ACT · Practice Sheet 22

1. 1.

   Physics

   Find the force required to accelerate a 24 kg mass at 5 m/s².

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

   $F = ma$

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2. 2.

   Mathematics

   Find the sum of the first 7 terms of a GP with first term 1 and common ratio 3.

   Formula:GP Sum of n Terms

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

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3. 3.

   Mathematics

   Find term number 6 of a geometric progression with first term 3 and common ratio 3.

   Formula:GP nth Term

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

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4. 4.

   Physics

   A constant force of 59 N moves an object 12 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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5. 5.

   Physics

   Find the density of an object with mass 318 g and volume 48 cm³.

   Formula:Density

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

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6. 6.

   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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7. 7.

   Mathematics

   Evaluate ∫ from 2 to 3 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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8. 8.

   Quantitative Aptitude

   Find the compound interest on $10,000 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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9. 9.

   Quantitative Aptitude

   A invests $5,000 and B invests $9,000 for the same period. If the total profit is $19,000, find A's share.

   Formula:Partnership (profit share)

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

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10. 10.

    Quantitative Aptitude

    Pipe A fills a tank in 4 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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11. 11.

    Quantitative Aptitude

    Find the compound interest on $2,000 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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12. 12.

    Mathematics

    Evaluate ∫ from 2 to 5 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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13. 13.

    Quantitative Aptitude

    Find the HCF and LCM of 15 and 20.

    Formula:LCM & HCF

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

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14. 14.

    Mathematics

    Find the sum of the first 7 terms of an AP with first term 2 and common difference 9.

    Formula:AP Sum of n Terms

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

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15. 15.

    Physics

    A force of 261 N acts on an area of 41 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Quantitative Aptitude

    The sum of the ages of two people is 69 years, and one is 9 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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17. 17.

    Physics

    Calculate the potential energy of a 44 kg object at a height of 47 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Quantitative Aptitude

    A can finish a job in 14 days and B in 9 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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19. 19.

    Mathematics

    Find the distance between the points (2, 5) and (5, 6).

    Formula:Distance Between Two Points

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

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20. 20.

    Mathematics

    Evaluate ∫ from 0 to 4 of 5x^2 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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