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A-Level Maths · Practice Sheet 17

Sheet code: A-LEVEL-MATHS-S17 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Quantitative Aptitude

    Find the average of these 10 numbers: 81, 31, 64, 63, 41, 88, 42, 23, 53, 40.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  2. 2.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 9?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  3. 3.
    Quantitative Aptitude

    Divide £2,860 between two people in the ratio 7:6. 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}}
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  4. 4.
    Mathematics

    Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  5. 5.
    Quantitative Aptitude

    A vehicle covers 405 km in 9 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  6. 6.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  7. 7.
    Mathematics

    Find the slope of the line through (-7, -7) and (-8, 2).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  8. 8.
    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 4.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  9. 9.
    Quantitative Aptitude

    The sum of the ages of two people is 44 years, and one is 12 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  10. 10.
    Mathematics

    In an arithmetic progression with first term 6 and common difference 5, find term number 20.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  11. 11.
    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  12. 12.
    Quantitative Aptitude

    A vehicle covers 328 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  13. 13.
    Quantitative Aptitude

    Divide £2,244 between two people in the ratio 5:6. 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}}
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  14. 14.
    Mathematics

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

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  15. 15.
    Quantitative Aptitude

    Find the HCF and LCM of 25 and 36.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  16. 16.
    Mathematics

    Find the slope of the line through (-4, 8) and (-2, 3).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  17. 17.
    Mathematics

    In an arithmetic progression with first term 19 and common difference 10, find term number 15.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  18. 18.
    Mathematics

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

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  19. 19.
    Quantitative Aptitude

    An item is bought for £300 and sold for £420. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  20. 20.
    Quantitative Aptitude

    What is 25% of 780?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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