Students take three multiple-choice tests, each with ten questions. A correct answer earns 5 marks. If no answer is given 1 mark is scored. An incorrect answer loses 2 marks. A student's final total mark is the sum of 20% of the mark in test 1, 30% of the mark in test 2 and 50% of the mark in test 3. One student's responses are summarized in the table below. Test 1 Test 2 Test 3 Correct answer 7 6 5 No answer 1 3 5 Incorrect answer 2 1 0 Write down three matrices such that matrix multiplication will give this student's final total mark and hence find this total mark.

Given that A = [[2, -1], [3, 5]], find the adjoint matrix of A.

Given that A = [[2, -1], [3, 5]], find A⁻¹.

Using your answer from part (i), or otherwise, find the value of a such that A[[a, b], [c, -1]] = [[7, 5], [17, d]] w...

Find the set of values of k for which the curve y = 2x² + kx + 2k – 6 lies above the x-axis for all values of x.

The normal to the curve y + 2 = 3 tan x, at the point on the curve where x = 3π/4, cuts the y-axis at the point P. Fi...

It is given that f(x) = 6x³ – 5x² + ax + b has a factor of x + 2 and leaves a remainder of 27 when divided by x – 1.