Physics & Maths — past paper.pdf

Lee las preguntas con las respuestas a la vista. Nada que corregir.

1. 1

   A car accelerates uniformly from rest at $3\,\text{m/s}^2$ for $4\,\text{s}$. What is its final velocity?

   • a)$7\,\text{m/s}$
   • b)$12\,\text{m/s}$
   • c)$0.75\,\text{m/s}$
   • d)$48\,\text{m/s}$

   Using $v = u + at$ with $u = 0$: $v = 3 \times 4 = 12\,\text{m/s}$.

2. 2

   Newton’s second law is usually written as:

   • a)$F = ma$
   • b)$F = mv$
   • c)$F = \frac{m}{a}$
   • d)$F = m + a$

   Resultant force equals mass times acceleration.

3. 3

   What is the kinetic energy of a $2\,\text{kg}$ mass moving at $3\,\text{m/s}$?

   • a)$6\,\text{J}$
   • b)$9\,\text{J}$
   • c)$18\,\text{J}$
   • d)$3\,\text{J}$

   $E_k = \tfrac{1}{2}mv^2 = 0.5 \times 2 \times 9 = 9\,\text{J}$.

4. 4

   Solve for $x$: $2x + 7 = 19$.

   • a)$x = 5$
   • b)$x = 6$
   • c)$x = 12$
   • d)$x = 13$

   Subtract 7 to get $2x = 12$, then divide by 2.

5. 5

   What are the roots of $x^2 - 5x + 6 = 0$?

   • a)$x = 1$ and $x = 6$
   • b)$x = 2$ and $x = 3$
   • c)$x = -2$ and $x = -3$
   • d)$x = 0$ and $x = 5$

   It factorises to $(x-2)(x-3) = 0$.

6. 6

   Ohm’s law relates voltage, current and resistance as:

   • a)$V = IR$
   • b)$V = \frac{I}{R}$
   • c)$V = I + R$
   • d)$V = I^2R^2$

   Voltage is the product of current and resistance.

7. 7

   A $12\,\text{V}$ supply drives $2\,\text{A}$ through a resistor. What is its resistance?

   • a)$24\,\Omega$
   • b)$6\,\Omega$
   • c)$10\,\Omega$
   • d)$0.17\,\Omega$

   Rearranging $V = IR$ gives $R = V/I = 12/2 = 6\,\Omega$.

8. 8

   In a right-angled triangle, $\sin\theta$ is defined as:

   • a)$\frac{\text{opposite}}{\text{hypotenuse}}$
   • b)$\frac{\text{adjacent}}{\text{hypotenuse}}$
   • c)$\frac{\text{opposite}}{\text{adjacent}}$
   • d)$\frac{\text{hypotenuse}}{\text{opposite}}$

   Opposite over hypotenuse — the "SOH" of SOH-CAH-TOA.

9. 9

   A wave has frequency $50\,\text{Hz}$ and wavelength $4\,\text{m}$. What is its speed?

   • a)$54\,\text{m/s}$
   • b)$200\,\text{m/s}$
   • c)$12.5\,\text{m/s}$
   • d)$0.08\,\text{m/s}$

   $v = f\lambda = 50 \times 4 = 200\,\text{m/s}$.

10. 10

    A $5\,\text{kg}$ box is pushed with $20\,\text{N}$ against $5\,\text{N}$ of friction. What is its acceleration?

    • a)$4\,\text{m/s}^2$
    • b)$3\,\text{m/s}^2$
    • c)$5\,\text{m/s}^2$
    • d)$1\,\text{m/s}^2$

    Resultant force is $20 - 5 = 15\,\text{N}$, so $a = F/m = 15/5 = 3\,\text{m/s}^2$.