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Mathematics · Self Assessment

Practice Test: Bearings, 3D Trigonometry & Graphing Functions

A 100-mark paper covering "Bearings & 3D Trigonometry" and "Graphing Functions: Quadratics, Cubics & Graphical Inequalities" — multiple choice, true/false, fill-in-the-blank, column matching, and short answer, all auto-graded instantly.

EDUSAMBAM Editorial Team · 45 questions · 100 marks · Instant self-assessment

Questions

100

Marks

Sections

100%

Auto-Graded

Section	Questions	Marks Each	Total
A — Multiple Choice	15	2	30
B — True / False	10	2	20
C — Fill in the Blank	10	2	20
D — Column Matching	5 pairs	2	10
E — Short Answer	5	4	20
Total	45	—	100

Fill-in-the-blank and short-answer questions are checked automatically against accepted answers — exact wording doesn't need to match, but the key term should be present.

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Section A — Multiple Choice

30 marks

15 questions · 2 marks each.

1.A bearing is measured:Basic2 pts

A. Anticlockwise from South

B. Clockwise from North

C. Clockwise from East

D. In any direction, as long as it is consistent

2.Bearings are always written using:Basic2 pts

A. Two figures

B. Compass letters only (N, S, E, W)

C. Fractions of a full turn

D. Exactly three figures

3.Due East as a bearing is:Basic2 pts

A. 000°

B. 180°

C. 090°

D. 270°

4.The bearing of B from A is 065°. The back bearing (A from B) is:Intermediate2 pts

A. 245°

B. 065°

C. 115°

D. 295°

5.A cuboid has length 3 cm, width 4 cm, and height 12 cm. Its base diagonal is:Intermediate2 pts

A. 7 cm

B. 12 cm

C. 5 cm

D. 25 cm

6.Using the cuboid above (base diagonal 5 cm, height 12 cm), the space diagonal is:Advanced2 pts

A. 13 cm

B. 17 cm

C. 7 cm

D. 60 cm

7.The correct method to find a cuboid's space diagonal is:Intermediate2 pts

A. Add length, width and height

B. Use the sine rule only

C. Multiply length by width by height

D. Find the base diagonal first, then combine it with the height using Pythagoras again

8.Plotted points on a quadratic graph should be joined with:Basic2 pts

A. Straight line segments

B. A single smooth curve

C. Dots only, unjoined

D. A dashed line

9.The shape of every quadratic graph is called a:Basic2 pts

A. Parabola

B. Hyperbola

C. S-curve

D. Ellipse

10.y = (x − 4)² + 7. The turning point is:Intermediate2 pts

A. (−4, 7)

B. (4, −7)

C. (4, 7)

D. (−4, −7)

11.y = (x − 3)(x − 9). The roots are at:Intermediate2 pts

A. x = −3 and x = −9

B. x = 3 and x = 9

C. x = 3 only

D. x = 27

12.A cubic graph with a positive x³ coefficient generally:Intermediate2 pts

A. Falls from left to right

B. Is a closed loop

C. Is a straight line

D. Rises from bottom-left to top-right in an S-shape

13.The solutions of f(x) = 0 can be found graphically by looking at:Intermediate2 pts

A. The y-intercept

B. The turning point

C. The steepest point

D. Where the curve crosses the x-axis

14.For a strict inequality such as y > 2x + 1, the boundary line should be drawn:Intermediate2 pts

A. As a thick solid line

B. As a dashed line

C. As a curve

D. In a different colour only

15.To decide which side of a boundary line to shade, you should:Intermediate2 pts

A. Test a convenient point, such as the origin

B. Always shade above the line

C. Always shade below the line

D. Guess based on the shape of the line

Section B — True / False

20 marks

10 questions · 2 marks each.

16.Due South as a bearing is 180°.Basic2 pts

True

False

17.The back bearing is found by adding 180° when the original bearing is already 180° or more.Intermediate2 pts

True

False

18.Bearing problems are usually solved using the sine rule, cosine rule, or SOH-CAH-TOA, once a triangle is identified.Intermediate2 pts

True

False

19.The space diagonal of a cuboid is the longest diagonal, from one corner through the interior to the opposite corner.Basic2 pts

True

False

20.To find a cuboid's space diagonal, you should multiply length × width × height.Intermediate2 pts

True

False

21.A cubic graph can have up to two turning points.Intermediate2 pts

True

False

22.A solid boundary line means the inequality is strict (< or >).Intermediate2 pts

True

False

23.Completing the square directly reveals a quadratic's turning point.Intermediate2 pts

True

False

24.The axis of symmetry of y = (x − a)(x − b) lies exactly halfway between the roots.Advanced2 pts

True

False

25.When several inequalities are combined on one graph, the answer region only needs to satisfy one of them.Intermediate2 pts

True

False

Section C — Fill in the Blank

20 marks

10 questions · 2 marks each. Type the missing word or term.

26.A bearing is measured clockwise from ______.Basic2 pts

27.The bearing of D from C is 230°. The back bearing (C from D) is ______ degrees.Intermediate2 pts

28.To find the angle between a space diagonal and the base of a cuboid, you use the right-angled triangle formed by the base diagonal and the ______.Advanced2 pts

29.A cuboid's space diagonal is found using Pythagoras' theorem applied ______ times.Intermediate2 pts

30.Writing a bearing as "45°" instead of "______" is a common mistake.Basic2 pts

31.Writing y = (x − p)² + q, the turning point is at (p, ______).Intermediate2 pts

32.A dashed boundary line on a graph means the inequality is ______.Intermediate2 pts

33.The point where a graph crosses the y-axis is called the ______.Basic2 pts

34.A parabola's line of symmetry is called the axis of ______.Basic2 pts

35.To solve f(x) = 0 graphically, you read the points where the curve crosses the ______-axis.Intermediate2 pts

Section D — Column Matching

10 marks

Match each term to its correct definition. Use the ▲▼ buttons to reorder Column B.

36–40.Match each term to its correct definition.Advanced10 pts

Column A

Back bearing

Space diagonal

Turning point

Cubic graph

Dashed line

Column B

An S-shaped curve from a function with an x³ term

The bearing of the return journey, found using ±180°

Boundary line used for a strict inequality (< or >)

The longest diagonal of a cuboid, running through the interior

The minimum or maximum point of a curve

Section E — Short Answer

20 marks

5 questions · 4 marks each. Answer in one or two sentences.

41.Explain how to find the back bearing of a given bearing.Intermediate4 pts

42.Describe the two-step method for finding the space diagonal of a cuboid.Advanced4 pts

43.Explain how completing the square helps you find the turning point of a quadratic graph.Advanced4 pts

44.Describe how to decide which side of an inequality's boundary line to shade.Intermediate4 pts

45.Explain the difference between a solid and a dashed boundary line on a graphical inequality.Intermediate4 pts

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