A-Level Physics · Practice Sheet 2

1. 1.

   Mathematics

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

   Formula:Distance Between Two Points

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

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2. 2.

   Mathematics

   If f(x) = 3x³ + 3x² + 7x, find f′(4).

   Formula:Derivative of a Polynomial

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

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3. 3.

   Physics

   A force of 656 N acts on an area of 22 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Mathematics

   Find term number 4 of a geometric progression with first term 5 and common ratio 2.

   Formula:GP nth Term

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

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5. 5.

   Mathematics

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

   Formula:Slope of a Line

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

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6. 6.

   Physics

   Find the momentum of a 20 kg body moving at 12 m/s.

   Formula:Linear Momentum

   $p = mv$

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7. 7.

   Physics

   A projectile is launched at 17 m/s at 30° 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 slope of the line through (-6, 4) and (-7, -5).

   Formula:Slope of a Line

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

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9. 9.

   Mathematics

   In an arithmetic progression with first term 11 and common difference 10, find term number 20.

   Formula:AP nth Term

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

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10. 10.

    Physics

    A force of 626 N acts on an area of 4 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Physics

    A body moving at 11 m/s accelerates at 5 m/s² for 7 s. Find the distance travelled.

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

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

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12. 12.

    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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13. 13.

    Physics

    A projectile is launched at 23 m/s at 30° 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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14. 14.

    Physics

    Find the force required to accelerate a 27 kg mass at 14 m/s².

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

    $F = ma$

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15. 15.

    Mathematics

    Find the sum of the first 19 terms of an AP with first term 19 and common difference 9.

    Formula:AP Sum of n Terms

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

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16. 16.

    Mathematics

    Find the slope of the line through (2, -7) and (5, -7).

    Formula:Slope of a Line

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

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17. 17.

    Physics

    Find the density of an object with mass 353 g and volume 19 cm³.

    Formula:Density

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

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18. 18.

    Physics

    Find the electrical power when 144 V drives a current of 15 A.

    Formula:Electrical Power

    $P = VI$

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19. 19.

    Mathematics

    Find term number 5 of a geometric progression with first term 5 and common ratio 2.

    Formula:GP nth Term

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

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20. 20.

    Mathematics

    Find the sum of the first 14 terms of an AP with first term 11 and common difference 2.

    Formula:AP Sum of n Terms

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

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