View solutions
FormulaWon

TMUA · Practice Sheet 35

Sheet code: TMUA-S35 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Find the slope of the line through (3, 1) and (4, -2).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
    View formula →
  2. 2.
    Mathematics

    Find the sum of the first 13 terms of an AP with first term 9 and common difference 4.

    Formula:AP Sum of n Terms
    Sn=n2 [2a+(n−1)d]S_n = \dfrac{n}{2}\,[2a+(n-1)d]
    View formula →
  3. 3.
    Quantitative Aptitude

    Find the average of these 6 numbers: 43, 40, 33, 44, 76, 68.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
    View formula →
  4. 4.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
    View formula →
  5. 5.
    Quantitative Aptitude

    The sum of the ages of two people is 52 years, and one is 18 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
    View formula →
  6. 6.
    Mathematics

    Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
    View formula →
  7. 7.
    Quantitative Aptitude

    The sum of the ages of two people is 83 years, and one is 3 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
    View formula →
  8. 8.
    Mathematics

    For the quadratic 1x² + 0x − 7 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)
    α+β=−ba,  αβ=ca\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}
    View formula →
  9. 9.
    Mathematics

    Find the slope of the line through (3, 8) and (-6, 7).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
    View formula →
  10. 10.
    Quantitative Aptitude

    A value changes from 200 to 140. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
    View formula →
  11. 11.
    Mathematics

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

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
    View formula →
  12. 12.
    Mathematics

    Evaluate ∫ from 0 to 3 of 5x^2 dx.

    Formula:Definite Integral of a Power
    ∫pqaxn dx=an+1[xn+1]pq\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}
    View formula →
  13. 13.
    Mathematics

    Find the distance between the points (7, 7) and (1, -6).

    Formula:Distance Between Two Points
    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
    View formula →
  14. 14.
    Mathematics

    If f(x) = 2x³ + 5x² + 2x, find f′(3).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
    View formula →
  15. 15.
    Quantitative Aptitude

    A vehicle covers 400 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
    View formula →
  16. 16.
    Quantitative Aptitude

    Divide £1,376 between two people in the ratio 2:6. How much does each receive?

    Formula:Sharing in a Ratio
    Share=Total×partsum of parts\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}
    View formula →
  17. 17.
    Mathematics

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

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
    View formula →
  18. 18.
    Quantitative Aptitude

    Find the simple interest on £34,000 at 10% per annum for 2 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
    View formula →
  19. 19.
    Quantitative Aptitude

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

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
    View formula →
  20. 20.
    Quantitative Aptitude

    An item is bought for £300 and sold for £360. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
    View formula →

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

Go to full solutions for this sheet