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A-Level Maths · Practice Sheet 50

Sheet code: A-LEVEL-MATHS-S50 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Find the sum of the first 7 terms of an AP with first term 7 and common difference 5.

    Formula:AP Sum of n Terms
    Sn=n2 [2a+(n−1)d]S_n = \dfrac{n}{2}\,[2a+(n-1)d]
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  2. 2.
    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
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  3. 3.
    Quantitative Aptitude

    Find the average of these 8 numbers: 50, 67, 36, 26, 75, 69, 41, 86.

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

    An item is bought for £200 and sold for £280. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  5. 5.
    Mathematics

    If f(x) = 2x³ + 1x² + 4x, find f′(5).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  6. 6.
    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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  7. 7.
    Quantitative Aptitude

    What is 15% of 1,000?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  8. 8.
    Mathematics

    Find the distance between the points (-1, 5) and (5, 4).

    Formula:Distance Between Two Points
    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
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  9. 9.
    Quantitative Aptitude

    The marked price of an item is £1,700. After a 5% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
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  10. 10.
    Mathematics

    Find the slope of the line through (-5, -4) and (-4, 3).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  11. 11.
    Mathematics

    In an arithmetic progression with first term 7 and common difference 5, find term number 22.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  12. 12.
    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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  13. 13.
    Quantitative Aptitude

    The sum of the ages of two people is 35 years, and one is 11 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  14. 14.
    Mathematics

    In an arithmetic progression with first term 6 and common difference 1, find term number 27.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  15. 15.
    Mathematics

    Find term number 6 of a geometric progression with first term 5 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  16. 16.
    Mathematics

    Find the sum of the first 6 terms of a GP with first term 5 and common ratio 3.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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  17. 17.
    Quantitative Aptitude

    Find the average of these 6 numbers: 54, 70, 54, 74, 63, 65.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  18. 18.
    Quantitative Aptitude

    An item is bought for £600 and sold for £840. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
    View formula →
  19. 19.
    Quantitative Aptitude

    The marked price of an item is £1,900. After a 30% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
    View formula →
  20. 20.
    Mathematics

    Find term number 5 of a geometric progression with first term 4 and common ratio 2.

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