11+ · Practice Sheet 48

1. 1.

   Quantitative Aptitude

   Find the simple interest on £24,000 at 5% per annum for 6 year(s).

   Formula:Simple Interest

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

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2. 2.

   Quantitative Aptitude

   The sum of the ages of two people is 52 years, and one is 6 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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3. 3.

   Mathematics

   Find the distance between the points (5, -1) and (8, -2).

   Formula:Distance Between Two Points

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

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4. 4.

   Quantitative Aptitude

   An item is bought for £300 and sold for £345. Find the profit percentage.

   Formula:Profit Percentage

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

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5. 5.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)

   Formula:Permutations

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

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6. 6.

   Quantitative Aptitude

   Find the HCF and LCM of 17 and 39.

   Formula:LCM & HCF

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

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7. 7.

   Quantitative Aptitude

   The marked price of an item is £1,400. After a 50% discount, find the selling price.

   Formula:Discount & Selling Price

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

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8. 8.

   Quantitative Aptitude

   Find the simple interest on £20,000 at 8% per annum for 2 year(s).

   Formula:Simple Interest

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

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9. 9.

   Quantitative Aptitude

   Find the HCF and LCM of 6 and 34.

   Formula:LCM & HCF

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

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10. 10.

    Mathematics

    If f(x) = 5x³ + 1x² + 5x, find f′(5).

    Formula:Derivative of a Polynomial

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

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11. 11.

    Mathematics

    For the quadratic 3x² − 5x + 2 = 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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12. 12.

    Quantitative Aptitude

    Pipe A fills a tank in 3 hours and pipe B in 14 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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13. 13.

    Mathematics

    Find the sum of the first 6 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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14. 14.

    Quantitative Aptitude

    What is 30% of 960?

    Formula:Percentage of a Number

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

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15. 15.

    Mathematics

    Evaluate ∫ from 2 to 4 of 3x^1 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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16. 16.

    Mathematics

    Find the slope of the line through (-6, -6) and (6, 2).

    Formula:Slope of a Line

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

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17. 17.

    Quantitative Aptitude

    Find the compound interest on £7,000 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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18. 18.

    Quantitative Aptitude

    What is 10% of 1,100?

    Formula:Percentage of a Number

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

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19. 19.

    Quantitative Aptitude

    The marked price of an item is £1,900. After a 25% discount, find the selling price.

    Formula:Discount & Selling Price

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

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20. 20.

    Mathematics

    For the quadratic 2x² − 9x − 3 = 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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