11+ · Practice Sheet 42

1. 1.

   Quantitative Aptitude

   Divide £1,836 between two people in the ratio 6:3. 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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2. 2.

   Mathematics

   For the quadratic 3x² + 9x + 5 = 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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3. 3.

   Quantitative Aptitude

   A can finish a job in 10 days and B in 12 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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4. 4.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 3.)

   Formula:Combinations

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

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5. 5.

   Quantitative Aptitude

   The sum of the ages of two people is 69 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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6. 6.

   Quantitative Aptitude

   Pipe A fills a tank in 15 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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7. 7.

   Mathematics

   Find the slope of the line through (3, -8) and (0, -4).

   Formula:Slope of a Line

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

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8. 8.

   Mathematics

   If f(x) = 4x³ + 2x² + 9x, find f′(5).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Mathematics

   Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

   Formula:Binomial Coefficient

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

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10. 10.

    Quantitative Aptitude

    What is 10% of 300?

    Formula:Percentage of a Number

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

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11. 11.

    Quantitative Aptitude

    Find the HCF and LCM of 10 and 16.

    Formula:LCM & HCF

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

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12. 12.

    Mathematics

    Evaluate log base 10 of 1,000,000.

    Formula:Logarithm Evaluation

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

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13. 13.

    Mathematics

    For the quadratic 2x² − 9x + 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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14. 14.

    Mathematics

    Find the sum of the first 12 terms of an AP with first term 4 and common difference 8.

    Formula:AP Sum of n Terms

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

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15. 15.

    Mathematics

    Find the slope of the line through (3, 1) and (4, 6).

    Formula:Slope of a Line

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

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16. 16.

    Quantitative Aptitude

    The marked price of an item is £1,900. After a 50% discount, find the selling price.

    Formula:Discount & Selling Price

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

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17. 17.

    Quantitative Aptitude

    What is 75% of 560?

    Formula:Percentage of a Number

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

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18. 18.

    Mathematics

    Find the distance between the points (2, 5) and (-4, 1).

    Formula:Distance Between Two Points

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

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19. 19.

    Quantitative Aptitude

    Two varieties costing £23 and £97 per kg are mixed to give a mixture worth £33 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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20. 20.

    Mathematics

    For the quadratic 3x² + 7x + 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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