Factorise completely x − 4x³ (3) Answer ANSWER Explanation Explanation Express 82x+3 in the form 2y , stating y in terms of x. (2) Answer ANSWER Explanation Explanation Express (5 − √8 )(1 +...
Find \(\int\)(6x² + 2/x² + 5) giving each term in its simplest form. (4) Answer ANSWER Explanation Explanation Evaluate (32)3/5, giving your answer as an integer. (2) Simplify fully (25×4/4)-¼(2) Answer ANSWER Explanation Explanation...
Find the value of 25½(1) 25-3/2(2) Answer ANSWER Explanation Explanation Given that y = 2×5 + 7 + 1/x³, x≠0 find, in their simplest form, dy/dx(3) \(\int\)y dx4) Answer ANSWER Explanation Explanation The points...
Express 2/(2r + 1)(2r + 3)in partial fractions. (2) Using your answer to (a), find, in terms of n, [IMAGE] Give your answer as a single fraction in its simplest form. (3) Answer ANSWER...
Find the set of values of x for which 3/x + 3 > x – 4/x (7) Answer ANSWER Explanation Explanation d²y/dx²= ex(2ydy/dx + y² + 1) Show that d³y/dx³= ex[2yd²y/dx² + 2(dy/dx)² +...
Find the set of values of x for which |x² – 4| > 3x Answer ANSWER Explanation Explanation The curve C has polar equation r = 1+ 2cosθ, 0≤θπ/2 At the point P on...
Using calculus, find the coordinates of the stationary point on the curve with equation y = 2x + 3 + 8/x², x>0 Answer ANSWER Explanation Explanation y = x/√(1 + x) Complete the table...
[In this question i and j are perpendicular unit vectors in a horizontal plane.] A particle P moves in such a way that its velocity v m s–1 at time t seconds is given...
A caravan of mass 600 kg is towed by a car of mass 900 kg along a straight horizontal road. The towbar joining the car to the caravan is modelled as a light rod...
A car of mass 1000 kg moves with constant speed V m s−1 up a straight road inclined at an angle θ to the horizontal, where sin θ = 1/30. The engine of the...
