ACT · Practice Sheet 14

1. 1.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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2. 2.

   Quantitative Aptitude

   A can finish a job in 17 days and B in 8 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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3. 3.

   Quantitative Aptitude

   A invests $2,000 and B invests $3,000 for the same period. If the total profit is $38,000, find A's share.

   Formula:Partnership (profit share)

   $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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4. 4.

   Mathematics

   Evaluate ∫ from 0 to 3 of 1x^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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5. 5.

   Physics

   Find the force required to accelerate a 44 kg mass at 18 m/s².

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

   $F = ma$

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6. 6.

   Quantitative Aptitude

   Pipe A fills a tank in 15 hours and pipe B in 6 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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7. 7.

   Mathematics

   Find the sum of the first 10 terms of an AP with first term 1 and common difference 3.

   Formula:AP Sum of n Terms

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

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8. 8.

   Quantitative Aptitude

   Find the average of these 10 numbers: 42, 37, 86, 42, 60, 34, 43, 50, 68, 23.

   Formula:Arithmetic Mean

   $\bar{x} = \dfrac{\sum x}{n}$

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9. 9.

   Quantitative Aptitude

   An item is bought for $700 and sold for $1,050. Find the profit percentage.

   Formula:Profit Percentage

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

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10. 10.

    Mathematics

    If f(x) = 3x³ + 3x² + 6x, find f′(5).

    Formula:Derivative of a Polynomial

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

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11. 11.

    Mathematics

    In an arithmetic progression with first term 14 and common difference 8, find term number 17.

    Formula:AP nth Term

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

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12. 12.

    Quantitative Aptitude

    An item is bought for $600 and sold for $780. Find the profit percentage.

    Formula:Profit Percentage

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

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13. 13.

    Quantitative Aptitude

    A can finish a job in 10 days and B in 11 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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14. 14.

    Physics

    Find the voltage across a 47 Ω resistor carrying a current of 2 A.

    Formula:Ohm's Law

    $V = IR$

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15. 15.

    Quantitative Aptitude

    Find the HCF and LCM of 15 and 8.

    Formula:LCM & HCF

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

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16. 16.

    Physics

    Find the force required to accelerate a 34 kg mass at 1 m/s².

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

    $F = ma$

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17. 17.

    Mathematics

    Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

    Formula:Binomial Coefficient

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

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18. 18.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 6 and common ratio 2.

    Formula:GP Sum of n Terms

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

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19. 19.

    Quantitative Aptitude

    What is 30% of 620?

    Formula:Percentage of a Number

    $\text{Value} = \dfrac{P}{100}\times N$

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20. 20.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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