A-Level Physics · Practice Sheet 13

1. 1.

   Mathematics

   Find the binomial coefficient C(8, 3) — the coefficient of x^3 in (1 + x)^8.

   Formula:Binomial Coefficient

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

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2. 2.

   Mathematics

   For the quadratic 3x² − 3x + 0 = 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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3. 3.

   Physics

   Find the electrical power when 19 V drives a current of 1 A.

   Formula:Electrical Power

   $P = VI$

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4. 4.

   Physics

   A force of 201 N acts on an area of 49 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Physics

   Calculate the potential energy of a 25 kg object at a height of 27 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Mathematics

   Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

   Formula:Binomial Coefficient

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

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7. 7.

   Physics

   Find the voltage across a 44 Ω resistor carrying a current of 14 A.

   Formula:Ohm's Law

   $V = IR$

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8. 8.

   Physics

   Calculate the potential energy of a 14 kg object at a height of 10 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Physics

   Find the force required to accelerate a 30 kg mass at 17 m/s².

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

   $F = ma$

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10. 10.

    Physics

    A constant force of 113 N moves an object 47 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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11. 11.

    Physics

    Find the density of an object with mass 58 g and volume 18 cm³.

    Formula:Density

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

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12. 12.

    Mathematics

    If f(x) = 5x³ + 2x² + 4x, find f′(1).

    Formula:Derivative of a Polynomial

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

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13. 13.

    Physics

    Find the kinetic energy of a 19 kg object moving at 28 m/s.

    Formula:Kinetic Energy

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

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14. 14.

    Mathematics

    Find the sum of the first 22 terms of an AP with first term 7 and common difference 3.

    Formula:AP Sum of n Terms

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

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15. 15.

    Mathematics

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

    Formula:GP nth Term

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

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16. 16.

    Mathematics

    Evaluate log base 5 of 15,625.

    Formula:Logarithm Evaluation

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

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17. 17.

    Mathematics

    For the quadratic 5x² − 6x − 4 = 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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18. 18.

    Mathematics

    Evaluate ∫ from 2 to 4 of 2x^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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19. 19.

    Mathematics

    Find the distance between the points (-5, -8) and (-4, 5).

    Formula:Distance Between Two Points

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

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20. 20.

    Mathematics

    In an arithmetic progression with first term 11 and common difference 9, find term number 21.

    Formula:AP nth Term

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

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