A-Level Physics · Practice Sheet 14

1. 1.

   Physics

   Calculate the potential energy of a 35 kg object at a height of 12 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Mathematics

   Evaluate log base 10 of 100.

   Formula:Logarithm Evaluation

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

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3. 3.

   Mathematics

   For the quadratic 2x² − 5x + 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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4. 4.

   Physics

   Find the force required to accelerate a 25 kg mass at 12 m/s².

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

   $F = ma$

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5. 5.

   Mathematics

   If f(x) = 3x³ + 1x² + 6x, find f′(2).

   Formula:Derivative of a Polynomial

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

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6. 6.

   Physics

   Find the electrical power when 172 V drives a current of 16 A.

   Formula:Electrical Power

   $P = VI$

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7. 7.

   Mathematics

   Evaluate ∫ from 1 to 4 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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8. 8.

   Mathematics

   Find the slope of the line through (-3, 5) and (-6, -3).

   Formula:Slope of a Line

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

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9. 9.

   Physics

   Find the momentum of a 26 kg body moving at 33 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Physics

    Find the force required to accelerate a 21 kg mass at 14 m/s².

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

    $F = ma$

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11. 11.

    Mathematics

    Find term number 6 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term

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

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12. 12.

    Physics

    Find the voltage across a 46 Ω resistor carrying a current of 12 A.

    Formula:Ohm's Law

    $V = IR$

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13. 13.

    Mathematics

    Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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14. 14.

    Mathematics

    Find the sum of the first 23 terms of an AP with first term 15 and common difference 4.

    Formula:AP Sum of n Terms

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

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15. 15.

    Mathematics

    If f(x) = 4x³ + 2x² + 8x, find f′(2).

    Formula:Derivative of a Polynomial

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

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16. 16.

    Physics

    If 4,088 J of work is done in 26 s, find the power.

    Formula:Power

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

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17. 17.

    Mathematics

    For the quadratic 2x² + 0x − 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.

    Physics

    A body moving at 7 m/s accelerates at 8 m/s² for 4 s. Find the distance travelled.

    Formula:Equation of Motion (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^{2}$

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19. 19.

    Physics

    Find the force required to accelerate a 32 kg mass at 3 m/s².

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

    $F = ma$

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20. 20.

    Mathematics

    Find the binomial coefficient C(7, 4) — the coefficient of x^4 in (1 + x)^7.

    Formula:Binomial Coefficient

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

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