A-Level Physics · Practice Sheet 15

1. 1.

   Physics

   A force of 269 N acts on an area of 28 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Physics

   Find the force required to accelerate a 8 kg mass at 19 m/s².

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

   $F = ma$

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3. 3.

   Physics

   A constant force of 94 N moves an object 13 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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4. 4.

   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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5. 5.

   Mathematics

   Find the sum of the first 5 terms of a GP with first term 6 and common ratio 2.

   Formula:GP Sum of n Terms

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

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6. 6.

   Mathematics

   Find the slope of the line through (-7, 4) and (2, 8).

   Formula:Slope of a Line

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

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7. 7.

   Physics

   A projectile is launched at 43 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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8. 8.

   Mathematics

   Find the sum of the first 3 terms of a GP with first term 2 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

   Find the slope of the line through (4, 4) and (-8, 8).

   Formula:Slope of a Line

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

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10. 10.

    Mathematics

    Find the binomial coefficient C(7, 4) — the coefficient of x^4 in (1 + x)^7.

    Formula:Binomial Coefficient

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

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11. 11.

    Mathematics

    Find the distance between the points (-4, 7) and (2, 3).

    Formula:Distance Between Two Points

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

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12. 12.

    Physics

    A body moving at 4 m/s accelerates at 6 m/s² for 9 s. Find the distance travelled.

    Formula:Equation of Motion (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^{2}$

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13. 13.

    Mathematics

    Find the slope of the line through (2, 3) and (8, -4).

    Formula:Slope of a Line

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

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14. 14.

    Mathematics

    Evaluate log base 5 of 15,625.

    Formula:Logarithm Evaluation

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

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15. 15.

    Physics

    A force of 279 N acts on an area of 14 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Mathematics

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

    Formula:GP nth Term

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

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17. 17.

    Mathematics

    Find the sum of the first 6 terms of an AP with first term 5 and common difference 7.

    Formula:AP Sum of n Terms

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

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18. 18.

    Mathematics

    Evaluate ∫ from 0 to 5 of 5x^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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19. 19.

    Physics

    Find the force required to accelerate a 41 kg mass at 3 m/s².

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

    $F = ma$

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20. 20.

    Physics

    Find the density of an object with mass 394 g and volume 15 cm³.

    Formula:Density

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

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