11+ · Practice Sheet 25

1. 1.

   Quantitative Aptitude

   The sum of the ages of two people is 89 years, and one is 19 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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2. 2.

   Mathematics

   In an arithmetic progression with first term 2 and common difference 10, find term number 23.

   Formula:AP nth Term

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

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3. 3.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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4. 4.

   Quantitative Aptitude

   What is 15% of 920?

   Formula:Percentage of a Number

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

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5. 5.

   Quantitative Aptitude

   A vehicle covers 201 km in 3 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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6. 6.

   Mathematics

   Find the binomial coefficient C(6, 4) — the coefficient of x^4 in (1 + x)^6.

   Formula:Binomial Coefficient

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

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7. 7.

   Quantitative Aptitude

   The marked price of an item is £400. After a 40% 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 average of these 10 numbers: 37, 81, 29, 20, 80, 55, 56, 71, 24, 74.

   Formula:Arithmetic Mean

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

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9. 9.

   Quantitative Aptitude

   Two varieties costing £14 and £99 per kg are mixed to give a mixture worth £50 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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10. 10.

    Mathematics

    Find the slope of the line through (1, -2) and (-5, -7).

    Formula:Slope of a Line

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

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11. 11.

    Mathematics

    Evaluate log base 3 of 9.

    Formula:Logarithm Evaluation

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

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12. 12.

    Quantitative Aptitude

    What is 15% of 780?

    Formula:Percentage of a Number

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

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13. 13.

    Quantitative Aptitude

    An item is bought for £200 and sold for £220. Find the profit percentage.

    Formula:Profit Percentage

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

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14. 14.

    Mathematics

    Find the slope of the line through (-1, 1) and (6, 6).

    Formula:Slope of a Line

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

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15. 15.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 4.)

    Formula:Combinations

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

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16. 16.

    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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17. 17.

    Mathematics

    Find the distance between the points (-5, -4) and (1, 1).

    Formula:Distance Between Two Points

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

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18. 18.

    Quantitative Aptitude

    An item is bought for £600 and sold for £840. Find the profit percentage.

    Formula:Profit Percentage

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

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19. 19.

    Mathematics

    Evaluate ∫ from 2 to 3 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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20. 20.

    Quantitative Aptitude

    Find the compound interest on £5,000 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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