AP Physics · Practice Sheet 1

1. 1.

   Physics

   Find the momentum of a 48 kg body moving at 39 m/s.

   Formula:Linear Momentum

   $p = mv$

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2. 2.

   Physics

   If 4,741 J of work is done in 41 s, find the power.

   Formula:Power

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

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3. 3.

   Mathematics

   Find the distance between the points (7, 0) and (-3, -5).

   Formula:Distance Between Two Points

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

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4. 4.

   Physics

   Find the density of an object with mass 180 g and volume 35 cm³.

   Formula:Density

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

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5. 5.

   Mathematics

   Find the binomial coefficient C(8, 3) — the coefficient of x^3 in (1 + x)^8.

   Formula:Binomial Coefficient

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

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6. 6.

   Mathematics

   Find the slope of the line through (-7, -4) and (2, -6).

   Formula:Slope of a Line

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

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7. 7.

   Mathematics

   If f(x) = 4x³ + 6x² + 1x, find f′(5).

   Formula:Derivative of a Polynomial

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

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8. 8.

   Mathematics

   Find the sum of the first 16 terms of an AP with first term 11 and common difference 4.

   Formula:AP Sum of n Terms

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

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9. 9.

   Physics

   Find the force required to accelerate a 28 kg mass at 18 m/s².

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

   $F = ma$

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10. 10.

    Mathematics

    Find the sum of the first 3 terms of a GP with first term 3 and common ratio 3.

    Formula:GP Sum of n Terms

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

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11. 11.

    Physics

    A projectile is launched at 46 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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12. 12.

    Physics

    A force of 220 N acts on an area of 8 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    Mathematics

    For the quadratic 2x² − 5x + 9 = 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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14. 14.

    Mathematics

    Find the distance between the points (-1, -2) and (3, -1).

    Formula:Distance Between Two Points

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

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15. 15.

    Mathematics

    Find term number 3 of a geometric progression with first term 1 and common ratio 2.

    Formula:GP nth Term

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

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16. 16.

    Physics

    Calculate the potential energy of a 33 kg object at a height of 36 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Mathematics

    In an arithmetic progression with first term 3 and common difference 10, find term number 12.

    Formula:AP nth Term

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

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18. 18.

    Mathematics

    Evaluate ∫ from 2 to 5 of 3x^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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19. 19.

    Mathematics

    For the quadratic 4x² + 5x + 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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20. 20.

    Physics

    An object starts at 1 m/s and accelerates at 5 m/s² for 11 s. Find its final velocity.

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

    $v = u + at$

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