Not every question of this paper is in the bank yet ("partial"), so it is offered for practice only. Practise this paper to see the correct answers and explanations: every answer is checked instantly (free account needed).
Mathematics 1. The points ( 0 , 2 ) (0, 2) ( 0 , 2 ) ( 6 , 4 ) (6, 4) ( 6 , 4 )
A. ( 2 , 0 ) (2, 0) ( 2 , 0 ) B. ( 3 , 0 ) (3, 0) ( 3 , 0 ) C. ( 5 , 0 ) (5, 0) ( 5 , 0 ) D. ( 4 , 0 ) (4, 0) ( 4 , 0 ) Tap an answer — the first 3 questions need no account
2. The acute angle between the lines y − 3 x + 1 = 0 y - \sqrt{3}x + 1 = 0 y − 3 x + 1 = 0 3 y − x + 3 = 0 \sqrt{3}y - x + 3 = 0 3 y − x + 3 = 0
A. 45 ∘ 45^{\circ} 4 5 ∘ B. 30 ∘ 30^{\circ} 3 0 ∘ C. 60 ∘ 60^{\circ} 6 0 ∘ D. 80 ∘ 80^{\circ} 8 0 ∘ Higher Math 1st Paper 3. ( x − 3 ) 2 + ( y − 3 ) 2 = 4 (x - 3)^2 + (y - 3)^2 = 4 ( x − 3 ) 2 + ( y − 3 ) 2 = 4
A. A and B both inside B. A and B both outside C. A inside and B outside D. A outside and B inside 4. If f ( x ) = sin x f(x) = \sin x f ( x ) = sin x lim x → 0 f ( x 2 ) x \lim_{x \to 0} \frac{f(x^2)}{x} lim x → 0 x f ( x 2 )
A. − 1 -1 − 1 B. 0 0 0 C. 1 1 1 D. Undefined See the answer 5. If y = x x 2 + 1 y=\frac{x}{\sqrt{x^2+1}} y = x 2 + 1 x d y d x = \frac{dy}{dx}= d x d y =
A. 1 x 2 + 1 \frac{1}{\sqrt{x^2+1}} x 2 + 1 1 B. − 1 x 2 + 1 \frac{-1}{\sqrt{x^2+1}} x 2 + 1 − 1 C. 1 2 x 2 + 1 \frac{1}{2\sqrt{x^2+1}} 2 x 2 + 1 1 D. 1 ( x 2 + 1 ) 3 2 \frac{1}{(x^2+1)^{\frac{3}{2}}} ( x 2 + 1 ) 2 3 1 See the answer 6. What is the differential coefficient of the function tan − 1 ( sec x + tan x ) \tan^{-1}(\sec x+\tan x) tan − 1 ( sec x + tan x )
A. 1 2 \frac{1}{2} 2 1 B. − 1 -1 − 1 C. − 2 sin x -2\sin x − 2 sin x D. x 2 x 2 − 1 \frac{x^2}{x^2-1} x 2 − 1 x 2 See the answer 7. What is the slope of the tangent of the parabola y 2 = 4 x y^2 = 4x y 2 = 4 x
A. − 1 -1 − 1 B. 1 1 1 C. ∞ \infty ∞ D. 0 0 0 See the answer Higher Math 2nd Paper 8. sin − 1 x \sin^{-1} x sin − 1 x
A. cot − 1 1 − x 2 x \cot^{-1} \frac{\sqrt{1-x^2}}{x} cot − 1 x 1 − x 2 B. cot − 1 x 1 − x 2 \cot^{-1} \frac{x}{\sqrt{1-x^2}} cot − 1 1 − x 2 x C. cot − 1 1 − x 2 \cot^{-1} \sqrt{1-x^2} cot − 1 1 − x 2 D. cot − 1 1 1 − x 2 \cot^{-1} \frac{1}{\sqrt{1-x^2}} cot − 1 1 − x 2 1 See the answer 9. Which one of the following relations is not true?
A. sin x = sin ( 2 n π + x ) \sin x = \sin(2n\pi + x) sin x = sin ( 2 nπ + x ) B. sin ( sin − 1 x ) = x \sin(\sin^{-1} x) = x sin ( sin − 1 x ) = x C. sin 2 x = ( − sin x ) 2 \sin^2 x = (-\sin x)^2 sin 2 x = ( − sin x ) 2 D. sin − 1 x = ( sin x ) − 1 \sin^{-1} x = (\sin x)^{-1} sin − 1 x = ( sin x ) − 1 See the answer 10. If tan 2 x tan x = 1 \tan 2x \tan x = 1 tan 2 x tan x = 1
A. 7 π 6 , 5 π 6 \frac{7\pi}{6}, \frac{5\pi}{6} 6 7 π , 6 5 π B. 13 π 6 , 15 π 6 \frac{13\pi}{6}, \frac{15\pi}{6} 6 13 π , 6 15 π C. 8 π 6 , 9 π 6 \frac{8\pi}{6}, \frac{9\pi}{6} 6 8 π , 6 9 π D. 13 π 6 , 11 π 6 \frac{13\pi}{6}, \frac{11\pi}{6} 6 13 π , 6 11 π See the answer See the other 4 questions