A-Level Physics · Practice Sheet 21

1. 1.

   Mathematics

   Find the sum of the first 7 terms of a GP with first term 6 and common ratio 3.

   Formula:GP Sum of n Terms

   $S_n = a\,\dfrac{r^{n}-1}{r-1}$

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2. 2.

   Mathematics

   If f(x) = 4x³ + 1x² + 6x, find f′(2).

   Formula:Derivative of a Polynomial

   $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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3. 3.

   Mathematics

   Evaluate log base 5 of 25.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

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4. 4.

   Mathematics

   Find the slope of the line through (5, -7) and (-5, 5).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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5. 5.

   Physics

   Find the momentum of a 25 kg body moving at 21 m/s.

   Formula:Linear Momentum

   $p = mv$

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6. 6.

   Physics

   Find the kinetic energy of a 8 kg object moving at 5 m/s.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2}mv^{2}$

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7. 7.

   Mathematics

   In an arithmetic progression with first term 10 and common difference 10, find term number 17.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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8. 8.

   Mathematics

   Find the sum of the first 6 terms of an AP with first term 12 and common difference 6.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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9. 9.

   Mathematics

   Find term number 6 of a geometric progression with first term 4 and common ratio 3.

   Formula:GP nth Term

   $a_n = a\,r^{\,n-1}$

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10. 10.

    Physics

    Calculate the potential energy of a 15 kg object at a height of 43 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Physics

    If 3,038 J of work is done in 29 s, find the power.

    Formula:Power

    $P = \dfrac{W}{t}$

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12. 12.

    Mathematics

    Find the distance between the points (6, -3) and (5, 8).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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13. 13.

    Physics

    A constant force of 189 N moves an object 15 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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14. 14.

    Physics

    Find the momentum of a 19 kg body moving at 38 m/s.

    Formula:Linear Momentum

    $p = mv$

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15. 15.

    Mathematics

    Find the distance between the points (0, -8) and (1, -8).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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16. 16.

    Physics

    Find the voltage across a 14 Ω resistor carrying a current of 3 A.

    Formula:Ohm's Law

    $V = IR$

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17. 17.

    Physics

    Find the force required to accelerate a 41 kg mass at 6 m/s².

    Formula:Newton's Second Law (F = ma)

    $F = ma$

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18. 18.

    Physics

    A force of 781 N acts on an area of 44 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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19. 19.

    Physics

    A projectile is launched at 25 m/s at 30° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

    $R = \dfrac{u^{2}\sin 2\theta}{g}$

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20. 20.

    Mathematics

    If f(x) = 1x³ + 6x² + 7x, find f′(5).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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