%. Find P(A and B) as a decimal.

0.38

0.86

0.46

0.95

Question Nr. 11out of 35

A perpendicular from a point to a plane has length 9 cm. What is the point-to-plane distance?

11 cm

21 cm

16 cm

9 cm

3 cm

Question Nr. 12out of 35

How many planes pass through three non-collinear points?

Exactly one plane

Infinitely many planes

No plane

Exactly two planes

Question Nr. 13out of 35

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

Question, data collection, analysis, interpretation and conclusion

Collect unrelated data

Conclusion before data

Graph only

Question Nr. 14out of 35

What shape results when a cylinder is cut by a plane through its axis?

A circle only

A rectangle whose sides are the cylinder height and diameter

A right triangle

A regular hexagon

Question Nr. 15out of 35

An independent event with probability 20% must occur three times in a row. Find the decimal probability.

0.54

0.19

0.26

0.37

0.01

Question Nr. 16out of 35

Solve cos x = 1/2 on [0°, 360°].

60° ir 300°

30° ir 150°

45° ir 315°

0° ir 180°

Question Nr. 17out of 35

When are identities useful in a trigonometric equation?

Use identities to reduce the equation to one trigonometric function

Square every term without checking

Replace every sine by x

Ignore the domain

Question Nr. 18out of 35

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

Both words always mean addition

The words have no mathematical role

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

Both always mean multiplication

Question Nr. 19out of 35

A box has 8 red and 4 blue balls. Two are drawn with replacement. Find the probability both are red.

4/12

4/9

7/11

8/12

Question Nr. 20out of 35

f(-4) = 8 and f(-1) = 2. Find the average rate of change on [-4, -1].

-4

-2

Question Nr. 21out of 35

A linear model has R² = 0.25. What percentage of data variation is explained?

27 %

35 %

25 %

73 %

91 %

Question Nr. 22out of 35

What shape is an axial section of a right cone?

A circle

An isosceles triangle with base equal to the diameter

A rectangle

A scalene triangle in every case

Question Nr. 23out of 35

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

Volume changes by k only

Both change by k

Surface area changes by k² and volume by k³

Both change by k²

Question Nr. 24out of 35

Solve 4 sin x + (2) = 0 on [0°, 360°].

45° ir 135°

210° ir 330°

90° ir 270°

60° ir 120°

Question Nr. 25out of 35

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. 26out of 35

Profit is P(x) = −5x² + 240x. Which x maximises profit?

Question Nr. 27out of 35

A box has 4 red and 4 blue balls. Two are drawn without replacement. Find the probability both are red.

3/7

3/14

4/8

Question Nr. 28out of 35

A rectangular prism measures 11 cm, 2 cm and 5 cm. Find total surface area.

174 cm²

126 cm²

220 cm²

43 cm²

175 cm²

Question Nr. 29out of 35

What is a dihedral angle?

The angle between two half-planes with a common edge

The angle at a triangle vertex

Any angle between two lines

A full rotation only

Question Nr. 30out of 35

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

Question Nr. 31out of 35

A cone has radius 10 cm and height 24 cm. Using π ≈ 3.14, find volume.

239.03 cm³

2512 cm³

431.53 cm³

832.4 cm³

2081.69 cm³

Question Nr. 32out of 35

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

77 cm²

55 cm²

99 cm²

115 cm²

56 cm²

Question Nr. 33out of 35

A sphere has radius 18 cm. Using π ≈ 3.14, find volume.

9087.76 cm³

520.08 cm³

13234.34 cm³

18756.18 cm³

24416.64 cm³

Question Nr. 34out of 35

How is an event probability calculated in a probability tree?

Multiply probabilities along a path and add probabilities of favourable disjoint paths

Multiply every branch in the whole tree

Ignore conditional probabilities

Add along every path

Question Nr. 35out of 35

A cylinder has radius 7 cm and height 3 cm. Using π ≈ 3.14, find total surface area.

139.78 cm²

439.6 cm²

119.21 cm²

190.89 cm²

476.06 cm²

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