A-Level Physics · Practice Sheet 6

1. 1.

   Physics

   Calculate the potential energy of a 20 kg object at a height of 22 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Mathematics

   Evaluate log base 5 of 25.

   Formula:Logarithm Evaluation

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

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3. 3.

   Mathematics

   If f(x) = 3x³ + 5x² + 7x, find f′(1).

   Formula:Derivative of a Polynomial

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

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4. 4.

   Mathematics

   Find the distance between the points (8, 1) and (-2, 2).

   Formula:Distance Between Two Points

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

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5. 5.

   Mathematics

   Find the binomial coefficient C(6, 4) — the coefficient of x^4 in (1 + x)^6.

   Formula:Binomial Coefficient

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

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6. 6.

   Physics

   A constant force of 24 N moves an object 35 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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7. 7.

   Mathematics

   In an arithmetic progression with first term 19 and common difference 6, find term number 9.

   Formula:AP nth Term

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

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8. 8.

   Physics

   Calculate the potential energy of a 47 kg object at a height of 47 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Physics

   Find the momentum of a 41 kg body moving at 40 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Mathematics

    Find the binomial coefficient C(6, 2) — the coefficient of x^2 in (1 + x)^6.

    Formula:Binomial Coefficient

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

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11. 11.

    Mathematics

    Find the sum of the first 18 terms of an AP with first term 8 and common difference 2.

    Formula:AP Sum of n Terms

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

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12. 12.

    Mathematics

    Find the distance between the points (6, 2) and (3, 3).

    Formula:Distance Between Two Points

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

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13. 13.

    Mathematics

    Evaluate ∫ from 0 to 5 of 1x^3 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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14. 14.

    Mathematics

    Find the slope of the line through (-6, 3) and (6, -8).

    Formula:Slope of a Line

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

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15. 15.

    Physics

    Find the momentum of a 40 kg body moving at 38 m/s.

    Formula:Linear Momentum

    $p = mv$

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16. 16.

    Physics

    A body moving at 13 m/s accelerates at 6 m/s² for 4 s. Find the distance travelled.

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

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

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17. 17.

    Physics

    An object starts at 6 m/s and accelerates at 4 m/s² for 7 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

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18. 18.

    Mathematics

    Find the sum of the first 22 terms of an AP with first term 15 and common difference 8.

    Formula:AP Sum of n Terms

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

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19. 19.

    Mathematics

    Find term number 3 of a geometric progression with first term 5 and common ratio 2.

    Formula:GP nth Term

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

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20. 20.

    Mathematics

    Find the sum of the first 14 terms of an AP with first term 18 and common difference 5.

    Formula:AP Sum of n Terms

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

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