AP Physics · Practice Sheet 32

1. 1.

   Physics

   A projectile is launched at 27 m/s at 45° 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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2. 2.

   Mathematics

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

   Formula:Slope of a Line

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

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3. 3.

   Mathematics

   In an arithmetic progression with first term 2 and common difference 6, find term number 10.

   Formula:AP nth Term

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

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4. 4.

   Mathematics

   Find the sum of the first 21 terms of an AP with first term 13 and common difference 8.

   Formula:AP Sum of n Terms

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

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5. 5.

   Physics

   Find the kinetic energy of a 11 kg object moving at 3 m/s.

   Formula:Kinetic Energy

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

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6. 6.

   Physics

   Find the density of an object with mass 283 g and volume 24 cm³.

   Formula:Density

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

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7. 7.

   Physics

   Find the voltage across a 25 Ω resistor carrying a current of 17 A.

   Formula:Ohm's Law

   $V = IR$

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8. 8.

   Physics

   A body moving at 14 m/s accelerates at 4 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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9. 9.

   Physics

   Find the momentum of a 35 kg body moving at 22 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Mathematics

    Find the slope of the line through (-6, -6) and (-1, -1).

    Formula:Slope of a Line

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

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11. 11.

    Physics

    Find the kinetic energy of a 16 kg object moving at 12 m/s.

    Formula:Kinetic Energy

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

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12. 12.

    Physics

    If 4,398 J of work is done in 36 s, find the power.

    Formula:Power

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

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13. 13.

    Mathematics

    Find the slope of the line through (5, 0) and (-5, -5).

    Formula:Slope of a Line

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

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14. 14.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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15. 15.

    Mathematics

    Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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16. 16.

    Physics

    Find the kinetic energy of a 11 kg object moving at 19 m/s.

    Formula:Kinetic Energy

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

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17. 17.

    Mathematics

    Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.

    Formula:Binomial Coefficient

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

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18. 18.

    Mathematics

    Find the sum of the first 3 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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19. 19.

    Mathematics

    Evaluate ∫ from 1 to 5 of 2x^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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20. 20.

    Mathematics

    For the quadratic 2x² − 5x + 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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