A-Level Physics · Practice Sheet 9

1. 1.

   Mathematics

   Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.

   Formula:Binomial Coefficient

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

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2. 2.

   Mathematics

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

   Formula:GP Sum of n Terms

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

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3. 3.

   Mathematics

   If f(x) = 1x³ + 3x² + 6x, find f′(4).

   Formula:Derivative of a Polynomial

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

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4. 4.

   Physics

   An object starts at 18 m/s and accelerates at 6 m/s² for 8 s. Find its final velocity.

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

   $v = u + at$

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5. 5.

   Physics

   Find the voltage across a 43 Ω resistor carrying a current of 11 A.

   Formula:Ohm's Law

   $V = IR$

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6. 6.

   Physics

   Find the electrical power when 159 V drives a current of 17 A.

   Formula:Electrical Power

   $P = VI$

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7. 7.

   Physics

   If 293 J of work is done in 8 s, find the power.

   Formula:Power

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

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8. 8.

   Mathematics

   Find the slope of the line through (-6, -2) and (-2, 3).

   Formula:Slope of a Line

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

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9. 9.

   Mathematics

   Find the binomial coefficient C(5, 4) — the coefficient of x^4 in (1 + x)^5.

   Formula:Binomial Coefficient

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

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10. 10.

    Physics

    An object starts at 9 m/s and accelerates at 8 m/s² for 12 s. Find its final velocity.

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

    $v = u + at$

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11. 11.

    Mathematics

    In an arithmetic progression with first term 19 and common difference 5, find term number 5.

    Formula:AP nth Term

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

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12. 12.

    Mathematics

    Evaluate log base 10 of 1,000,000.

    Formula:Logarithm Evaluation

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

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13. 13.

    Physics

    Find the electrical power when 67 V drives a current of 4 A.

    Formula:Electrical Power

    $P = VI$

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14. 14.

    Physics

    Calculate the potential energy of a 50 kg object at a height of 47 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 5 and common ratio 3.

    Formula:GP Sum of n Terms

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

    View formula →
16. 16.

    Physics

    A projectile is launched at 47 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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17. 17.

    Physics

    An object starts at 3 m/s and accelerates at 4 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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18. 18.

    Physics

    A force of 346 N acts on an area of 40 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Mathematics

    Find term number 4 of a geometric progression with first term 5 and common ratio 3.

    Formula:GP nth Term

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

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20. 20.

    Mathematics

    If f(x) = 5x³ + 4x² + 7x, find f′(5).

    Formula:Derivative of a Polynomial

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

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