A-Level Maths · Practice Sheet 22

1. 1.

   Quantitative Aptitude

   A value changes from 400 to 520. Find the percentage increase.

   Formula:Percentage Change

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

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2. 2.

   Mathematics

   Evaluate ∫ from 1 to 4 of 3x^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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3. 3.

   Mathematics

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

   Formula:GP Sum of n Terms

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

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4. 4.

   Mathematics

   Find the binomial coefficient C(8, 3) — the coefficient of x^3 in (1 + x)^8.

   Formula:Binomial Coefficient

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

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5. 5.

   Quantitative Aptitude

   What is 60% of 640?

   Formula:Percentage of a Number

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

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6. 6.

   Mathematics

   Evaluate ∫ from 2 to 5 of 4x^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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7. 7.

   Quantitative Aptitude

   What is 30% of 1,080?

   Formula:Percentage of a Number

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

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8. 8.

   Mathematics

   For the quadratic 4x² − 8x − 1 = 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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9. 9.

   Quantitative Aptitude

   A can finish a job in 18 days and B in 14 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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10. 10.

    Quantitative Aptitude

    A value changes from 300 to 450. Find the percentage increase.

    Formula:Percentage Change

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

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11. 11.

    Mathematics

    Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.

    Formula:Binomial Coefficient

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

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12. 12.

    Quantitative Aptitude

    Find the simple interest on £6,000 at 4% per annum for 6 year(s).

    Formula:Simple Interest

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

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13. 13.

    Mathematics

    In an arithmetic progression with first term 14 and common difference 6, find term number 11.

    Formula:AP nth Term

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

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14. 14.

    Mathematics

    Evaluate log base 5 of 15,625.

    Formula:Logarithm Evaluation

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

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15. 15.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)

    Formula:Permutations

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

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16. 16.

    Mathematics

    Find the slope of the line through (-4, -2) and (-8, -6).

    Formula:Slope of a Line

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

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17. 17.

    Mathematics

    In an arithmetic progression with first term 3 and common difference 8, find term number 29.

    Formula:AP nth Term

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

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18. 18.

    Quantitative Aptitude

    A value changes from 900 to 720. Find the percentage decrease.

    Formula:Percentage Change

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

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19. 19.

    Quantitative Aptitude

    Find the compound interest on £17,000 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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20. 20.

    Quantitative Aptitude

    A value changes from 200 to 250. Find the percentage increase.

    Formula:Percentage Change

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

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