A-Level Physics · Practice Sheet 5

1. 1.

   Mathematics

   Find the sum of the first 14 terms of an AP with first term 6 and common difference 3.

   Formula:AP Sum of n Terms

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

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2. 2.

   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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3. 3.

   Mathematics

   For the quadratic 1x² + 4x + 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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4. 4.

   Mathematics

   Evaluate ∫ from 1 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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5. 5.

   Physics

   Find the momentum of a 45 kg body moving at 33 m/s.

   Formula:Linear Momentum

   $p = mv$

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6. 6.

   Mathematics

   For the quadratic 3x² − 8x + 1 = 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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7. 7.

   Physics

   Find the density of an object with mass 382 g and volume 33 cm³.

   Formula:Density

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

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8. 8.

   Mathematics

   Evaluate log base 5 of 3,125.

   Formula:Logarithm Evaluation

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

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9. 9.

   Physics

   Find the voltage across a 28 Ω resistor carrying a current of 3 A.

   Formula:Ohm's Law

   $V = IR$

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10. 10.

    Physics

    Find the momentum of a 27 kg body moving at 26 m/s.

    Formula:Linear Momentum

    $p = mv$

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11. 11.

    Mathematics

    For the quadratic 5x² + 0x + 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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12. 12.

    Physics

    Find the force required to accelerate a 38 kg mass at 3 m/s².

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

    $F = ma$

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13. 13.

    Mathematics

    Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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14. 14.

    Mathematics

    In an arithmetic progression with first term 19 and common difference 7, find term number 10.

    Formula:AP nth Term

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

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15. 15.

    Physics

    A force of 323 N acts on an area of 9 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Physics

    A body moving at 6 m/s accelerates at 8 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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17. 17.

    Physics

    Find the force required to accelerate a 40 kg mass at 8 m/s².

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

    $F = ma$

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18. 18.

    Mathematics

    Evaluate log base 3 of 729.

    Formula:Logarithm Evaluation

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

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19. 19.

    Mathematics

    In an arithmetic progression with first term 16 and common difference 7, find term number 20.

    Formula:AP nth Term

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

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20. 20.

    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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