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Matric past papers · DBE (CAPS) · Paper 2

DBE Grade 12 Trigonometry

Every trigonometry question from the DBE NSC Paper 2 papers of November 2021–2024 and May/June 2021, 2022, 2024, 2025, in one booklet — 28 questions, 385 marks, with the official marking guideline for every one of them. Free to download, in English and Afrikaans.

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Each question is a clip of the original DBE page: the wording, the mark allocations and the diagrams are exactly as they were printed. Only the blank answer space has been removed, so work in a separate book. The solutions booklet is the board’s own marking guideline, not a rewritten one.

What is in it

28 questions in 3 chapters, ordered so you can work through one skill at a time.

#QuestionSkillsMarksFrom
1Simplify to one ratio, then a sum of two sinesReduction formulae, Compound angles, Proving an identity12May/June 2022 Q6
2cos A from a point, then the double and compound anglesRatios from a point, and the quadrants, Double angles, Compound angles12November 2024 Q5
3Two identities to prove, one of them a difference of sinesProving an identity, Compound angles, Double angles13May/June 2025 Q6
4Derive cos(alpha + beta), then use it to simplifyCompound angles, Proving an identity, General solutions15November 2021 Q6
5Reduce to a single ratio, then prove an identityReduction formulae, Proving an identity, General solutions17November 2021 Q5
6Simplify, then everything in terms of cos 35 = mReduction formulae, Ratios from a point, and the quadrants, Compound angles18May/June 2021 Q5
7A point in the second quadrant, and the ratios it fixesRatios from a point, and the quadrants, Reduction formulae, Double angles18May/June 2022 Q5
8Derive cos(x + y) from the identity given, then apply itCompound angles, Proving an identity, General solutions18November 2024 Q6
9cos theta = 5/13 with the quadrant given, then a simplificationRatios from a point, and the quadrants, Reduction formulae, Compound angles19May/June 2025 Q5
10Everything in terms of sin 40 = p, then an identity to proveRatios from a point, and the quadrants, Reduction formulae, Proving an identity26May/June 2024 Q5
1113 sin x + 3 = 0, and the whole chain that follows from itRatios from a point, and the quadrants, Reduction formulae, Proving an identity, General solutions30November 2022 Q5
12sin beta given with its quadrant - the longest question in the bookRatios from a point, and the quadrants, Double angles, Proving an identity, General solutions31November 2023 Q5
13Draw a cosine onto a sine that is already sketchedThe graphs of sin, cos and tan, Period, amplitude and asymptotes8November 2021 Q7
14A cosine and a shifted sine on one set of axesThe graphs of sin, cos and tan, Where two trig graphs meet10May/June 2022 Q7
15tan x against 2 sin 2x, and where the two crossThe graphs of sin, cos and tan, Where two trig graphs meet10November 2022 Q6
16Find a from where cos(x + a) meets sin 2xThe graphs of sin, cos and tan, Where two trig graphs meet, Period, amplitude and asymptotes10May/June 2024 Q6
17Range, period, and where 2 cos x + 1 meets sin 2xThe graphs of sin, cos and tan, Period, amplitude and asymptotes, Where two trig graphs meet10May/June 2025 Q7
18The asymptote of tan x, and reading the graph around itThe graphs of sin, cos and tan, Period, amplitude and asymptotes11November 2024 Q7
19Period, amplitude, and a point that lies on fThe graphs of sin, cos and tan, Period, amplitude and asymptotes, Where two trig graphs meet12November 2023 Q6
20cos 2x against minus sin x, without a calculatorThe graphs of sin, cos and tan, Where two trig graphs meet, Ratios from a point, and the quadrants13May/June 2021 Q6
21A vertical tower, an angle of depression, and an area qThree-dimensional problems, The area rule, Angles of elevation and depression7November 2023 Q7
22A ramp into a building: its height, its angle and its lengthAngles of elevation and depression, The sine rule8May/June 2022 Q8
23A point directly above a triangle, with 2AD = BCThree-dimensional problems, The cosine rule, The sine rule8May/June 2025 Q8
24Two boards meeting at right anglesThree-dimensional problems, The cosine rule9May/June 2021 Q7
25Two observers 19 m apart, and a building 16 m highThree-dimensional problems, Angles of elevation and depression, The cosine rule9November 2024 Q8
26A hook on a gallery ceiling, seen from three pointsThree-dimensional problems, Angles of elevation and depression, The sine rule10November 2021 Q8
27A flagpole and the two cables anchoring itThree-dimensional problems, The sine rule, The cosine rule10November 2022 Q7
28Derive the area rule, then put it to workThe area rule, The sine rule11May/June 2024 Q7