A-Level Maths · Practice Sheet 12

1. 1.

   Mathematics

   Find the sum of the first 7 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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2. 2.

   Mathematics

   If f(x) = 1x³ + 1x² + 2x, find f′(5).

   Formula:Derivative of a Polynomial

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

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3. 3.

   Quantitative Aptitude

   Divide £1,392 between two people in the ratio 7:5. 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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4. 4.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

   Formula:Probability (two dice)

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

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5. 5.

   Quantitative Aptitude

   Two varieties costing £34 and £98 per kg are mixed to give a mixture worth £58 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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6. 6.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)

   Formula:Combinations

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

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7. 7.

   Quantitative Aptitude

   A can finish a job in 13 days and B in 20 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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8. 8.

   Mathematics

   Find term number 3 of a geometric progression with first term 2 and common ratio 3.

   Formula:GP nth Term

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

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9. 9.

   Mathematics

   Find the distance between the points (-8, 7) and (8, -8).

   Formula:Distance Between Two Points

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

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10. 10.

    Quantitative Aptitude

    What is 75% of 680?

    Formula:Percentage of a Number

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

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11. 11.

    Quantitative Aptitude

    A value changes from 700 to 350. Find the percentage decrease.

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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12. 12.

    Quantitative Aptitude

    Find the average of these 8 numbers: 41, 53, 29, 51, 28, 43, 40, 59.

    Formula:Arithmetic Mean

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

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13. 13.

    Quantitative Aptitude

    What is 30% of 580?

    Formula:Percentage of a Number

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

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14. 14.

    Mathematics

    Evaluate log base 3 of 9.

    Formula:Logarithm Evaluation

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

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15. 15.

    Quantitative Aptitude

    Pipe A fills a tank in 15 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

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16. 16.

    Quantitative Aptitude

    What is 50% of 380?

    Formula:Percentage of a Number

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

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17. 17.

    Mathematics

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

    Formula:GP nth Term

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

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18. 18.

    Quantitative Aptitude

    The sum of the ages of two people is 59 years, and one is 17 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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19. 19.

    Quantitative Aptitude

    Find the simple interest on £37,000 at 10% per annum for 3 year(s).

    Formula:Simple Interest

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

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20. 20.

    Mathematics

    For the quadratic 5x² + 8x − 6 = 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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