AP Physics · Practice Sheet 9

1. 1.

   Mathematics

   If f(x) = 1x³ + 5x² + 1x, find f′(4).

   Formula:Derivative of a Polynomial

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

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2. 2.

   Mathematics

   Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

   Formula:Binomial Coefficient

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

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3. 3.

   Physics

   If 4,572 J of work is done in 40 s, find the power.

   Formula:Power

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

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4. 4.

   Mathematics

   Find the sum of the first 20 terms of an AP with first term 4 and common difference 3.

   Formula:AP Sum of n Terms

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

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5. 5.

   Mathematics

   Find the sum of the first 3 terms of a GP with first term 6 and common ratio 3.

   Formula:GP Sum of n Terms

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

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6. 6.

   Mathematics

   Evaluate log base 10 of 100.

   Formula:Logarithm Evaluation

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

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7. 7.

   Physics

   Find the momentum of a 31 kg body moving at 14 m/s.

   Formula:Linear Momentum

   $p = mv$

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8. 8.

   Physics

   Find the electrical power when 211 V drives a current of 4 A.

   Formula:Electrical Power

   $P = VI$

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9. 9.

   Physics

   If 3,115 J of work is done in 12 s, find the power.

   Formula:Power

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

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10. 10.

    Mathematics

    Find the slope of the line through (7, 4) and (4, -8).

    Formula:Slope of a Line

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

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11. 11.

    Physics

    A projectile is launched at 35 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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12. 12.

    Mathematics

    Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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13. 13.

    Physics

    Find the density of an object with mass 283 g and volume 2 cm³.

    Formula:Density

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

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14. 14.

    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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15. 15.

    Physics

    Find the electrical power when 77 V drives a current of 2 A.

    Formula:Electrical Power

    $P = VI$

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16. 16.

    Physics

    A constant force of 68 N moves an object 9 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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17. 17.

    Physics

    A force of 773 N acts on an area of 28 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Physics

    Find the momentum of a 40 kg body moving at 3 m/s.

    Formula:Linear Momentum

    $p = mv$

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19. 19.

    Physics

    Find the kinetic energy of a 1 kg object moving at 25 m/s.

    Formula:Kinetic Energy

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

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20. 20.

    Mathematics

    Evaluate ∫ from 2 to 3 of 1x^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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