If z = f(x) g(y), find dz/dt in terms of dy/dt and dx/dt. (without implicit differentiation) If $z=text{f}left( x right)text{g}left( y right)$, where $x$ and $y$ each vary with time
Finding Equations of Tangents to a Circle Drawn from Origin The circle ${{C}_{1}}$ has an equation of ${{x}^{2}}+{{y}^{2}}-4x+8y+16=0$. (a) Find the centre of another circle which is a reflection of
Finding The Smallest Circle Through a Point and Centre On a Line The equation of circle, ${{C}_{1}}$, is ${{x}^{2}}+{{y}^{2}}-4x-2y-20=0$. (i) Find the centre and the radius of the circle. (ii)
AM Unit 9 Trigonometric Identities and Formulae Practice Q2: If sin(A+B)=2sin(A-B), find tan B/ tan A Given that $sin left( A+B right)=2sin left( A-B right)$, evaluate $frac{tan B}{tan A}$. Suggested
AM Unit 9 Trigonometric Identities and Formulae Practice Q1: Solve cos x cos 3x – sin x sin 3x = 0 between 0 and 2π Solve $cos xcos 3x-sin xsin 3x=0$
AM Binomial Theorem Practice Question 1: How to determine if 37¹¹-1 is divisible by 396 Using binomial expansion of ${{left( 1+x right)}^{n}},$ determine if ${{37}^{11}}-1$ is divisible by $396$. Suggested
AM Simultaneous Equations, Polynomials, Partial Fractions Question 2 The expressions ${{x}^{3}}-2{{x}^{2}}-3x-11$ and ${{x}^{3}}-{{x}^{2}}-9$ leave the same remainder when divided by $x+a$. Find (i) the two possible values of $a$, (ii)
AM Applications of Differentiation Practice Question 2 Given that $y=a{{x}^{5}}$, where $ane 0$ , and $frac{text{d}y}{text{d}x}=frac{3}{2}$ at $left( 1,b right)$, find (i) the value of $a$ and of $b$, (ii)
AM Proofs in Plane Geometry Practice Question 2 In the diagram, $AT$ and $DT$ are tangents to the circle at $A$ and $D$ respectively. $O$ is the centre of the
AM Proofs in Plane Geometry Practice Question 1 In the figure, $AB$ is the tangent to the circle at $B$ and $DC$ bisects angle $BCA$. The line $BD$ produced meets