A-Level Physics · Practice Sheet 36

1. 1.

   Physics

   A projectile is launched at 17 m/s at 45° 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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2. 2.

   Physics

   Find the kinetic energy of a 11 kg object moving at 7 m/s.

   Formula:Kinetic Energy

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

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3. 3.

   Mathematics

   Evaluate log base 2 of 8.

   Formula:Logarithm Evaluation

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

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4. 4.

   Physics

   A constant force of 53 N moves an object 45 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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5. 5.

   Physics

   Find the electrical power when 154 V drives a current of 18 A.

   Formula:Electrical Power

   $P = VI$

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6. 6.

   Physics

   A constant force of 26 N moves an object 38 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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7. 7.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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8. 8.

   Mathematics

   Find term number 7 of a geometric progression with first term 3 and common ratio 2.

   Formula:GP nth Term

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

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9. 9.

   Mathematics

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

   Formula:GP Sum of n Terms

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

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10. 10.

    Physics

    Find the density of an object with mass 335 g and volume 49 cm³.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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11. 11.

    Physics

    A force of 95 N acts on an area of 9 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Mathematics

    Find the sum of the first 13 terms of an AP with first term 7 and common difference 8.

    Formula:AP Sum of n Terms

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

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13. 13.

    Physics

    Find the density of an object with mass 351 g and volume 15 cm³.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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14. 14.

    Mathematics

    Evaluate log base 3 of 729.

    Formula:Logarithm Evaluation

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

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15. 15.

    Physics

    A body moving at 12 m/s accelerates at 7 m/s² for 8 s. Find the distance travelled.

    Formula:Equation of Motion (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^{2}$

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16. 16.

    Mathematics

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

    Formula:Distance Between Two Points

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

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17. 17.

    Mathematics

    Evaluate ∫ from 1 to 3 of 5x^1 dx.

    Formula:Definite Integral of a Power

    $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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18. 18.

    Mathematics

    Find the binomial coefficient C(9, 2) — the coefficient of x^2 in (1 + x)^9.

    Formula:Binomial Coefficient

    $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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19. 19.

    Physics

    Calculate the potential energy of a 6 kg object at a height of 33 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Physics

    Find the momentum of a 38 kg body moving at 31 m/s.

    Formula:Linear Momentum

    $p = mv$

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