A-Level Maths · Practice Sheet 5

1. 1.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 4.)

   Formula:Combinations

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

   View formula →
2. 2.

   Mathematics

   Find the slope of the line through (-4, -3) and (3, 2).

   Formula:Slope of a Line

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

   View formula →
3. 3.

   Mathematics

   If f(x) = 2x³ + 1x² + 4x, find f′(4).

   Formula:Derivative of a Polynomial

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

   View formula →
4. 4.

   Quantitative Aptitude

   Find the HCF and LCM of 20 and 10.

   Formula:LCM & HCF

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

   View formula →
5. 5.

   Mathematics

   Find term number 4 of a geometric progression with first term 5 and common ratio 3.

   Formula:GP nth Term

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

   View formula →
6. 6.

   Mathematics

   Evaluate log base 10 of 1,000,000.

   Formula:Logarithm Evaluation

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

   View formula →
7. 7.

   Quantitative Aptitude

   Find the average of these 6 numbers: 39, 62, 83, 63, 42, 64.

   Formula:Arithmetic Mean

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

   View formula →
8. 8.

   Mathematics

   Find the distance between the points (-8, 3) and (3, 5).

   Formula:Distance Between Two Points

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

   View formula →
9. 9.

   Mathematics

   In an arithmetic progression with first term 9 and common difference 10, find term number 26.

   Formula:AP nth Term

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

   View formula →
10. 10.

    Quantitative Aptitude

    A can finish a job in 16 days and B in 15 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

    View formula →
11. 11.

    Quantitative Aptitude

    Find the average of these 6 numbers: 79, 86, 74, 28, 27, 84.

    Formula:Arithmetic Mean

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

    View formula →
12. 12.

    Quantitative Aptitude

    Find the HCF and LCM of 16 and 8.

    Formula:LCM & HCF

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

    View formula →
13. 13.

    Quantitative Aptitude

    A invests £7,000 and B invests £10,000 for the same period. If the total profit is £18,000, find A's share.

    Formula:Partnership (profit share)

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

    View formula →
14. 14.

    Mathematics

    Evaluate ∫ from 2 to 3 of 5x^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 →
15. 15.

    Quantitative Aptitude

    Find the simple interest on £49,000 at 4% per annum for 4 year(s).

    Formula:Simple Interest

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

    View formula →
16. 16.

    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 →
17. 17.

    Quantitative Aptitude

    Two varieties costing £11 and £86 per kg are mixed to give a mixture worth £78 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

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

    View formula →
18. 18.

    Quantitative Aptitude

    A invests £7,000 and B invests £4,000 for the same period. If the total profit is £21,000, find A's share.

    Formula:Partnership (profit share)

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

    View formula →
19. 19.

    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

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

    View formula →
20. 20.

    Mathematics

    In an arithmetic progression with first term 17 and common difference 8, find term number 16.

    Formula:AP nth Term

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

    View formula →

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