11+ · Practice Sheet 1

1. 1.

   Mathematics

   Find the slope of the line through (8, 5) and (-5, -2).

   Formula:Slope of a Line

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

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2. 2.

   Mathematics

   Evaluate log base 3 of 81.

   Formula:Logarithm Evaluation

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

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3. 3.

   Mathematics

   In an arithmetic progression with first term 13 and common difference 10, find term number 8.

   Formula:AP nth Term

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

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4. 4.

   Mathematics

   Find the slope of the line through (-3, 2) and (-7, -5).

   Formula:Slope of a Line

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

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5. 5.

   Quantitative Aptitude

   A can finish a job in 14 days and B in 13 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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6. 6.

   Quantitative Aptitude

   An item is bought for £600 and sold for £900. Find the profit percentage.

   Formula:Profit Percentage

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

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7. 7.

   Quantitative Aptitude

   What is 40% of 920?

   Formula:Percentage of a Number

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

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8. 8.

   Mathematics

   Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

   Formula:Binomial Coefficient

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

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9. 9.

   Quantitative Aptitude

   A vehicle covers 405 km in 5 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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10. 10.

    Quantitative Aptitude

    Find the HCF and LCM of 37 and 36.

    Formula:LCM & HCF

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

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11. 11.

    Quantitative Aptitude

    A can finish a job in 13 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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12. 12.

    Quantitative Aptitude

    Find the HCF and LCM of 30 and 9.

    Formula:LCM & HCF

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

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13. 13.

    Quantitative Aptitude

    What is 50% of 880?

    Formula:Percentage of a Number

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

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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.

    Quantitative Aptitude

    A vehicle covers 432 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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16. 16.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)

    Formula:Combinations

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

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17. 17.

    Quantitative Aptitude

    What is 25% of 1,060?

    Formula:Percentage of a Number

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

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18. 18.

    Mathematics

    Evaluate ∫ from 0 to 3 of 3x^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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19. 19.

    Quantitative Aptitude

    A vehicle covers 240 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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20. 20.

    Quantitative Aptitude

    Two varieties costing £40 and £89 per kg are mixed to give a mixture worth £54 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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