ACT · Practice Sheet 25

1. 1.

   Mathematics

   In an arithmetic progression with first term 19 and common difference 3, find term number 19.

   Formula:AP nth Term

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

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2. 2.

   Physics

   Find the electrical power when 67 V drives a current of 19 A.

   Formula:Electrical Power

   $P = VI$

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3. 3.

   Mathematics

   In an arithmetic progression with first term 19 and common difference 9, find term number 6.

   Formula:AP nth Term

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

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4. 4.

   Mathematics

   Find the slope of the line through (-8, -5) and (-3, 1).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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5. 5.

   Mathematics

   Find the sum of the first 13 terms of an AP with first term 9 and common difference 5.

   Formula:AP Sum of n Terms

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

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6. 6.

   Quantitative Aptitude

   The marked price of an item is $300. After a 5% discount, find the selling price.

   Formula:Discount & Selling Price

   $SP = MP\left(1-\dfrac{d}{100}\right)$

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7. 7.

   Mathematics

   Find the distance between the points (2, 5) and (-4, -3).

   Formula:Distance Between Two Points

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

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8. 8.

   Quantitative Aptitude

   What is 15% of 1,200?

   Formula:Percentage of a Number

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

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9. 9.

   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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10. 10.

    Physics

    A projectile is launched at 50 m/s at 45° 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

    A invests $4,000 and B invests $4,000 for the same period. If the total profit is $16,000, find A's share.

    Formula:Partnership (profit share)

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

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12. 12.

    Physics

    Calculate the potential energy of a 18 kg object at a height of 14 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Mathematics

    Evaluate ∫ from 2 to 4 of 2x^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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14. 14.

    Quantitative Aptitude

    What is 50% of 640?

    Formula:Percentage of a Number

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

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15. 15.

    Mathematics

    Find the slope of the line through (4, -8) and (6, 4).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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16. 16.

    Quantitative Aptitude

    Find the HCF and LCM of 28 and 35.

    Formula:LCM & HCF

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

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17. 17.

    Mathematics

    Find the slope of the line through (7, 4) and (-1, -4).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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18. 18.

    Quantitative Aptitude

    Find the average of these 8 numbers: 75, 84, 33, 44, 39, 24, 86, 43.

    Formula:Arithmetic Mean

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

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19. 19.

    Physics

    A force of 920 N acts on an area of 3 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Quantitative Aptitude

    Find the average of these 10 numbers: 27, 37, 53, 31, 44, 27, 72, 22, 77, 23.

    Formula:Arithmetic Mean

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

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