A-Level Maths · Practice Sheet 39

1. 1.

   Mathematics

   Evaluate log base 3 of 27.

   Formula:Logarithm Evaluation

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

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2. 2.

   Mathematics

   In an arithmetic progression with first term 1 and common difference 4, find term number 6.

   Formula:AP nth Term

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

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3. 3.

   Quantitative Aptitude

   Find the average of these 5 numbers: 36, 64, 88, 48, 69.

   Formula:Arithmetic Mean

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

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4. 4.

   Quantitative Aptitude

   Divide £2,893 between two people in the ratio 5:6. 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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5. 5.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 2.)

   Formula:Combinations

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

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6. 6.

   Quantitative Aptitude

   Find the average of these 5 numbers: 65, 59, 65, 21, 71.

   Formula:Arithmetic Mean

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

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7. 7.

   Mathematics

   Find the binomial coefficient C(5, 4) — the coefficient of x^4 in (1 + x)^5.

   Formula:Binomial Coefficient

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

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8. 8.

   Quantitative Aptitude

   Pipe A fills a tank in 8 hours and pipe B in 14 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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9. 9.

   Quantitative Aptitude

   A value changes from 300 to 225. Find the percentage decrease.

   Formula:Percentage Change

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

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10. 10.

    Quantitative Aptitude

    Find the simple interest on £44,000 at 4% per annum for 4 year(s).

    Formula:Simple Interest

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

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11. 11.

    Quantitative Aptitude

    Find the average of these 8 numbers: 82, 23, 42, 51, 86, 23, 78, 60.

    Formula:Arithmetic Mean

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

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12. 12.

    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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13. 13.

    Quantitative Aptitude

    What is 60% of 440?

    Formula:Percentage of a Number

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

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14. 14.

    Mathematics

    Find term number 4 of a geometric progression with first term 3 and common ratio 2.

    Formula:GP nth Term

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

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15. 15.

    Quantitative Aptitude

    What is 60% of 320?

    Formula:Percentage of a Number

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

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16. 16.

    Quantitative Aptitude

    A value changes from 200 to 120. Find the percentage decrease.

    Formula:Percentage Change

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

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17. 17.

    Quantitative Aptitude

    Find the compound interest on £6,000 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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18. 18.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 4 and common ratio 3.

    Formula:GP Sum of n Terms

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

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19. 19.

    Quantitative Aptitude

    Find the HCF and LCM of 15 and 22.

    Formula:LCM & HCF

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

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20. 20.

    Mathematics

    Evaluate ∫ from 1 to 4 of 2x^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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