A-Level Physics · Practice Sheet 40

1. 1.

   Mathematics

   Find the distance between the points (-2, -7) and (2, 3).

   Formula:Distance Between Two Points

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

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2. 2.

   Mathematics

   If f(x) = 4x³ + 2x² + 7x, find f′(1).

   Formula:Derivative of a Polynomial

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

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3. 3.

   Physics

   Find the force required to accelerate a 33 kg mass at 6 m/s².

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

   $F = ma$

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4. 4.

   Mathematics

   Find term number 7 of a geometric progression with first term 4 and common ratio 3.

   Formula:GP nth Term

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

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5. 5.

   Physics

   Find the voltage across a 30 Ω resistor carrying a current of 3 A.

   Formula:Ohm's Law

   $V = IR$

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6. 6.

   Physics

   An object starts at 20 m/s and accelerates at 9 m/s² for 5 s. Find its final velocity.

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

   $v = u + at$

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7. 7.

   Physics

   A constant force of 191 N moves an object 45 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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8. 8.

   Mathematics

   Evaluate ∫ from 1 to 4 of 5x^2 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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9. 9.

   Mathematics

   Find term number 4 of a geometric progression with first term 6 and common ratio 3.

   Formula:GP nth Term

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

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10. 10.

    Physics

    A projectile is launched at 25 m/s at 45° 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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11. 11.

    Physics

    Find the kinetic energy of a 8 kg object moving at 22 m/s.

    Formula:Kinetic Energy

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

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12. 12.

    Mathematics

    For the quadratic 2x² + 3x − 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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13. 13.

    Mathematics

    Find term number 3 of a geometric progression with first term 1 and common ratio 2.

    Formula:GP nth Term

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

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14. 14.

    Physics

    A projectile is launched at 36 m/s at 30° 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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15. 15.

    Mathematics

    Find the sum of the first 7 terms of an AP with first term 1 and common difference 4.

    Formula:AP Sum of n Terms

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

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16. 16.

    Mathematics

    If f(x) = 5x³ + 2x² + 4x, find f′(5).

    Formula:Derivative of a Polynomial

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

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17. 17.

    Mathematics

    Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

    Formula:Binomial Coefficient

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

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18. 18.

    Mathematics

    Evaluate ∫ from 2 to 4 of 4x^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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19. 19.

    Physics

    Calculate the potential energy of a 13 kg object at a height of 40 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Physics

    Find the voltage across a 38 Ω resistor carrying a current of 3 A.

    Formula:Ohm's Law

    $V = IR$

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