A-Level Maths · Practice Sheet 21

1. 1.

   Mathematics

   Find the sum of the first 17 terms of an AP with first term 11 and common difference 3.

   Formula:AP Sum of n Terms

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

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2. 2.

   Quantitative Aptitude

   A can finish a job in 17 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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3. 3.

   Mathematics

   Find the sum of the first 6 terms of a GP with first term 2 and common ratio 2.

   Formula:GP Sum of n Terms

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

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4. 4.

   Quantitative Aptitude

   Find the simple interest on £7,000 at 12% per annum for 2 year(s).

   Formula:Simple Interest

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

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5. 5.

   Quantitative Aptitude

   Find the compound interest on £1,000 at 10% per annum compounded annually for 2 years.

   Formula:Compound Interest

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

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6. 6.

   Quantitative Aptitude

   What is 50% of 100?

   Formula:Percentage of a Number

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

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7. 7.

   Mathematics

   Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.

   Formula:Binomial Coefficient

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

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8. 8.

   Quantitative Aptitude

   A invests £8,000 and B invests £8,000 for the same period. If the total profit is £37,000, find A's share.

   Formula:Partnership (profit share)

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

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9. 9.

   Quantitative Aptitude

   Divide £1,463 between two people in the ratio 5:2. 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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10. 10.

    Quantitative Aptitude

    Find the HCF and LCM of 11 and 20.

    Formula:LCM & HCF

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

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11. 11.

    Mathematics

    Evaluate ∫ from 1 to 5 of 5x^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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12. 12.

    Quantitative Aptitude

    Find the simple interest on £18,000 at 5% per annum for 4 year(s).

    Formula:Simple Interest

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

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13. 13.

    Mathematics

    Find the slope of the line through (-4, -3) and (-5, -1).

    Formula:Slope of a Line

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

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14. 14.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 1 and common ratio 2.

    Formula:GP Sum of n Terms

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

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15. 15.

    Mathematics

    If f(x) = 5x³ + 5x² + 7x, find f′(1).

    Formula:Derivative of a Polynomial

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

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16. 16.

    Mathematics

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

    Formula:GP nth Term

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

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17. 17.

    Quantitative Aptitude

    An item is bought for £600 and sold for £750. Find the profit percentage.

    Formula:Profit Percentage

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

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18. 18.

    Quantitative Aptitude

    Divide £2,880 between two people in the ratio 7:3. 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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19. 19.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 2 and common ratio 2.

    Formula:GP Sum of n Terms

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

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20. 20.

    Quantitative Aptitude

    What is 15% of 340?

    Formula:Percentage of a Number

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

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