A-Level Physics · Practice Sheet 25

1. 1.

   Mathematics

   For the quadratic 3x² − 5x + 6 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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2. 2.

   Physics

   A constant force of 48 N moves an object 48 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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3. 3.

   Mathematics

   If f(x) = 3x³ + 6x² + 1x, 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 sum of the first 22 terms of an AP with first term 5 and common difference 9.

   Formula:AP Sum of n Terms

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

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5. 5.

   Mathematics

   Find term number 7 of a geometric progression with first term 1 and common ratio 2.

   Formula:GP nth Term

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

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6. 6.

   Physics

   Find the momentum of a 15 kg body moving at 24 m/s.

   Formula:Linear Momentum

   $p = mv$

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7. 7.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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8. 8.

   Mathematics

   Evaluate log base 10 of 100.

   Formula:Logarithm Evaluation

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

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9. 9.

   Physics

   A constant force of 140 N moves an object 34 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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10. 10.

    Mathematics

    Find the slope of the line through (-5, -1) and (0, 8).

    Formula:Slope of a Line

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

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11. 11.

    Physics

    Find the kinetic energy of a 18 kg object moving at 18 m/s.

    Formula:Kinetic Energy

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

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12. 12.

    Mathematics

    Find the binomial coefficient C(5, 4) — the coefficient of x^4 in (1 + x)^5.

    Formula:Binomial Coefficient

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

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13. 13.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 2 and common ratio 3.

    Formula:GP Sum of n Terms

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

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14. 14.

    Mathematics

    Find the slope of the line through (-7, -6) and (7, 2).

    Formula:Slope of a Line

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

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15. 15.

    Physics

    A body moving at 3 m/s accelerates at 5 m/s² for 6 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.

    Physics

    Find the force required to accelerate a 8 kg mass at 18 m/s².

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

    $F = ma$

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17. 17.

    Mathematics

    Evaluate log base 5 of 15,625.

    Formula:Logarithm Evaluation

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

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18. 18.

    Physics

    Find the force required to accelerate a 27 kg mass at 4 m/s².

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

    $F = ma$

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19. 19.

    Physics

    Find the electrical power when 230 V drives a current of 17 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    Physics

    Find the density of an object with mass 382 g and volume 26 cm³.

    Formula:Density

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

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