ACT · Practice Sheet 32

1. 1.

   Mathematics

   Find the slope of the line through (5, 3) and (-8, -2).

   Formula:Slope of a Line

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

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2. 2.

   Quantitative Aptitude

   A value changes from 900 to 1,350. Find the percentage increase.

   Formula:Percentage Change

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

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3. 3.

   Mathematics

   For the quadratic 4x² + 4x − 4 = 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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4. 4.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 3.)

   Formula:Combinations

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

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5. 5.

   Quantitative Aptitude

   A can finish a job in 16 days and B in 18 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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6. 6.

   Quantitative Aptitude

   Find the compound interest on $9,000 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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7. 7.

   Physics

   A force of 168 N acts on an area of 50 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Quantitative Aptitude

   Find the average of these 5 numbers: 36, 75, 33, 63, 38.

   Formula:Arithmetic Mean

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

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9. 9.

   Quantitative Aptitude

   Divide $1,332 between two people in the ratio 7:2. 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.

    Physics

    A force of 124 N acts on an area of 19 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Mathematics

    Find term number 5 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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12. 12.

    Physics

    Find the voltage across a 17 Ω resistor carrying a current of 18 A.

    Formula:Ohm's Law

    $V = IR$

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13. 13.

    Mathematics

    Find the distance between the points (-6, -8) and (3, -2).

    Formula:Distance Between Two Points

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

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14. 14.

    Quantitative Aptitude

    A value changes from 400 to 420. Find the percentage increase.

    Formula:Percentage Change

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

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15. 15.

    Quantitative Aptitude

    A vehicle covers 318 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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16. 16.

    Mathematics

    Find term number 7 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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17. 17.

    Physics

    Find the density of an object with mass 224 g and volume 14 cm³.

    Formula:Density

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

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18. 18.

    Quantitative Aptitude

    Two varieties costing $40 and $71 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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19. 19.

    Physics

    A constant force of 154 N moves an object 22 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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20. 20.

    Mathematics

    Find the sum of the first 4 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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