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GCSE Maths · Practice Sheet 1

Sheet code: GCSE-MATHS-S01 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    If f(x) = 2x³ + 5x² + 1x, 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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  2. 2.
    Mathematics

    Evaluate log base 5 of 625.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  3. 3.
    Mathematics

    Find the slope of the line through (1, 2) and (-6, -2).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  4. 4.
    Quantitative Aptitude

    A value changes from 800 to 640. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  5. 5.
    Quantitative Aptitude

    Divide £1,776 between two people in the ratio 5:3. 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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  6. 6.
    Quantitative Aptitude

    The sum of the ages of two people is 62 years, and one is 6 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  7. 7.
    Quantitative Aptitude

    Find the average of these 6 numbers: 74, 55, 47, 51, 80, 82.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  8. 8.
    Mathematics

    Find the distance between the points (6, 4) and (1, 8).

    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

    A vehicle covers 318 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  10. 10.
    Quantitative Aptitude

    The sum of the ages of two people is 85 years, and one is 7 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  11. 11.
    Mathematics

    Find term number 5 of a geometric progression with first term 2 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  12. 12.
    Quantitative Aptitude

    A invests £8,000 and B invests £9,000 for the same period. If the total profit is £29,000, find A's share.

    Formula:Partnership (profit share)
    ShareA=Profit×AA+B\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}
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  13. 13.
    Quantitative Aptitude

    Pipe A fills a tank in 6 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
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  14. 14.
    Quantitative Aptitude

    Find the average of these 5 numbers: 57, 49, 64, 40, 65.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  15. 15.
    Quantitative Aptitude

    The marked price of an item is £1,500. After a 15% 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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  16. 16.
    Mathematics

    Find the slope of the line through (0, 0) and (1, 2).

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

    A invests £8,000 and B invests £3,000 for the same period. If the total profit is £36,000, find A's share.

    Formula:Partnership (profit share)
    ShareA=Profit×AA+B\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}
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  18. 18.
    Quantitative Aptitude

    A can finish a job in 13 days and B in 12 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  19. 19.
    Mathematics

    Find the distance between the points (-6, 7) and (1, 2).

    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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  20. 20.
    Mathematics

    Find term number 4 of a geometric progression with first term 6 and common ratio 3.

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