ACT · Practice Sheet 37

1. 1.

   Physics

   A projectile is launched at 11 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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2. 2.

   Quantitative Aptitude

   Find the HCF and LCM of 10 and 15.

   Formula:LCM & HCF

   $\text{LCM}\times\text{HCF} = a\times b$

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3. 3.

   Physics

   Find the voltage across a 12 Ω resistor carrying a current of 6 A.

   Formula:Ohm's Law

   $V = IR$

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4. 4.

   Physics

   Find the density of an object with mass 398 g and volume 26 cm³.

   Formula:Density

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

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5. 5.

   Physics

   A body moving at 2 m/s accelerates at 6 m/s² for 4 s. Find the distance travelled.

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

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

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6. 6.

   Quantitative Aptitude

   Divide $981 between two people in the ratio 3:6. How much does each receive?

   Formula:Sharing in a Ratio

   $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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7. 7.

   Physics

   Find the force required to accelerate a 31 kg mass at 9 m/s².

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

   $F = ma$

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8. 8.

   Mathematics

   If f(x) = 4x³ + 4x² + 8x, find f′(1).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Quantitative Aptitude

   Find the compound interest on $3,000 at 10% per annum compounded annually for 3 years.

   Formula:Compound Interest

   $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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10. 10.

    Mathematics

    Evaluate log base 10 of 1,000.

    Formula:Logarithm Evaluation

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

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11. 11.

    Mathematics

    In an arithmetic progression with first term 8 and common difference 4, find term number 29.

    Formula:AP nth Term

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

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12. 12.

    Physics

    Find the voltage across a 37 Ω resistor carrying a current of 12 A.

    Formula:Ohm's Law

    $V = IR$

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13. 13.

    Physics

    If 2,019 J of work is done in 24 s, find the power.

    Formula:Power

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

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14. 14.

    Quantitative Aptitude

    Divide $864 between two people in the ratio 2:2. How much does each receive?

    Formula:Sharing in a Ratio

    $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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15. 15.

    Physics

    A projectile is launched at 30 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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16. 16.

    Mathematics

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

    Formula:Distance Between Two Points

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

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17. 17.

    Physics

    An object starts at 4 m/s and accelerates at 6 m/s² for 8 s. Find its final velocity.

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

    $v = u + at$

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18. 18.

    Mathematics

    Find the slope of the line through (-4, 3) and (2, 6).

    Formula:Slope of a Line

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

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19. 19.

    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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20. 20.

    Mathematics

    Evaluate log base 5 of 15,625.

    Formula:Logarithm Evaluation

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

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