ACT · Practice Sheet 3

1. 1.

   Physics

   Find the momentum of a 50 kg body moving at 15 m/s.

   Formula:Linear Momentum

   $p = mv$

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2. 2.

   Mathematics

   For the quadratic 3x² + 3x + 2 = 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.

   Quantitative Aptitude

   Pipe A fills a tank in 4 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

   $T = \dfrac{xy}{x+y}$

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4. 4.

   Mathematics

   Find the sum of the first 6 terms of a GP with first term 5 and common ratio 2.

   Formula:GP Sum of n Terms

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

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5. 5.

   Quantitative Aptitude

   A vehicle covers 301 km in 7 hours. Find its average speed.

   Formula:Speed, Distance & Time

   $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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6. 6.

   Mathematics

   Find the sum of the first 14 terms of an AP with first term 12 and common difference 9.

   Formula:AP Sum of n Terms

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

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7. 7.

   Quantitative Aptitude

   A can finish a job in 17 days and B in 15 days. Working together, how long will they take?

   Formula:Time & Work (combined)

   $T = \dfrac{xy}{x+y}$

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8. 8.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 2.)

   Formula:Permutations

   $^{n}P_{r} = \dfrac{n!}{(n-r)!}$

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9. 9.

   Quantitative Aptitude

   A vehicle covers 558 km in 9 hours. Find its average speed.

   Formula:Speed, Distance & Time

   $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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10. 10.

    Physics

    Find the density of an object with mass 461 g and volume 48 cm³.

    Formula:Density

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

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11. 11.

    Quantitative Aptitude

    An item is bought for $900 and sold for $1,260. Find the profit percentage.

    Formula:Profit Percentage

    $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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12. 12.

    Mathematics

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

    Formula:Distance Between Two Points

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

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13. 13.

    Quantitative Aptitude

    Find the simple interest on $10,000 at 5% per annum for 5 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

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14. 14.

    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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15. 15.

    Quantitative Aptitude

    Pipe A fills a tank in 9 hours and pipe B in 11 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

    $T = \dfrac{xy}{x+y}$

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16. 16.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 5 and common ratio 3.

    Formula:GP Sum of n Terms

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

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17. 17.

    Quantitative Aptitude

    A can finish a job in 18 days and B in 5 days. Working together, how long will they take?

    Formula:Time & Work (combined)

    $T = \dfrac{xy}{x+y}$

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18. 18.

    Mathematics

    Evaluate log base 3 of 729.

    Formula:Logarithm Evaluation

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

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19. 19.

    Quantitative Aptitude

    Find the simple interest on $7,000 at 6% per annum for 2 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

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20. 20.

    Mathematics

    Find the sum of the first 24 terms of an AP with first term 6 and common difference 7.

    Formula:AP Sum of n Terms

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

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