A-Level Physics · Practice Sheet 22

1. 1.

   Mathematics

   Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

   Formula:Binomial Coefficient

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

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2. 2.

   Physics

   A body moving at 2 m/s accelerates at 2 m/s² for 10 s. Find the distance travelled.

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

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

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3. 3.

   Physics

   Find the force required to accelerate a 9 kg mass at 12 m/s².

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

   $F = ma$

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4. 4.

   Mathematics

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

   Formula:Slope of a Line

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

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5. 5.

   Physics

   If 1,791 J of work is done in 27 s, find the power.

   Formula:Power

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

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6. 6.

   Physics

   Find the kinetic energy of a 4 kg object moving at 3 m/s.

   Formula:Kinetic Energy

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

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7. 7.

   Mathematics

   Find the binomial coefficient C(5, 3) — the coefficient of x^3 in (1 + x)^5.

   Formula:Binomial Coefficient

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

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8. 8.

   Mathematics

   If f(x) = 3x³ + 6x² + 7x, find f′(4).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Mathematics

   Find the distance between the points (5, 8) and (-6, 6).

   Formula:Distance Between Two Points

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

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10. 10.

    Physics

    Find the voltage across a 28 Ω resistor carrying a current of 18 A.

    Formula:Ohm's Law

    $V = IR$

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11. 11.

    Mathematics

    Evaluate ∫ from 2 to 4 of 2x^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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12. 12.

    Physics

    Find the voltage across a 35 Ω resistor carrying a current of 1 A.

    Formula:Ohm's Law

    $V = IR$

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13. 13.

    Mathematics

    For the quadratic 2x² + 7x − 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 sum of the first 17 terms of an AP with first term 9 and common difference 6.

    Formula:AP Sum of n Terms

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

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15. 15.

    Physics

    A body moving at 8 m/s accelerates at 8 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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16. 16.

    Physics

    If 1,784 J of work is done in 14 s, find the power.

    Formula:Power

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

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17. 17.

    Mathematics

    For the quadratic 1x² + 9x + 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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18. 18.

    Physics

    Find the kinetic energy of a 8 kg object moving at 25 m/s.

    Formula:Kinetic Energy

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

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19. 19.

    Physics

    Find the momentum of a 7 kg body moving at 36 m/s.

    Formula:Linear Momentum

    $p = mv$

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20. 20.

    Physics

    An object starts at 10 m/s and accelerates at 7 m/s² for 4 s. Find its final velocity.

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

    $v = u + at$

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