11+ · Practice Sheet 6

1. 1.

   Mathematics

   Find the sum of the first 7 terms of a GP with first term 4 and common ratio 3.

   Formula:GP Sum of n Terms

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

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2. 2.

   Mathematics

   Evaluate log base 2 of 32.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

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3. 3.

   Quantitative Aptitude

   Find the simple interest on £34,000 at 10% per annum for 2 year(s).

   Formula:Simple Interest

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

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4. 4.

   Quantitative Aptitude

   A can finish a job in 14 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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5. 5.

   Mathematics

   If f(x) = 5x³ + 3x² + 5x, find f′(4).

   Formula:Derivative of a Polynomial

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

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6. 6.

   Mathematics

   Find the sum of the first 5 terms of an AP with first term 7 and common difference 9.

   Formula:AP Sum of n Terms

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

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7. 7.

   Quantitative Aptitude

   Pipe A fills a tank in 6 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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8. 8.

   Mathematics

   Evaluate ∫ from 2 to 4 of 2x^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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9. 9.

   Mathematics

   Find the distance between the points (-7, -5) and (-5, -1).

   Formula:Distance Between Two Points

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

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10. 10.

    Mathematics

    Find term number 7 of a geometric progression with first term 3 and common ratio 2.

    Formula:GP nth Term

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

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11. 11.

    Quantitative Aptitude

    A value changes from 300 to 255. Find the percentage decrease.

    Formula:Percentage Change

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

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12. 12.

    Mathematics

    If f(x) = 3x³ + 3x² + 6x, find f′(4).

    Formula:Derivative of a Polynomial

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

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13. 13.

    Mathematics

    In an arithmetic progression with first term 8 and common difference 2, find term number 13.

    Formula:AP nth Term

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

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14. 14.

    Mathematics

    Find the sum of the first 10 terms of an AP with first term 11 and common difference 10.

    Formula:AP Sum of n Terms

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

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15. 15.

    Mathematics

    If f(x) = 5x³ + 2x² + 5x, find f′(1).

    Formula:Derivative of a Polynomial

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

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16. 16.

    Quantitative Aptitude

    An item is bought for £700 and sold for £875. Find the profit percentage.

    Formula:Profit Percentage

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

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17. 17.

    Quantitative Aptitude

    A value changes from 700 to 595. Find the percentage decrease.

    Formula:Percentage Change

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

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18. 18.

    Quantitative Aptitude

    Find the simple interest on £36,000 at 5% per annum for 5 year(s).

    Formula:Simple Interest

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

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19. 19.

    Quantitative Aptitude

    What is 60% of 380?

    Formula:Percentage of a Number

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

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20. 20.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 3.)

    Formula:Combinations

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

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