11+ · Practice Sheet 26

1. 1.

   Mathematics

   Evaluate ∫ from 1 to 4 of 3x^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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2. 2.

   Quantitative Aptitude

   An item is bought for £200 and sold for £280. Find the profit percentage.

   Formula:Profit Percentage

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

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3. 3.

   Quantitative Aptitude

   Find the simple interest on £3,000 at 4% per annum for 1 year(s).

   Formula:Simple Interest

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

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4. 4.

   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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5. 5.

   Mathematics

   Evaluate log base 10 of 1,000,000.

   Formula:Logarithm Evaluation

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

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6. 6.

   Quantitative Aptitude

   Find the HCF and LCM of 8 and 26.

   Formula:LCM & HCF

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

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7. 7.

   Quantitative Aptitude

   An item is bought for £600 and sold for £720. Find the profit percentage.

   Formula:Profit Percentage

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

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8. 8.

   Mathematics

   Find the slope of the line through (-6, 8) and (-3, -8).

   Formula:Slope of a Line

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

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9. 9.

   Quantitative Aptitude

   The sum of the ages of two people is 85 years, and one is 11 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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10. 10.

    Quantitative Aptitude

    Find the compound interest on £2,000 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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11. 11.

    Quantitative Aptitude

    Pipe A fills a tank in 13 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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12. 12.

    Mathematics

    If f(x) = 5x³ + 2x² + 5x, find f′(3).

    Formula:Derivative of a Polynomial

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

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13. 13.

    Quantitative Aptitude

    The marked price of an item is £500. After a 25% discount, find the selling price.

    Formula:Discount & Selling Price

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

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14. 14.

    Mathematics

    Find term number 5 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term

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

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15. 15.

    Mathematics

    In an arithmetic progression with first term 16 and common difference 1, find term number 9.

    Formula:AP nth Term

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

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16. 16.

    Mathematics

    If f(x) = 4x³ + 2x² + 9x, find f′(4).

    Formula:Derivative of a Polynomial

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

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17. 17.

    Mathematics

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

    Formula:GP nth Term

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

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18. 18.

    Quantitative Aptitude

    A vehicle covers 384 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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19. 19.

    Quantitative Aptitude

    A can finish a job in 8 days and B in 14 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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20. 20.

    Quantitative Aptitude

    Find the HCF and LCM of 14 and 25.

    Formula:LCM & HCF

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

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