Why students lose marks in trigonometry and it is almost always a habit of dividing instead of factorising
Trigonometry is the topic where students who know every formula still lose marks, because the formulae are rarely the problem, the habits around solving and proving are. A student who reaches sinx(2cosx – 1) = 0 and divides through by sinx loses an entire branch of solutions without realising it. A student who expands cos(A – B) with the wrong sign spends the rest of the proof chasing an answer that can never appear. In 25 years of teaching, these two habits, dividing instead of factorising, and mismatching the sign in a compound angle or R-formula expansion, account for more lost marks than any gap in knowledge of the formulae themselves. The mark scheme does not award marks for a correct formula applied with the wrong sign or for a solution set missing a branch. These worksheets train the habit of factorising every equation and checking which sign belongs to which formula, every single time.
Recognition Training
Trigonometry - Mistake Analysis - Set I
Six questions on compound angle formulae for sin(A + B) and cos(x - 30), writing cos2x in terms of cosx, expressing 3sinx + 4cosx in the form Rsin(x + a), and proving the identity (sinx + cosx)^2 = 1 + sin2x that leads into the R-formula. Mistake analysis on every question.
Trigonometry - Mistake Analysis - Set II
Six questions on solving trigonometric equations by factorising, including 2cos^2x - 3cosx + 1 = 0, sin2x = sinx, and tanx = 2sinx, alongside proofs of the compound angle formula for tan(A + B) and an identity in sin^2x and sin^2y, plus a double angle question finding sin2theta, cos2theta and tan2theta from a given value of tantheta.
Trigonometry - Mistake Analysis - Set III
Six questions on the Rsin(x - a) form for 5sinx - 12cosx, two identity proofs involving reciprocal trig expressions and tanx, solving sin(x + pi/6) = cosx and 3cos^2x = 2 - sinx, and finding exact values of sin(pi/12) and sin(5pi/12) using the compound angle formula.
The 4 Patterns Behind Every Lost Mark
Dividing Both Sides by a Trig Expression
When an equation like sinx(2cosx - 1) = 0 appears, students sometimes divide both sides by sinx to leave a simpler equation in cosx. This removes the entire family of solutions where sinx = 0. The safe habit is to factorise and set each factor to zero, never to divide by an expression that could itself be zero.
Wrong Sign in Compound Angle and R-Formula Expansions
cos(A - B) expands as cosA cosB + sinA sinB, with a plus sign, yet many students write a minus sign and end up proving cos(A + B) instead. The same mix up appears with Rsin(x + a) versus Rsin(x - a). A difference such as asinx - bcosx must take the minus form, not the plus form.
Taking the Wrong Sign for sintheta or costheta in a Given Quadrant
In quadrant based questions, the quadrant of theta fixes the signs of sintheta and costheta before any double angle work begins. A student who carries the wrong sign through from the first step ends up placing the double angle in the wrong quadrant entirely.
Stopping After One Solution from costheta = k or costheta = cosphi
costheta = k, where k is positive, has two solutions in [0, 2pi], and costheta = cosphi means theta = plus or minus phi + 2npi, not theta = phi. Students who round arccos on a calculator and stop, or who write 2x = x directly, lose an entire branch of the solution set.
The Full Diagnostic Path
- 50 original exam-style questions across 5 core trigonometry areas
- Full worked solutions with M1/A1/R1 IB mark scheme annotations
- Mistake analysis on every question targeting sign errors, lost solution branches, and identity proof shortcuts
- Sections: compound angle formulae, double angle formulae, the R-formula, trigonometric equations, identity proofs
- IB Examiner commentary per section on where marks are most commonly lost
Need one-to-one help with Trigonometry?
Book a session with Abdul Wadood and work through the techniques that are costing you marks.