AP Physics · Practice Sheet 24

1. 1.

   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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2. 2.

   Mathematics

   Find the slope of the line through (-8, -6) and (7, -5).

   Formula:Slope of a Line

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

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3. 3.

   Physics

   If 4,427 J of work is done in 2 s, find the power.

   Formula:Power

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

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4. 4.

   Mathematics

   Find term number 6 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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5. 5.

   Physics

   A body moving at 12 m/s accelerates at 4 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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6. 6.

   Physics

   Find the force required to accelerate a 5 kg mass at 13 m/s².

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

   $F = ma$

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7. 7.

   Physics

   Find the electrical power when 218 V drives a current of 17 A.

   Formula:Electrical Power

   $P = VI$

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8. 8.

   Physics

   Find the force required to accelerate a 40 kg mass at 19 m/s².

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

   $F = ma$

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9. 9.

   Mathematics

   Evaluate log base 2 of 64.

   Formula:Logarithm Evaluation

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

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10. 10.

    Physics

    Calculate the potential energy of a 10 kg object at a height of 25 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Physics

    Find the kinetic energy of a 16 kg object moving at 28 m/s.

    Formula:Kinetic Energy

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

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12. 12.

    Mathematics

    Find the distance between the points (6, 3) and (-5, -6).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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13. 13.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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14. 14.

    Mathematics

    Find the sum of the first 22 terms of an AP with first term 5 and common difference 3.

    Formula:AP Sum of n Terms

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

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15. 15.

    Mathematics

    Find the slope of the line through (-3, -1) and (-6, 7).

    Formula:Slope of a Line

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

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16. 16.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 1 and common ratio 2.

    Formula:GP Sum of n Terms

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

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17. 17.

    Physics

    Find the kinetic energy of a 4 kg object moving at 27 m/s.

    Formula:Kinetic Energy

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

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18. 18.

    Mathematics

    If f(x) = 5x³ + 4x² + 9x, find f′(1).

    Formula:Derivative of a Polynomial

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

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19. 19.

    Mathematics

    For the quadratic 4x² − 3x + 1 = 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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20. 20.

    Physics

    Find the electrical power when 129 V drives a current of 15 A.

    Formula:Electrical Power

    $P = VI$

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