Daily Practice · Higher Plus

Daily Practice - Higher Plus

Grades 8-9 - exam-stretch algebra, geometry and reasoning.

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10th January 2023

5 questions · 14 marks · Grades 8-9 · 51 question types in this band

  1. 1
    Perpendicular Lines and the equation of a tangent3 marks

    The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.

  2. 2
    Conditional Probability3 marks

    A bag holds 4 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

  3. 3
    Histograms2 marks

    On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

  4. 4
    Surds3 marks

    Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).

  5. 5
    Proof3 marks

    Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.

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