AP Physics · Practice Sheet 12

1. 1.

   Physics

   Find the kinetic energy of a 17 kg object moving at 9 m/s.

   Formula:Kinetic Energy

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

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2. 2.

   Mathematics

   For the quadratic 1x² − 3x − 6 = 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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3. 3.

   Physics

   A constant force of 35 N moves an object 10 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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4. 4.

   Physics

   An object starts at 16 m/s and accelerates at 2 m/s² for 10 s. Find its final velocity.

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

   $v = u + at$

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5. 5.

   Physics

   A constant force of 68 N moves an object 4 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 sum of the first 7 terms of an AP with first term 6 and common difference 5.

   Formula:AP Sum of n Terms

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

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7. 7.

   Mathematics

   If f(x) = 1x³ + 4x² + 8x, find f′(4).

   Formula:Derivative of a Polynomial

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

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8. 8.

   Mathematics

   Find term number 4 of a geometric progression with first term 3 and common ratio 3.

   Formula:GP nth Term

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

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9. 9.

   Physics

   Find the electrical power when 167 V drives a current of 5 A.

   Formula:Electrical Power

   $P = VI$

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10. 10.

    Mathematics

    If f(x) = 3x³ + 6x² + 8x, find f′(2).

    Formula:Derivative of a Polynomial

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

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11. 11.

    Mathematics

    For the quadratic 4x² − 9x + 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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12. 12.

    Mathematics

    In an arithmetic progression with first term 17 and common difference 6, find term number 27.

    Formula:AP nth Term

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

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13. 13.

    Mathematics

    Evaluate ∫ from 2 to 4 of 4x^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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14. 14.

    Mathematics

    Find the sum of the first 5 terms of an AP with first term 2 and common difference 10.

    Formula:AP Sum of n Terms

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

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15. 15.

    Physics

    Find the density of an object with mass 277 g and volume 40 cm³.

    Formula:Density

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

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16. 16.

    Mathematics

    For the quadratic 3x² − 2x − 6 = 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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17. 17.

    Physics

    Find the voltage across a 47 Ω resistor carrying a current of 11 A.

    Formula:Ohm's Law

    $V = IR$

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18. 18.

    Mathematics

    Find the sum of the first 19 terms of an AP with first term 12 and common difference 5.

    Formula:AP Sum of n Terms

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

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19. 19.

    Mathematics

    Evaluate ∫ from 1 to 4 of 5x^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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20. 20.

    Physics

    Find the force required to accelerate a 15 kg mass at 17 m/s².

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

    $F = ma$

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