The following is an incomplete table for the relation \(y = 2x^{2} - 5x + 1\)

(a) Copy and complete the table.

(b) Using a scale of 2cm to 1 unit on the x- axis and 2cm to 10 units on the y- axis, draw the graph of the relation \(y = 2x^{2} - 5x + 1\) for \(-3 \leq x \leq 5\).

(c) Using the same scale and axes, draw the graph of \(y = x + 6\).

(d) Estimate from your graphs, correct to one decimal place : (i) the least value of y and the value of x for which it occurs ; (ii) the solution of the equation \(2x^{2} - 5x + 1 = x + 6\).

In a class of 40 students, 25 speak Hausa, 16 speak Igbo, 21 speak Yoruba and each of the students speak at least one of the these three languages. If 8 speak Hausa and Igbo, 11 speak Hausa and Yoruba and 6 speak Igbo and Yoruba.

(a) Draw a Venn diagram to illustrate the information, using x to represent the number of students that speak all three languages.

(b) calculate the value of x.

An aeroplane flies from a town P(lat. 40°N, 38°E) to another town Q(lat. 40°N, 22°W). It later flies to a third town T(28°N, 22°W). Calculate the :

(a) distance between P and Q along their parallel of latitude ;

(b) distance between Q and T along their line of longitudes;

(c) average speed at which the aeroplane will fly from P to T via Q, if the journey takes 12 hours, correct to 3 significant figures. [Take the radius of the earth = 6400km ; \(\pi = 3.142\)]

(a) Without using Mathematical tables, find x, given that \(6 \log (x + 4) = \log 64\)

(b) If \(U = {1, 2, 3,4, 5, 6, 7, 8, 9, 10}, X = {1, 2, 4, 6, 7, 8, 9}, Y = {1, 2, 3, 4, 7, 9}\) and \(Z = {2, 3, 4, 7, 9}\). What is \(X \cap Y \cap Z' \)?

The table shows the weights, to the nearest kilogram, of twelve students in a Further Mathematics class

(a) Draw a bar chart to illustrate the above information;

(b) What is (i) the mode; (ii) the median of the distribution?

(c) Calculate the mean weight correct to the nearest kilogram.