A-Level Physics · Practice Sheet 23

1. 1.

   Mathematics

   Find the sum of the first 12 terms of an AP with first term 2 and common difference 6.

   Formula:AP Sum of n Terms

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

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2. 2.

   Mathematics

   For the quadratic 1x² − 7x + 7 = 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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3. 3.

   Mathematics

   In an arithmetic progression with first term 5 and common difference 2, find term number 12.

   Formula:AP nth Term

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

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4. 4.

   Physics

   Find the voltage across a 23 Ω resistor carrying a current of 13 A.

   Formula:Ohm's Law

   $V = IR$

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5. 5.

   Mathematics

   Find term number 5 of a geometric progression with first term 3 and common ratio 2.

   Formula:GP nth Term

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

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6. 6.

   Physics

   Calculate the potential energy of a 35 kg object at a height of 14 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   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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8. 8.

   Mathematics

   Evaluate log base 2 of 16.

   Formula:Logarithm Evaluation

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

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9. 9.

   Physics

   A body moving at 10 m/s accelerates at 7 m/s² for 2 s. Find the distance travelled.

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

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

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10. 10.

    Mathematics

    Find the slope of the line through (-2, -5) and (-3, -1).

    Formula:Slope of a Line

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

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11. 11.

    Physics

    A force of 214 N acts on an area of 27 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Physics

    Find the density of an object with mass 101 g and volume 5 cm³.

    Formula:Density

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

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13. 13.

    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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14. 14.

    Physics

    Find the force required to accelerate a 11 kg mass at 12 m/s².

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

    $F = ma$

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15. 15.

    Mathematics

    Evaluate log base 10 of 1,000,000.

    Formula:Logarithm Evaluation

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

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16. 16.

    Mathematics

    Find the sum of the first 7 terms of an AP with first term 11 and common difference 1.

    Formula:AP Sum of n Terms

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

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17. 17.

    Mathematics

    Find the slope of the line through (4, -2) and (-3, 1).

    Formula:Slope of a Line

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

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18. 18.

    Mathematics

    Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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19. 19.

    Physics

    A constant force of 111 N moves an object 12 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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20. 20.

    Mathematics

    Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.

    Formula:Binomial Coefficient

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

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