A-Level Physics · Practice Sheet 50

1. 1.

   Physics

   Find the voltage across a 16 Ω resistor carrying a current of 18 A.

   Formula:Ohm's Law

   $V = IR$

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2. 2.

   Mathematics

   Find the sum of the first 22 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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3. 3.

   Mathematics

   Evaluate ∫ from 1 to 4 of 5x^2 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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4. 4.

   Physics

   An object starts at 14 m/s and accelerates at 8 m/s² for 4 s. Find its final velocity.

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

   $v = u + at$

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5. 5.

   Mathematics

   For the quadratic 1x² + 2x − 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

   If 2,704 J of work is done in 5 s, find the power.

   Formula:Power

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

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7. 7.

   Physics

   Find the electrical power when 66 V drives a current of 1 A.

   Formula:Electrical Power

   $P = VI$

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8. 8.

   Mathematics

   In an arithmetic progression with first term 8 and common difference 7, find term number 10.

   Formula:AP nth Term

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

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9. 9.

   Mathematics

   Evaluate log base 3 of 729.

   Formula:Logarithm Evaluation

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

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10. 10.

    Mathematics

    Find term number 6 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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11. 11.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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12. 12.

    Mathematics

    Evaluate ∫ from 1 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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13. 13.

    Physics

    Find the momentum of a 12 kg body moving at 29 m/s.

    Formula:Linear Momentum

    $p = mv$

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14. 14.

    Physics

    A constant force of 141 N moves an object 11 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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15. 15.

    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation

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

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16. 16.

    Physics

    Find the force required to accelerate a 45 kg mass at 17 m/s².

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

    $F = ma$

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17. 17.

    Physics

    Find the momentum of a 32 kg body moving at 9 m/s.

    Formula:Linear Momentum

    $p = mv$

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18. 18.

    Physics

    If 4,146 J of work is done in 45 s, find the power.

    Formula:Power

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

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19. 19.

    Physics

    A projectile is launched at 32 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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20. 20.

    Physics

    Find the electrical power when 238 V drives a current of 5 A.

    Formula:Electrical Power

    $P = VI$

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