ACT · Practice Sheet 31

1. 1.

   Quantitative Aptitude

   A invests $8,000 and B invests $6,000 for the same period. If the total profit is $14,000, find A's share.

   Formula:Partnership (profit share)

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

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2. 2.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

   Formula:Probability (two dice)

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

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3. 3.

   Physics

   Find the momentum of a 37 kg body moving at 31 m/s.

   Formula:Linear Momentum

   $p = mv$

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4. 4.

   Quantitative Aptitude

   Find the compound interest on $20,000 at 20% per annum compounded annually for 3 years.

   Formula:Compound Interest

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

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5. 5.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)

   Formula:Combinations

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

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6. 6.

   Quantitative Aptitude

   A can finish a job in 14 days and B in 10 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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7. 7.

   Quantitative Aptitude

   A value changes from 500 to 600. Find the percentage increase.

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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8. 8.

   Physics

   Calculate the potential energy of a 20 kg object at a height of 36 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Physics

   Find the momentum of a 47 kg body moving at 27 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Physics

    A projectile is launched at 11 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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11. 11.

    Quantitative Aptitude

    Divide $2,148 between two people in the ratio 6:6. 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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12. 12.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

    Formula:Probability (two dice)

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

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13. 13.

    Physics

    If 4,572 J of work is done in 22 s, find the power.

    Formula:Power

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

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14. 14.

    Quantitative Aptitude

    Find the compound interest on $16,000 at 10% per annum compounded annually for 2 years.

    Formula:Compound Interest

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

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15. 15.

    Physics

    If 1,259 J of work is done in 4 s, find the power.

    Formula:Power

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

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16. 16.

    Quantitative Aptitude

    A can finish a job in 11 days and B in 20 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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17. 17.

    Quantitative Aptitude

    Find the compound interest on $7,000 at 20% per annum compounded annually for 3 years.

    Formula:Compound Interest

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

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18. 18.

    Mathematics

    In an arithmetic progression with first term 9 and common difference 2, find term number 16.

    Formula:AP nth Term

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

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19. 19.

    Mathematics

    Evaluate ∫ from 0 to 4 of 2x^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.

    Physics

    Find the voltage across a 46 Ω resistor carrying a current of 17 A.

    Formula:Ohm's Law

    $V = IR$

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