A-Level Maths · Practice Sheet 10

1. 1.

   Mathematics

   Evaluate log base 5 of 625.

   Formula:Logarithm Evaluation

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

   View formula →
2. 2.

   Mathematics

   If f(x) = 3x³ + 3x² + 6x, find f′(2).

   Formula:Derivative of a Polynomial

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

   View formula →
3. 3.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)

   Formula:Combinations

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

   View formula →
4. 4.

   Quantitative Aptitude

   In how many ways can 4 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 4.)

   Formula:Permutations

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

   View formula →
5. 5.

   Quantitative Aptitude

   An item is bought for £800 and sold for £960. Find the profit percentage.

   Formula:Profit Percentage

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

   View formula →
6. 6.

   Quantitative Aptitude

   Two varieties costing £36 and £82 per kg are mixed to give a mixture worth £66 per kg. Find the mixing ratio.

   Formula:Alligation (Mixtures)

   $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

   View formula →
7. 7.

   Quantitative Aptitude

   An item is bought for £700 and sold for £1,050. Find the profit percentage.

   Formula:Profit Percentage

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

   View formula →
8. 8.

   Mathematics

   In an arithmetic progression with first term 11 and common difference 10, find term number 6.

   Formula:AP nth Term

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

   View formula →
9. 9.

   Quantitative Aptitude

   Pipe A fills a tank in 11 hours and pipe B in 3 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

   View formula →
10. 10.

    Mathematics

    Find the slope of the line through (1, 0) and (5, 0).

    Formula:Slope of a Line

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

    View formula →
11. 11.

    Quantitative Aptitude

    Find the HCF and LCM of 36 and 24.

    Formula:LCM & HCF

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

    View formula →
12. 12.

    Mathematics

    Find the binomial coefficient C(6, 4) — the coefficient of x^4 in (1 + x)^6.

    Formula:Binomial Coefficient

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

    View formula →
13. 13.

    Quantitative Aptitude

    What is 50% of 720?

    Formula:Percentage of a Number

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

    View formula →
14. 14.

    Mathematics

    Evaluate ∫ from 0 to 5 of 5x^1 dx.

    Formula:Definite Integral of a Power

    $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

    View formula →
15. 15.

    Quantitative Aptitude

    A value changes from 600 to 840. Find the percentage increase.

    Formula:Percentage Change

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

    View formula →
16. 16.

    Quantitative Aptitude

    An item is bought for £200 and sold for £240. Find the profit percentage.

    Formula:Profit Percentage

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

    View formula →
17. 17.

    Quantitative Aptitude

    A vehicle covers 441 km in 9 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

    View formula →
18. 18.

    Quantitative Aptitude

    What is 15% of 440?

    Formula:Percentage of a Number

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

    View formula →
19. 19.

    Mathematics

    Evaluate ∫ from 0 to 5 of 4x^3 dx.

    Formula:Definite Integral of a Power

    $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

    View formula →
20. 20.

    Quantitative Aptitude

    Pipe A fills a tank in 7 hours and pipe B in 4 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.