A-Level Physics · Practice Sheet 33

1. 1.

   Physics

   Find the kinetic energy of a 4 kg object moving at 13 m/s.

   Formula:Kinetic Energy

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

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2. 2.

   Physics

   Find the momentum of a 20 kg body moving at 25 m/s.

   Formula:Linear Momentum

   $p = mv$

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3. 3.

   Mathematics

   If f(x) = 5x³ + 2x² + 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

   In an arithmetic progression with first term 15 and common difference 2, find term number 21.

   Formula:AP nth Term

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

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5. 5.

   Mathematics

   Find the slope of the line through (0, -6) and (1, -6).

   Formula:Slope of a Line

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

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6. 6.

   Physics

   A body moving at 5 m/s accelerates at 8 m/s² for 5 s. Find the distance travelled.

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

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

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7. 7.

   Physics

   Find the force required to accelerate a 50 kg mass at 20 m/s².

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

   $F = ma$

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8. 8.

   Mathematics

   If f(x) = 2x³ + 3x² + 1x, find f′(4).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Mathematics

   Evaluate log base 10 of 100.

   Formula:Logarithm Evaluation

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

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10. 10.

    Mathematics

    Find the sum of the first 17 terms of an AP with first term 13 and common difference 4.

    Formula:AP Sum of n Terms

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

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11. 11.

    Mathematics

    Find term number 7 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term

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

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12. 12.

    Mathematics

    Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.

    Formula:Binomial Coefficient

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

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13. 13.

    Physics

    If 3,309 J of work is done in 34 s, find the power.

    Formula:Power

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

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14. 14.

    Physics

    Find the density of an object with mass 315 g and volume 42 cm³.

    Formula:Density

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

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15. 15.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 1 and common ratio 3.

    Formula:GP Sum of n Terms

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

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16. 16.

    Mathematics

    In an arithmetic progression with first term 14 and common difference 1, find term number 25.

    Formula:AP nth Term

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

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17. 17.

    Physics

    A body moving at 9 m/s accelerates at 5 m/s² for 2 s. Find the distance travelled.

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

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

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18. 18.

    Mathematics

    In an arithmetic progression with first term 13 and common difference 2, find term number 21.

    Formula:AP nth Term

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

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19. 19.

    Physics

    An object starts at 11 m/s and accelerates at 7 m/s² for 9 s. Find its final velocity.

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

    $v = u + at$

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20. 20.

    Mathematics

    Find the slope of the line through (2, -5) and (-5, 2).

    Formula:Slope of a Line

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

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