1. (a) Find the value of a (b) Use a non-programmable calculator to find the mean and standard deviation of the scores from the following data of 80 students: class 90.5 80.5 70.5 60.5 50.5 40.5 30.5 20.5 mark Frequency 4 17 16 8 a 7 12 3

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Support briefly by giving four reasons the statement that; “Students’ progressive report keeping is an important aspect for motivation in learning Mathematics”.

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(a) Given that, the roots of the quadratic equation ax^2 + bx + c differ by 2, then show that 4ac = b^2 – 4a (b) Given that; x + 2 and 2x - 1 are factors of the quadratic equation ax^2 + x – c. Find the values of a and c.

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Given the function f(x) = cosh^-1 x (a) sketch the locus of the function using the table of values such that 1<=x<=4 (b) determine for the values of x and y where the function is defined.

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Find the value of a in surd form if ∫₁ᵃ (x+1) dx = ∫₀^𝜋/2 4sin²x dx

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(a) Determine the values of and such that the points (-1, 3, 2), (-4, 2, -2) and (5, , ) lie on a straight line. (b) Given that; if i, j, k are unit vectors, find |̅i + ̅j| (c) Find the angle between the vectors giving your answer in correct to two decimal places.

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