Practise Question bank Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.
Sign in to check answers. Your attempts build your mastery and error book.
13 questions
SA-9709-P3-T34-G01 3 marks L1 Foundation Calculator R-form
Express 3 sin θ + cos θ \sqrt3\sin\theta+\cos\theta 3 sin θ + cos θ R sin ( θ + α ) R\sin(\theta+\alpha) R sin ( θ + α ) R > 0 R>0 R > 0 0 ∘ < α < 90 ∘ 0^\circ<\alpha<90^\circ 0 ∘ < α < 9 0 ∘
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T34-Q01 1 mark L1 Foundation Calculator R-form
When a sin θ + b cos θ a\sin\theta+b\cos\theta a sin θ + b cos θ R sin ( θ + α ) R\sin(\theta+\alpha) R sin ( θ + α ) R R R
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T34-001 3 marks L2 Standard Calculator R-form
Express 5 cos x + 12 sin x 5\cos x+12\sin x 5 cos x + 12 sin x R cos ( x − α ) R\cos(x-\alpha) R cos ( x − α ) R > 0 R>0 R > 0 0 ∘ < α < 90 ∘ 0^\circ<\alpha<90^\circ 0 ∘ < α < 9 0 ∘ α \alpha α
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T34-002 2 marks L2 Standard Calculator Max and min
Find the exact greatest value of 2 sin θ + 2 cos θ 2\sin\theta+2\cos\theta 2 sin θ + 2 cos θ
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T34-003 3 marks L2 Standard Calculator Max and min
Find the greatest and least values of 6 + 3 sin x − 4 cos x 6+3\sin x-4\cos x 6 + 3 sin x − 4 cos x
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T34-005 3 marks L2 Standard Calculator R-form
Express cos θ + sin θ \cos\theta+\sin\theta cos θ + sin θ R cos ( θ − α ) R\cos(\theta-\alpha) R cos ( θ − α ) R > 0 R>0 R > 0 0 ∘ < α < 90 ∘ 0^\circ<\alpha<90^\circ 0 ∘ < α < 9 0 ∘
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-009 3 marks L2 Standard Calculator R-form
Express 3 sin θ + 4 cos θ 3\sin\theta+4\cos\theta 3 sin θ + 4 cos θ R sin ( θ + α ) R\sin(\theta+\alpha) R sin ( θ + α ) R > 0 R>0 R > 0 0 ∘ < α < 90 ∘ 0^\circ<\alpha<90^\circ 0 ∘ < α < 9 0 ∘ α \alpha α
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T34-004 4 marks L3 Exam Calculator Equations
Solve 3 sin x + cos x = 1 \sqrt3\sin x+\cos x=1 3 sin x + cos x = 1 0 ∘ ≤ x ≤ 360 ∘ 0^\circ\le x\le360^\circ 0 ∘ ≤ x ≤ 36 0 ∘
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-010 3 marks L3 Exam Calculator Max and min
Given 3 sin θ + 4 cos θ = 5 sin ( θ + 53.13 ∘ ) 3\sin\theta+4\cos\theta=5\sin(\theta+53.13^\circ) 3 sin θ + 4 cos θ = 5 sin ( θ + 53.1 3 ∘ ) 3 sin θ + 4 cos θ + 2 3\sin\theta+4\cos\theta+2 3 sin θ + 4 cos θ + 2 θ \theta θ
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-011 6 marks L3 Exam Calculator Equations
Express 3 cos x − sin x \sqrt3\cos x-\sin x 3 cos x − sin x R cos ( x + α ) R\cos(x+\alpha) R cos ( x + α ) R > 0 R>0 R > 0 0 ∘ < α < 90 ∘ 0^\circ<\alpha<90^\circ 0 ∘ < α < 9 0 ∘ 3 cos x − sin x = 1 \sqrt3\cos x-\sin x=1 3 cos x − sin x = 1 0 ∘ ≤ x ≤ 360 ∘ 0^\circ\le x\le360^\circ 0 ∘ ≤ x ≤ 36 0 ∘
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T34-006 3 marks L4 Challenging Calculator Max and min
Find the greatest and least values of 1 10 + 3 cos x + 4 sin x \dfrac{1}{10+3\cos x+4\sin x} 10 + 3 cos x + 4 sin x 1
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T34-007 5 marks L4 Challenging Calculator Equations
By writing 3 cos x − 4 sin x 3\cos x-4\sin x 3 cos x − 4 sin x R cos ( x + α ) R\cos(x+\alpha) R cos ( x + α ) 3 cos x − 4 sin x = 2.5 3\cos x-4\sin x=2.5 3 cos x − 4 sin x = 2.5 0 ∘ ≤ x ≤ 360 ∘ 0^\circ\le x\le360^\circ 0 ∘ ≤ x ≤ 36 0 ∘
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-017 6 marks L5 Extension Calculator Equations
Express 5 sin x − 12 cos x 5\sin x-12\cos x 5 sin x − 12 cos x R sin ( x − α ) R\sin(x-\alpha) R sin ( x − α ) R > 0 R>0 R > 0 0 ∘ < α < 90 ∘ 0^\circ<\alpha<90^\circ 0 ∘ < α < 9 0 ∘ α \alpha α 20 5 sin x − 12 cos x + 17 \dfrac{20}{5\sin x-12\cos x+17} 5 sin x − 12 cos x + 17 20
Salam Academy Original Practice · Proposed mark scheme