AP Physics · Practice Sheet 27

1. 1.

   Mathematics

   Find the sum of the first 6 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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2. 2.

   Mathematics

   Find the slope of the line through (7, -5) and (-2, 7).

   Formula:Slope of a Line

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

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3. 3.

   Mathematics

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

   Formula:GP Sum of n Terms

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

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4. 4.

   Physics

   Calculate the potential energy of a 13 kg object at a height of 41 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   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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6. 6.

   Physics

   Calculate the potential energy of a 5 kg object at a height of 38 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Mathematics

   If f(x) = 5x³ + 1x² + 3x, find f′(3).

   Formula:Derivative of a Polynomial

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

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8. 8.

   Mathematics

   Evaluate ∫ from 1 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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9. 9.

   Physics

   Find the force required to accelerate a 15 kg mass at 8 m/s².

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

   $F = ma$

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10. 10.

    Mathematics

    Find the slope of the line through (0, -1) and (-8, -6).

    Formula:Slope of a Line

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

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11. 11.

    Physics

    Calculate the potential energy of a 36 kg object at a height of 50 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Physics

    A projectile is launched at 35 m/s at 30° 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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13. 13.

    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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14. 14.

    Physics

    Find the density of an object with mass 38 g and volume 47 cm³.

    Formula:Density

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

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15. 15.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 4 and common ratio 2.

    Formula:GP Sum of n Terms

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

    View formula →
16. 16.

    Physics

    Find the density of an object with mass 262 g and volume 45 cm³.

    Formula:Density

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

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17. 17.

    Physics

    Find the force required to accelerate a 24 kg mass at 13 m/s².

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

    $F = ma$

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18. 18.

    Mathematics

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

    Formula:Slope of a Line

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

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19. 19.

    Physics

    An object starts at 12 m/s and accelerates at 1 m/s² for 11 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

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20. 20.

    Physics

    Calculate the potential energy of a 7 kg object at a height of 31 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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