AP Physics · Practice Sheet 41

1. 1.

   Mathematics

   For the quadratic 1x² − 8x + 0 = 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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2. 2.

   Physics

   Find the kinetic energy of a 2 kg object moving at 8 m/s.

   Formula:Kinetic Energy

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

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3. 3.

   Physics

   Find the electrical power when 135 V drives a current of 7 A.

   Formula:Electrical Power

   $P = VI$

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4. 4.

   Physics

   Find the voltage across a 3 Ω resistor carrying a current of 20 A.

   Formula:Ohm's Law

   $V = IR$

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5. 5.

   Physics

   A constant force of 153 N moves an object 26 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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6. 6.

   Mathematics

   Find the distance between the points (-5, -7) and (2, -2).

   Formula:Distance Between Two Points

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

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7. 7.

   Physics

   If 299 J of work is done in 37 s, find the power.

   Formula:Power

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

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8. 8.

   Physics

   A force of 889 N acts on an area of 12 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Physics

   Find the density of an object with mass 406 g and volume 49 cm³.

   Formula:Density

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

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10. 10.

    Mathematics

    In an arithmetic progression with first term 20 and common difference 8, find term number 24.

    Formula:AP nth Term

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

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11. 11.

    Physics

    A force of 546 N acts on an area of 16 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Physics

    A projectile is launched at 20 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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13. 13.

    Physics

    An object starts at 20 m/s and accelerates at 4 m/s² for 3 s. Find its final velocity.

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

    $v = u + at$

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14. 14.

    Mathematics

    Find the sum of the first 7 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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15. 15.

    Mathematics

    If f(x) = 3x³ + 2x² + 4x, find f′(4).

    Formula:Derivative of a Polynomial

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

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16. 16.

    Mathematics

    Find the slope of the line through (-2, 7) and (5, -4).

    Formula:Slope of a Line

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

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17. 17.

    Physics

    An object starts at 9 m/s and accelerates at 6 m/s² for 5 s. Find its final velocity.

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

    $v = u + at$

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18. 18.

    Physics

    A constant force of 53 N moves an object 37 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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19. 19.

    Mathematics

    Evaluate log base 5 of 3,125.

    Formula:Logarithm Evaluation

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

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20. 20.

    Mathematics

    Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

    Formula:Binomial Coefficient

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

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