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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 in the form R sin ( θ + α ) R\sin(\theta+\alpha) R sin ( θ + α ) , where R > 0 R>0 R > 0 and 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 is written as R sin ( θ + α ) R\sin(\theta+\alpha) R sin ( θ + α ) , R R R equals
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 in the form R cos ( x − α ) R\cos(x-\alpha) R cos ( x − α ) , where R > 0 R>0 R > 0 and 0 ∘ < α < 90 ∘ 0^\circ<\alpha<90^\circ 0 ∘ < α < 9 0 ∘ . Give α \alpha α to 2 decimal places.
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 in the form R cos ( θ − α ) R\cos(\theta-\alpha) R cos ( θ − α ) , where R > 0 R>0 R > 0 and 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 in the form R sin ( θ + α ) R\sin(\theta+\alpha) R sin ( θ + α ) , where R > 0 R>0 R > 0 and 0 ∘ < α < 90 ∘ 0^\circ<\alpha<90^\circ 0 ∘ < α < 9 0 ∘ . Give α \alpha α correct to 2 decimal places.
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 for 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 ∘ ) , find the greatest value of 3 sin θ + 4 cos θ + 2 3\sin\theta+4\cos\theta+2 3 sin θ + 4 cos θ + 2 and the smallest positive value of θ \theta θ at which it occurs, correct to 2 decimal places.
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 in the form R cos ( x + α ) R\cos(x+\alpha) R cos ( x + α ) , where R > 0 R>0 R > 0 and 0 ∘ < α < 90 ∘ 0^\circ<\alpha<90^\circ 0 ∘ < α < 9 0 ∘ . Hence solve 3 cos x − sin x = 1 \sqrt3\cos x-\sin x=1 3 cos x − sin x = 1 for 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 in the form R cos ( x + α ) R\cos(x+\alpha) R cos ( x + α ) , solve 3 cos x − 4 sin x = 2.5 3\cos x-4\sin x=2.5 3 cos x − 4 sin x = 2.5 for 0 ∘ ≤ x ≤ 360 ∘ 0^\circ\le x\le360^\circ 0 ∘ ≤ x ≤ 36 0 ∘ , giving answers to 1 decimal place.
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 in the form R sin ( x − α ) R\sin(x-\alpha) R sin ( x − α ) , where R > 0 R>0 R > 0 and 0 ∘ < α < 90 ∘ 0^\circ<\alpha<90^\circ 0 ∘ < α < 9 0 ∘ , giving α \alpha α to 2 decimal places. Hence find the greatest value of 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