AP Physics · Practice Sheet 15

1. 1.

   Physics

   Find the density of an object with mass 90 g and volume 34 cm³.

   Formula:Density

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

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2. 2.

   Mathematics

   If f(x) = 2x³ + 4x² + 1x, find f′(1).

   Formula:Derivative of a Polynomial

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

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3. 3.

   Physics

   Find the voltage across a 13 Ω resistor carrying a current of 11 A.

   Formula:Ohm's Law

   $V = IR$

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4. 4.

   Mathematics

   Find the sum of the first 5 terms of a GP with first term 5 and common ratio 2.

   Formula:GP Sum of n Terms

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

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5. 5.

   Mathematics

   Find the slope of the line through (-8, -6) and (8, 5).

   Formula:Slope of a Line

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

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6. 6.

   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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7. 7.

   Mathematics

   In an arithmetic progression with first term 14 and common difference 9, find term number 20.

   Formula:AP nth Term

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

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8. 8.

   Physics

   Find the electrical power when 25 V drives a current of 6 A.

   Formula:Electrical Power

   $P = VI$

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9. 9.

   Mathematics

   Find the slope of the line through (5, 4) and (8, 7).

   Formula:Slope of a Line

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

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10. 10.

    Mathematics

    Find the sum of the first 25 terms of an AP with first term 14 and common difference 2.

    Formula:AP Sum of n Terms

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

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11. 11.

    Mathematics

    Evaluate log base 2 of 4.

    Formula:Logarithm Evaluation

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

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12. 12.

    Physics

    A constant force of 12 N moves an object 28 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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13. 13.

    Physics

    Calculate the potential energy of a 43 kg object at a height of 36 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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15. 15.

    Physics

    A body moving at 12 m/s accelerates at 7 m/s² for 2 s. Find the distance travelled.

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

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

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16. 16.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 1 and common ratio 3.

    Formula:GP Sum of n Terms

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

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17. 17.

    Mathematics

    Evaluate log base 3 of 27.

    Formula:Logarithm Evaluation

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

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18. 18.

    Physics

    A force of 926 N acts on an area of 32 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Mathematics

    Find the sum of the first 20 terms of an AP with first term 8 and common difference 10.

    Formula:AP Sum of n Terms

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

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20. 20.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 3 and common ratio 3.

    Formula:GP Sum of n Terms

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

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