11+ · Practice Sheet 2

1. 1.

   Mathematics

   Find the distance between the points (2, -4) and (-5, -8).

   Formula:Distance Between Two Points

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

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2. 2.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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3. 3.

   Mathematics

   Evaluate log base 10 of 1,000.

   Formula:Logarithm Evaluation

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

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4. 4.

   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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5. 5.

   Mathematics

   For the quadratic 2x² + 7x + 3 = 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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6. 6.

   Mathematics

   Find the sum of the first 18 terms of an AP with first term 17 and common difference 6.

   Formula:AP Sum of n Terms

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

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7. 7.

   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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8. 8.

   Mathematics

   In an arithmetic progression with first term 20 and common difference 1, find term number 28.

   Formula:AP nth Term

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

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9. 9.

   Mathematics

   Evaluate ∫ from 0 to 3 of 4x^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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10. 10.

    Quantitative Aptitude

    A invests £9,000 and B invests £5,000 for the same period. If the total profit is £17,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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11. 11.

    Mathematics

    In an arithmetic progression with first term 4 and common difference 9, find term number 18.

    Formula:AP nth Term

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

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12. 12.

    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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13. 13.

    Mathematics

    In an arithmetic progression with first term 6 and common difference 10, find term number 23.

    Formula:AP nth Term

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

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14. 14.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

    Formula:Probability (two dice)

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

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15. 15.

    Mathematics

    Find term number 4 of a geometric progression with first term 5 and common ratio 3.

    Formula:GP nth Term

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

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16. 16.

    Quantitative Aptitude

    Find the HCF and LCM of 33 and 13.

    Formula:LCM & HCF

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

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17. 17.

    Quantitative Aptitude

    Find the compound interest on £16,000 at 20% per annum compounded annually for 3 years.

    Formula:Compound Interest

    $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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18. 18.

    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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19. 19.

    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation

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

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20. 20.

    Mathematics

    In an arithmetic progression with first term 1 and common difference 4, find term number 7.

    Formula:AP nth Term

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

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