ACT · Practice Sheet 11

1. 1.

   Quantitative Aptitude

   A value changes from 900 to 720. Find the percentage decrease.

   Formula:Percentage Change

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

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2. 2.

   Quantitative Aptitude

   An item is bought for $700 and sold for $840. Find the profit percentage.

   Formula:Profit Percentage

   $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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3. 3.

   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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4. 4.

   Mathematics

   In an arithmetic progression with first term 10 and common difference 3, find term number 26.

   Formula:AP nth Term

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

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5. 5.

   Quantitative Aptitude

   Find the simple interest on $19,000 at 8% per annum for 5 year(s).

   Formula:Simple Interest

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

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6. 6.

   Mathematics

   Find term number 3 of a geometric progression with first term 4 and common ratio 2.

   Formula:GP nth Term

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

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7. 7.

   Quantitative Aptitude

   An item is bought for $600 and sold for $690. Find the profit percentage.

   Formula:Profit Percentage

   $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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8. 8.

   Physics

   A projectile is launched at 47 m/s at 60° 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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9. 9.

   Quantitative Aptitude

   Find the simple interest on $24,000 at 12% per annum for 2 year(s).

   Formula:Simple Interest

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

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10. 10.

    Mathematics

    For the quadratic 4x² + 2x − 9 = 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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11. 11.

    Mathematics

    Evaluate ∫ from 2 to 3 of 1x^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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12. 12.

    Quantitative Aptitude

    Find the average of these 5 numbers: 53, 38, 20, 21, 21.

    Formula:Arithmetic Mean

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

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13. 13.

    Physics

    If 4,988 J of work is done in 19 s, find the power.

    Formula:Power

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

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14. 14.

    Physics

    Find the momentum of a 21 kg body moving at 7 m/s.

    Formula:Linear Momentum

    $p = mv$

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15. 15.

    Mathematics

    If f(x) = 4x³ + 3x² + 7x, find f′(4).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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16. 16.

    Mathematics

    Find the sum of the first 22 terms of an AP with first term 13 and common difference 4.

    Formula:AP Sum of n Terms

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

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17. 17.

    Quantitative Aptitude

    Divide $1,080 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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18. 18.

    Quantitative Aptitude

    Find the HCF and LCM of 23 and 20.

    Formula:LCM & HCF

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

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19. 19.

    Quantitative Aptitude

    The marked price of an item is $1,300. After a 40% discount, find the selling price.

    Formula:Discount & Selling Price

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

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20. 20.

    Quantitative Aptitude

    Divide $1,221 between two people in the ratio 5:6. 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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