ACT · Practice Sheet 44

1. 1.

   Mathematics

   Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.

   Formula:Binomial Coefficient

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

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2. 2.

   Physics

   Find the momentum of a 20 kg body moving at 23 m/s.

   Formula:Linear Momentum

   $p = mv$

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3. 3.

   Quantitative Aptitude

   Find the compound interest on $4,000 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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4. 4.

   Mathematics

   Find term number 3 of a geometric progression with first term 2 and common ratio 3.

   Formula:GP nth Term

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

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5. 5.

   Mathematics

   Find the distance between the points (-7, -8) and (-8, 6).

   Formula:Distance Between Two Points

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

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6. 6.

   Physics

   An object starts at 1 m/s and accelerates at 8 m/s² for 10 s. Find its final velocity.

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

   $v = u + at$

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7. 7.

   Quantitative Aptitude

   Two varieties costing $20 and $60 per kg are mixed to give a mixture worth $45 per kg. Find the mixing ratio.

   Formula:Alligation (Mixtures)

   $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

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8. 8.

   Mathematics

   Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.

   Formula:Binomial Coefficient

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

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9. 9.

   Quantitative Aptitude

   Divide $693 between two people in the ratio 5:2. 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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10. 10.

    Quantitative Aptitude

    Find the simple interest on $23,000 at 8% per annum for 6 year(s).

    Formula:Simple Interest

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

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11. 11.

    Mathematics

    Find the binomial coefficient C(7, 4) — the coefficient of x^4 in (1 + x)^7.

    Formula:Binomial Coefficient

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

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12. 12.

    Quantitative Aptitude

    A can finish a job in 18 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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13. 13.

    Quantitative Aptitude

    Two varieties costing $40 and $78 per kg are mixed to give a mixture worth $51 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

    $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

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14. 14.

    Mathematics

    Find the sum of the first 6 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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15. 15.

    Quantitative Aptitude

    A can finish a job in 19 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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16. 16.

    Mathematics

    Find term number 4 of a geometric progression with first term 4 and common ratio 3.

    Formula:GP nth Term

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

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17. 17.

    Physics

    Find the momentum of a 43 kg body moving at 26 m/s.

    Formula:Linear Momentum

    $p = mv$

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18. 18.

    Mathematics

    For the quadratic 2x² − 1x − 5 = 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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19. 19.

    Physics

    A projectile is launched at 42 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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20. 20.

    Physics

    A constant force of 53 N moves an object 41 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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