11+ · Practice Sheet 8

1. 1.

   Mathematics

   Find the sum of the first 5 terms of an AP with first term 3 and common difference 7.

   Formula:AP Sum of n Terms

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

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2. 2.

   Quantitative Aptitude

   Pipe A fills a tank in 4 hours and pipe B in 10 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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3. 3.

   Mathematics

   Find the slope of the line through (-3, -7) and (-6, -2).

   Formula:Slope of a Line

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

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4. 4.

   Mathematics

   Evaluate ∫ from 2 to 5 of 1x^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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5. 5.

   Quantitative Aptitude

   What is 75% of 400?

   Formula:Percentage of a Number

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

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6. 6.

   Mathematics

   In an arithmetic progression with first term 4 and common difference 3, find term number 10.

   Formula:AP nth Term

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

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7. 7.

   Quantitative Aptitude

   Find the simple interest on £7,000 at 6% per annum for 6 year(s).

   Formula:Simple Interest

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

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8. 8.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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9. 9.

   Quantitative Aptitude

   Find the HCF and LCM of 11 and 11.

   Formula:LCM & HCF

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

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10. 10.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 9?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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11. 11.

    Quantitative Aptitude

    Find the average of these 6 numbers: 83, 49, 20, 66, 42, 39.

    Formula:Arithmetic Mean

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

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12. 12.

    Mathematics

    Find term number 6 of a geometric progression with first term 6 and common ratio 3.

    Formula:GP nth Term

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

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13. 13.

    Mathematics

    Find the binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.

    Formula:Binomial Coefficient

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

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14. 14.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 2 and common ratio 3.

    Formula:GP Sum of n Terms

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

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15. 15.

    Quantitative Aptitude

    The marked price of an item is £1,100. After a 30% discount, find the selling price.

    Formula:Discount & Selling Price

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

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16. 16.

    Quantitative Aptitude

    The sum of the ages of two people is 94 years, and one is 20 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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17. 17.

    Mathematics

    Find the distance between the points (7, 5) and (-2, 5).

    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 £800 and sold for £880. Find the profit percentage.

    Formula:Profit Percentage

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

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19. 19.

    Mathematics

    Find the slope of the line through (0, -7) and (-1, 3).

    Formula:Slope of a Line

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

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20. 20.

    Mathematics

    If f(x) = 4x³ + 6x² + 6x, find f′(5).

    Formula:Derivative of a Polynomial

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

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