AP Physics · Practice Sheet 22

1. 1.

   Mathematics

   Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

   Formula:Binomial Coefficient

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

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2. 2.

   Physics

   Find the electrical power when 94 V drives a current of 3 A.

   Formula:Electrical Power

   $P = VI$

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3. 3.

   Physics

   A body moving at 3 m/s accelerates at 5 m/s² for 9 s. Find the distance travelled.

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

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

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4. 4.

   Physics

   Find the electrical power when 67 V drives a current of 18 A.

   Formula:Electrical Power

   $P = VI$

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5. 5.

   Mathematics

   Evaluate ∫ from 0 to 5 of 5x^2 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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6. 6.

   Mathematics

   In an arithmetic progression with first term 7 and common difference 3, find term number 17.

   Formula:AP nth Term

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

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7. 7.

   Mathematics

   For the quadratic 4x² + 7x − 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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8. 8.

   Mathematics

   If f(x) = 2x³ + 6x² + 7x, find f′(5).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Mathematics

   Find the binomial coefficient C(6, 2) — the coefficient of x^2 in (1 + x)^6.

   Formula:Binomial Coefficient

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

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10. 10.

    Physics

    Find the kinetic energy of a 2 kg object moving at 13 m/s.

    Formula:Kinetic Energy

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

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11. 11.

    Mathematics

    Evaluate log base 3 of 243.

    Formula:Logarithm Evaluation

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

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12. 12.

    Physics

    If 3,954 J of work is done in 45 s, find the power.

    Formula:Power

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

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13. 13.

    Physics

    A force of 735 N acts on an area of 6 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Physics

    Find the voltage across a 35 Ω resistor carrying a current of 11 A.

    Formula:Ohm's Law

    $V = IR$

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15. 15.

    Physics

    Find the density of an object with mass 316 g and volume 41 cm³.

    Formula:Density

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

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16. 16.

    Physics

    Calculate the potential energy of a 16 kg object at a height of 26 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Physics

    Find the force required to accelerate a 50 kg mass at 11 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 (-4, -2) and (-3, -2).

    Formula:Slope of a Line

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

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19. 19.

    Mathematics

    Evaluate log base 2 of 64.

    Formula:Logarithm Evaluation

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

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20. 20.

    Mathematics

    Find the sum of the first 22 terms of an AP with first term 3 and common difference 4.

    Formula:AP Sum of n Terms

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

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