AP Physics · Practice Sheet 21

1. 1.

   Mathematics

   Find term number 6 of a geometric progression with first term 2 and common ratio 2.

   Formula:GP nth Term

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

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2. 2.

   Physics

   Find the momentum of a 44 kg body moving at 10 m/s.

   Formula:Linear Momentum

   $p = mv$

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3. 3.

   Mathematics

   Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

   Formula:Binomial Coefficient

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

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4. 4.

   Mathematics

   Find the sum of the first 23 terms of an AP with first term 9 and common difference 7.

   Formula:AP Sum of n Terms

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

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5. 5.

   Mathematics

   In an arithmetic progression with first term 15 and common difference 9, find term number 13.

   Formula:AP nth Term

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

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6. 6.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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7. 7.

   Mathematics

   Evaluate ∫ from 1 to 3 of 4x^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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8. 8.

   Mathematics

   Find the sum of the first 3 terms of a GP with first term 6 and common ratio 3.

   Formula:GP Sum of n Terms

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

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9. 9.

   Mathematics

   Evaluate log base 5 of 125.

   Formula:Logarithm Evaluation

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

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10. 10.

    Physics

    If 3,173 J of work is done in 22 s, find the power.

    Formula:Power

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

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11. 11.

    Physics

    Find the force required to accelerate a 31 kg mass at 4 m/s².

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

    $F = ma$

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12. 12.

    Mathematics

    If f(x) = 2x³ + 4x² + 8x, find f′(5).

    Formula:Derivative of a Polynomial

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

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13. 13.

    Physics

    If 2,986 J of work is done in 25 s, find the power.

    Formula:Power

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

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14. 14.

    Mathematics

    Find term number 4 of a geometric progression with first term 2 and common ratio 2.

    Formula:GP nth Term

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

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15. 15.

    Physics

    If 3,860 J of work is done in 13 s, find the power.

    Formula:Power

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

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16. 16.

    Mathematics

    Find the sum of the first 7 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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17. 17.

    Physics

    Find the momentum of a 12 kg body moving at 39 m/s.

    Formula:Linear Momentum

    $p = mv$

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18. 18.

    Physics

    A projectile is launched at 39 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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19. 19.

    Physics

    A force of 802 N acts on an area of 34 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Mathematics

    Find the slope of the line through (-7, 5) and (7, 0).

    Formula:Slope of a Line

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

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