A-Level Physics · Practice Sheet 49

1. 1.

   Mathematics

   Evaluate ∫ from 0 to 3 of 4x^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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2. 2.

   Mathematics

   For the quadratic 5x² + 3x + 5 = 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 8 and common difference 4, find term number 11.

   Formula:AP nth Term

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

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4. 4.

   Physics

   A force of 890 N acts on an area of 29 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Physics

   Find the density of an object with mass 236 g and volume 32 cm³.

   Formula:Density

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

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6. 6.

   Physics

   Find the voltage across a 17 Ω resistor carrying a current of 6 A.

   Formula:Ohm's Law

   $V = IR$

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7. 7.

   Physics

   Find the density of an object with mass 392 g and volume 21 cm³.

   Formula:Density

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

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8. 8.

   Physics

   A constant force of 126 N moves an object 29 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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9. 9.

   Physics

   Find the force required to accelerate a 50 kg mass at 13 m/s².

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

   $F = ma$

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10. 10.

    Mathematics

    Find the distance between the points (3, -5) and (-4, 8).

    Formula:Distance Between Two Points

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

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11. 11.

    Physics

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

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

    $v = u + at$

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12. 12.

    Physics

    A body moving at 4 m/s accelerates at 1 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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13. 13.

    Mathematics

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

    Formula:AP nth Term

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

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14. 14.

    Mathematics

    Find the distance between the points (-6, 7) and (6, -5).

    Formula:Distance Between Two Points

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

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15. 15.

    Mathematics

    Evaluate ∫ from 1 to 4 of 2x^3 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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16. 16.

    Mathematics

    If f(x) = 1x³ + 6x² + 2x, find f′(2).

    Formula:Derivative of a Polynomial

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

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17. 17.

    Mathematics

    Find the sum of the first 18 terms of an AP with first term 5 and common difference 4.

    Formula:AP Sum of n Terms

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

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18. 18.

    Physics

    An object starts at 15 m/s and accelerates at 8 m/s² for 9 s. Find its final velocity.

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

    $v = u + at$

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19. 19.

    Mathematics

    Find term number 6 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 distance between the points (-1, 3) and (-7, -2).

    Formula:Distance Between Two Points

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

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