A-Level Physics · Practice Sheet 46

1. 1.

   Mathematics

   Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.

   Formula:Binomial Coefficient

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

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2. 2.

   Physics

   Find the voltage across a 34 Ω resistor carrying a current of 13 A.

   Formula:Ohm's Law

   $V = IR$

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3. 3.

   Mathematics

   Evaluate log base 5 of 25.

   Formula:Logarithm Evaluation

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

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4. 4.

   Physics

   Find the density of an object with mass 132 g and volume 45 cm³.

   Formula:Density

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

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5. 5.

   Mathematics

   Evaluate log base 2 of 4.

   Formula:Logarithm Evaluation

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

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6. 6.

   Physics

   Find the density of an object with mass 485 g and volume 10 cm³.

   Formula:Density

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

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7. 7.

   Physics

   Find the kinetic energy of a 20 kg object moving at 11 m/s.

   Formula:Kinetic Energy

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

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8. 8.

   Physics

   Calculate the potential energy of a 9 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

   A force of 334 N acts on an area of 34 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Mathematics

    For the quadratic 2x² + 6x − 7 = 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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11. 11.

    Mathematics

    In an arithmetic progression with first term 14 and common difference 5, find term number 6.

    Formula:AP nth Term

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

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12. 12.

    Physics

    A force of 600 N acts on an area of 23 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    Physics

    If 3,321 J of work is done in 11 s, find the power.

    Formula:Power

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

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14. 14.

    Physics

    A constant force of 43 N moves an object 50 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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15. 15.

    Physics

    Find the force required to accelerate a 33 kg mass at 10 m/s².

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

    $F = ma$

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16. 16.

    Physics

    A projectile is launched at 38 m/s at 30° 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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17. 17.

    Mathematics

    For the quadratic 1x² + 5x − 9 = 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 log base 2 of 4.

    Formula:Logarithm Evaluation

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

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19. 19.

    Physics

    Find the electrical power when 100 V drives a current of 12 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    Mathematics

    Find the slope of the line through (-7, 6) and (2, -4).

    Formula:Slope of a Line

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

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