A-Level Physics · Practice Sheet 7

1. 1.

   Mathematics

   Find the slope of the line through (2, 3) and (-1, -8).

   Formula:Slope of a Line

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

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2. 2.

   Physics

   A constant force of 172 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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3. 3.

   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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4. 4.

   Physics

   A body moving at 0 m/s accelerates at 1 m/s² for 3 s. Find the distance travelled.

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

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

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5. 5.

   Physics

   A force of 818 N acts on an area of 20 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Physics

   A body moving at 2 m/s accelerates at 3 m/s² for 8 s. Find the distance travelled.

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

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

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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.

   Physics

   Find the force required to accelerate a 38 kg mass at 19 m/s².

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

   $F = ma$

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9. 9.

   Physics

   If 1,614 J of work is done in 30 s, find the power.

   Formula:Power

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

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10. 10.

    Mathematics

    Evaluate ∫ from 2 to 5 of 1x^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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11. 11.

    Mathematics

    Find the distance between the points (2, -6) and (6, -7).

    Formula:Distance Between Two Points

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

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12. 12.

    Mathematics

    Evaluate log base 5 of 625.

    Formula:Logarithm Evaluation

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

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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

    Find the voltage across a 25 Ω resistor carrying a current of 3 A.

    Formula:Ohm's Law

    $V = IR$

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15. 15.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 3 and common ratio 2.

    Formula:GP Sum of n Terms

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

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16. 16.

    Mathematics

    Evaluate log base 10 of 1,000.

    Formula:Logarithm Evaluation

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

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17. 17.

    Physics

    A projectile is launched at 46 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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18. 18.

    Mathematics

    Evaluate log base 2 of 32.

    Formula:Logarithm Evaluation

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

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19. 19.

    Physics

    If 4,188 J of work is done in 7 s, find the power.

    Formula:Power

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

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20. 20.

    Mathematics

    If f(x) = 1x³ + 6x² + 7x, find f′(4).

    Formula:Derivative of a Polynomial

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

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