A-Level Physics · Practice Sheet 34

1. 1.

   Physics

   Find the density of an object with mass 328 g and volume 35 cm³.

   Formula:Density

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

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2. 2.

   Mathematics

   For the quadratic 5x² − 7x − 1 = 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.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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4. 4.

   Physics

   Calculate the potential energy of a 29 kg object at a height of 28 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Mathematics

   Find the slope of the line through (4, -2) and (5, 6).

   Formula:Slope of a Line

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

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6. 6.

   Mathematics

   Evaluate ∫ from 2 to 3 of 4x^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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7. 7.

   Physics

   Find the kinetic energy of a 5 kg object moving at 10 m/s.

   Formula:Kinetic Energy

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

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8. 8.

   Mathematics

   Find term number 5 of a geometric progression with first term 4 and common ratio 3.

   Formula:GP nth Term

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

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9. 9.

   Mathematics

   Find the sum of the first 23 terms of an AP with first term 6 and common difference 1.

   Formula:AP Sum of n Terms

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

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10. 10.

    Physics

    A constant force of 115 N moves an object 32 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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11. 11.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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12. 12.

    Mathematics

    Find the slope of the line through (3, -8) and (-2, 6).

    Formula:Slope of a Line

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

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13. 13.

    Mathematics

    Evaluate log base 2 of 8.

    Formula:Logarithm Evaluation

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

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14. 14.

    Physics

    A projectile is launched at 17 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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15. 15.

    Physics

    A force of 543 N acts on an area of 24 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Physics

    A projectile is launched at 33 m/s at 60° 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.

    Physics

    Find the voltage across a 48 Ω resistor carrying a current of 1 A.

    Formula:Ohm's Law

    $V = IR$

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18. 18.

    Physics

    Find the force required to accelerate a 15 kg mass at 9 m/s².

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

    $F = ma$

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19. 19.

    Physics

    Find the electrical power when 163 V drives a current of 14 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    Mathematics

    For the quadratic 2x² + 4x − 5 = 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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