EmSAT Achieve · Practice Sheet 39

1. 1.

   Physics

   Find the voltage across a 26 Ω resistor carrying a current of 6 A.

   Formula:Ohm's Law

   $V = IR$

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2. 2.

   Physics

   A constant force of 96 N moves an object 27 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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3. 3.

   Physics

   A force of 520 N acts on an area of 48 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Mathematics

   Evaluate ∫ from 1 to 3 of 3x^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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5. 5.

   Physics

   A constant force of 194 N moves an object 18 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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6. 6.

   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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7. 7.

   Mathematics

   In an arithmetic progression with first term 8 and common difference 9, find term number 12.

   Formula:AP nth Term

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

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8. 8.

   Mathematics

   Find the sum of the first 9 terms of an AP with first term 8 and common difference 6.

   Formula:AP Sum of n Terms

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

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9. 9.

   Physics

   Find the density of an object with mass 72 g and volume 14 cm³.

   Formula:Density

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

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10. 10.

    Physics

    A body moving at 4 m/s accelerates at 8 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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11. 11.

    Physics

    An object starts at 12 m/s and accelerates at 5 m/s² for 10 s. Find its final velocity.

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

    $v = u + at$

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12. 12.

    Chemistry

    A solution is made by dissolving 9 g of solute in 186 g of solvent. Find the mass percentage of the solute.

    Formula:Mass Percentage

    $\%\,\text{mass} = \dfrac{\text{solute}}{\text{solution}}\times 100$

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13. 13.

    Mathematics

    If f(x) = 3x³ + 5x² + 3x, find f′(1).

    Formula:Derivative of a Polynomial

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

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14. 14.

    Physics

    Find the force required to accelerate a 12 kg mass at 5 m/s².

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

    $F = ma$

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15. 15.

    Physics

    Find the momentum of a 42 kg body moving at 11 m/s.

    Formula:Linear Momentum

    $p = mv$

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16. 16.

    Mathematics

    For the quadratic 4x² − 1x − 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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17. 17.

    Physics

    A body moving at 8 m/s accelerates at 4 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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18. 18.

    Physics

    Find the force required to accelerate a 46 kg mass at 9 m/s².

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

    $F = ma$

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19. 19.

    Physics

    A force of 638 N acts on an area of 28 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Physics

    An object starts at 17 m/s and accelerates at 2 m/s² for 8 s. Find its final velocity.

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

    $v = u + at$

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