A-Level Physics · Practice Sheet 3

1. 1.

   Mathematics

   Find term number 7 of a geometric progression with first term 6 and common ratio 2.

   Formula:GP nth Term

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

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2. 2.

   Physics

   A force of 778 N acts on an area of 27 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Physics

   Find the momentum of a 19 kg body moving at 11 m/s.

   Formula:Linear Momentum

   $p = mv$

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4. 4.

   Physics

   A projectile is launched at 45 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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5. 5.

   Mathematics

   Find the sum of the first 12 terms of an AP with first term 12 and common difference 3.

   Formula:AP Sum of n Terms

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

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6. 6.

   Physics

   Find the momentum of a 14 kg body moving at 18 m/s.

   Formula:Linear Momentum

   $p = mv$

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7. 7.

   Physics

   Find the density of an object with mass 348 g and volume 42 cm³.

   Formula:Density

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

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8. 8.

   Mathematics

   If f(x) = 5x³ + 2x² + 3x, find f′(5).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Mathematics

   Find term number 5 of a geometric progression with first term 6 and common ratio 3.

   Formula:GP nth Term

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

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10. 10.

    Physics

    Find the electrical power when 108 V drives a current of 11 A.

    Formula:Electrical Power

    $P = VI$

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11. 11.

    Physics

    Find the momentum of a 32 kg body moving at 15 m/s.

    Formula:Linear Momentum

    $p = mv$

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12. 12.

    Mathematics

    Evaluate ∫ from 0 to 4 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.

    Mathematics

    Find the binomial coefficient C(9, 2) — the coefficient of x^2 in (1 + x)^9.

    Formula:Binomial Coefficient

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

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14. 14.

    Mathematics

    Find term number 7 of a geometric progression with first term 3 and common ratio 3.

    Formula:GP nth Term

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

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15. 15.

    Mathematics

    Find the sum of the first 7 terms of an AP with first term 11 and common difference 5.

    Formula:AP Sum of n Terms

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

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16. 16.

    Physics

    Find the density of an object with mass 483 g and volume 12 cm³.

    Formula:Density

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

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17. 17.

    Mathematics

    Find the sum of the first 9 terms of an AP with first term 8 and common difference 7.

    Formula:AP Sum of n Terms

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

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18. 18.

    Physics

    Find the electrical power when 63 V drives a current of 9 A.

    Formula:Electrical Power

    $P = VI$

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19. 19.

    Physics

    Find the momentum of a 41 kg body moving at 37 m/s.

    Formula:Linear Momentum

    $p = mv$

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20. 20.

    Mathematics

    Evaluate ∫ from 2 to 4 of 5x^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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