AP Physics · Practice Sheet 50

1. 1.

   Physics

   Calculate the potential energy of a 11 kg object at a height of 46 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Mathematics

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

   Formula:Slope of a Line

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

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3. 3.

   Mathematics

   In an arithmetic progression with first term 9 and common difference 8, find term number 5.

   Formula:AP nth Term

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

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4. 4.

   Mathematics

   Find the sum of the first 8 terms of an AP with first term 5 and common difference 8.

   Formula:AP Sum of n Terms

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

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5. 5.

   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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6. 6.

   Mathematics

   In an arithmetic progression with first term 10 and common difference 10, find term number 21.

   Formula:AP nth Term

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

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7. 7.

   Physics

   Find the kinetic energy of a 8 kg object moving at 20 m/s.

   Formula:Kinetic Energy

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

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8. 8.

   Mathematics

   Find the distance between the points (1, 8) and (1, 7).

   Formula:Distance Between Two Points

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

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9. 9.

   Physics

   A force of 404 N acts on an area of 32 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Mathematics

    If f(x) = 4x³ + 6x² + 9x, find f′(3).

    Formula:Derivative of a Polynomial

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

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11. 11.

    Mathematics

    Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.

    Formula:Binomial Coefficient

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

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12. 12.

    Mathematics

    Evaluate log base 5 of 125.

    Formula:Logarithm Evaluation

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

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13. 13.

    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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14. 14.

    Mathematics

    Find the slope of the line through (-5, -4) and (-6, -4).

    Formula:Slope of a Line

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

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15. 15.

    Physics

    Find the density of an object with mass 383 g and volume 22 cm³.

    Formula:Density

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

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16. 16.

    Mathematics

    For the quadratic 3x² + 1x + 8 = 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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17. 17.

    Mathematics

    In an arithmetic progression with first term 18 and common difference 5, find term number 30.

    Formula:AP nth Term

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

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18. 18.

    Mathematics

    Find term number 3 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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19. 19.

    Mathematics

    For the quadratic 3x² − 9x − 2 = 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.

    Mathematics

    Find the slope of the line through (7, 3) and (-8, 7).

    Formula:Slope of a Line

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

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