AP Physics · Practice Sheet 10

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.

   Physics

   A body moving at 15 m/s accelerates at 6 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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3. 3.

   Physics

   A projectile is launched at 26 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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4. 4.

   Physics

   A constant force of 19 N moves an object 48 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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5. 5.

   Mathematics

   For the quadratic 1x² + 1x − 9 = 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.

   Mathematics

   Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.

   Formula:Binomial Coefficient

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

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7. 7.

   Mathematics

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

   Formula:Slope of a Line

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

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8. 8.

   Physics

   Find the density of an object with mass 378 g and volume 16 cm³.

   Formula:Density

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

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9. 9.

   Physics

   An object starts at 12 m/s and accelerates at 10 m/s² for 5 s. Find its final velocity.

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

   $v = u + at$

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10. 10.

    Mathematics

    For the quadratic 4x² + 7x + 4 = 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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11. 11.

    Physics

    A force of 541 N acts on an area of 18 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Physics

    A body moving at 6 m/s accelerates at 5 m/s² for 10 s. Find the distance travelled.

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

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

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13. 13.

    Mathematics

    Find the sum of the first 6 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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14. 14.

    Physics

    If 4,028 J of work is done in 11 s, find the power.

    Formula:Power

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

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15. 15.

    Physics

    Find the momentum of a 30 kg body moving at 19 m/s.

    Formula:Linear Momentum

    $p = mv$

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16. 16.

    Mathematics

    In an arithmetic progression with first term 5 and common difference 4, find term number 7.

    Formula:AP nth Term

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

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17. 17.

    Mathematics

    Find the distance between the points (0, 0) and (-5, 0).

    Formula:Distance Between Two Points

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

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18. 18.

    Mathematics

    If f(x) = 5x³ + 3x² + 7x, find f′(5).

    Formula:Derivative of a Polynomial

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

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19. 19.

    Physics

    Find the momentum of a 41 kg body moving at 12 m/s.

    Formula:Linear Momentum

    $p = mv$

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20. 20.

    Mathematics

    Find the sum of the first 20 terms of an AP with first term 3 and common difference 2.

    Formula:AP Sum of n Terms

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

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