A-Level Physics · Practice Sheet 28

1. 1.

   Mathematics

   Evaluate log base 10 of 100,000.

   Formula:Logarithm Evaluation

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

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2. 2.

   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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3. 3.

   Physics

   A constant force of 19 N moves an object 23 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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4. 4.

   Mathematics

   If f(x) = 2x³ + 1x² + 9x, find f′(1).

   Formula:Derivative of a Polynomial

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

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5. 5.

   Mathematics

   For the quadratic 5x² − 6x + 3 = 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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6. 6.

   Physics

   A projectile is launched at 18 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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7. 7.

   Mathematics

   For the quadratic 4x² − 5x + 3 = 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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8. 8.

   Mathematics

   Find the sum of the first 15 terms of an AP with first term 13 and common difference 10.

   Formula:AP Sum of n Terms

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

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9. 9.

   Mathematics

   Evaluate ∫ from 0 to 5 of 3x^1 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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10. 10.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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11. 11.

    Physics

    A force of 839 N acts on an area of 2 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Physics

    Calculate the potential energy of a 42 kg object at a height of 34 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Physics

    Find the momentum of a 2 kg body moving at 20 m/s.

    Formula:Linear Momentum

    $p = mv$

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14. 14.

    Physics

    A constant force of 133 N moves an object 14 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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15. 15.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 4 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

    Find the distance between the points (-5, -6) and (-1, -8).

    Formula:Distance Between Two Points

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

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17. 17.

    Physics

    Find the voltage across a 2 Ω resistor carrying a current of 6 A.

    Formula:Ohm's Law

    $V = IR$

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18. 18.

    Mathematics

    Find the sum of the first 8 terms of an AP with first term 17 and common difference 2.

    Formula:AP Sum of n Terms

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

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19. 19.

    Physics

    An object starts at 15 m/s and accelerates at 4 m/s² for 10 s. Find its final velocity.

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

    $v = u + at$

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20. 20.

    Physics

    Find the kinetic energy of a 18 kg object moving at 27 m/s.

    Formula:Kinetic Energy

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

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