Learn Extracted exam questions A-Level Mathematics 9709 Mathematics November 2025 Question Paper 42
9709 Mathematics November 2025 Question Paper 42
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The diagram shows the displacement-time graph for the motion of a particle. The particle starts from rest at a point $O$ and travels with constant acceleration $a\text{ m s}^{-2}$, taking 4 s to move a distance of $x$ m. The particle then returns to $O$ with constant speed of $40\text{ m s}^{-1}$, over a period of 2 s. Find the value of $x$ and the value of $a$.
A railway locomotive of mass 240000 kg is towing a coach of mass 36000 kg down a hill inclined at an angle of $\sin^{-1} 0.04$ to the horizontal. The driving force produced by the locomotive is 450000 N and there are resistances to motion of 120000 N on the locomotive and 15000 N on the coach. The coupling between the locomotive and the coach is light, rigid and parallel to the hill. Find the acceleration of the locomotive and the tension in the coupling.
A car of mass 1400 kg travelling on a straight horizontal road accelerates uniformly from a speed of $15\text{ m s}^{-1}$ to $20\text{ m s}^{-1}$ over a distance of 175 m.
Find the time taken to travel the 175 m.
There is a constant resistance force of 800 N to the motion of the car.
Use an energy method throughout to find the average power of the car's engine as the speed increases from $15\text{ m s}^{-1}$ to $20\text{ m s}^{-1}$.
Find the steady speed that the car could maintain on the horizontal road if the engine is working at the power found in (b)(i).
A particle $P$ of mass 0.1 kg is projected vertically upwards with speed $30\text{ m s}^{-1}$ from horizontal ground. At the same instant a particle $Q$ of mass 0.4 kg is projected vertically upwards with speed $10\text{ m s}^{-1}$ from a height of 15 m above the ground. $P$ and $Q$ move in the same vertical line.
Find the height above the ground at which $P$ and $Q$ collide.
When $P$ and $Q$ collide, they coalesce. Find the speed of the combined particle at the instant that it reaches the ground.
A block of mass 5 kg is being pulled straight down a line of greatest slope of a rough plane by a force of magnitude 20 N. The plane is inclined at an angle of $10\degree$ to the horizontal and the 20 N force acts at an angle of $35\degree$ above the line of greatest slope of the plane (see diagram). The coefficient of friction between the block and the plane is 0.4. The speed of the block when it passes a point $O$ is $2\text{ m s}^{-1}$. Find the speed of the block when it has moved 3 m down the plane from $O$.
A particle starts from rest at a point $O$. The acceleration of the particle at time $t$ s after leaving $O$ is $a\text{ m s}^{-2}$, where $a = 2(t+1)^{-\frac{1}{2}} - 1$ for $t \geqslant 0$. Find the distance that the particle travels from $O$ until the time at which its acceleration is zero.
Four coplanar forces of magnitudes 20 N, 30 N, 15 N and 25 N act at a point $P$ in the directions shown in Fig. 7.1. The forces act in a vertical plane. The resultant of these forces has magnitude $S$ N and acts at an angle $\alpha\degree$ below the horizontal as shown in Fig. 7.2.
Find the value of $S$ and the value of $\alpha$.
A small ring of mass 0.6 kg is threaded on a rough straight horizontal wire. The four forces shown in Fig. 7.1 act on the ring and are in the same vertical plane as the wire. The ring starts from rest and takes 3 s to travel a distance of 2 m along the wire. Find the coefficient of friction between the ring and the wire.