AP Physics · Practice Sheet 7

1. 1.

   Physics

   Find the force required to accelerate a 8 kg mass at 4 m/s².

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

   $F = ma$

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2. 2.

   Mathematics

   Find the sum of the first 6 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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3. 3.

   Physics

   A force of 851 N acts on an area of 40 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Mathematics

   If f(x) = 3x³ + 1x² + 7x, find f′(5).

   Formula:Derivative of a Polynomial

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

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5. 5.

   Mathematics

   Evaluate ∫ from 1 to 5 of 2x^1 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.

   Physics

   Find the density of an object with mass 260 g and volume 30 cm³.

   Formula:Density

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

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7. 7.

   Physics

   Find the electrical power when 37 V drives a current of 12 A.

   Formula:Electrical Power

   $P = VI$

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8. 8.

   Physics

   Find the force required to accelerate a 31 kg mass at 5 m/s².

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

   $F = ma$

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9. 9.

   Physics

   If 1,987 J of work is done in 46 s, find the power.

   Formula:Power

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

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10. 10.

    Physics

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

    Formula:Ohm's Law

    $V = IR$

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11. 11.

    Mathematics

    Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.

    Formula:Binomial Coefficient

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

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12. 12.

    Mathematics

    For the quadratic 4x² − 9x − 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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13. 13.

    Mathematics

    Evaluate log base 10 of 1,000,000.

    Formula:Logarithm Evaluation

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

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14. 14.

    Mathematics

    For the quadratic 4x² − 8x + 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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15. 15.

    Mathematics

    Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.

    Formula:Binomial Coefficient

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

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16. 16.

    Mathematics

    If f(x) = 4x³ + 6x² + 8x, find f′(3).

    Formula:Derivative of a Polynomial

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

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17. 17.

    Physics

    Find the force required to accelerate a 36 kg mass at 12 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, 5) and (-7, -2).

    Formula:Slope of a Line

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

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19. 19.

    Physics

    Find the electrical power when 10 V drives a current of 13 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    Physics

    Find the voltage across a 20 Ω resistor carrying a current of 17 A.

    Formula:Ohm's Law

    $V = IR$

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