Mathematics Past Questions and Answers

(a) Simplify : \(\frac{\frac{1}{3}c^{2} - \frac{2}{3}cd}{\frac{1}{2}d^{2} - \frac{1}{4}cd}\)
(b)
In the diagram, YPF is a straight line. < XPY = 44°, < MPF = 46°, < XYP = < MFP = 90°, /XY/ = 7cm and /MP/ = 9 cm.
(i) Calculate, correct to 3 significant figures, /XM/ and /YF/ ; (ii) Find < XMP.

The table shows the monthly contributions and expenditure pattern of an employee in 1999.

Item	Percentage
Pension	5
Income Tax	25
Food	40
Transport	10
Rent	12.5
Others	7.5

(a) Draw a pie chart to illustrate the data.
(b) If the employee's gross monthly salary was N10,800.00, calculate (i) the pension contribution of the employee ; (ii) the income tax paid by the employee.
(c) If the pension contribution and income tax were deducted from the gross monthly salary, before payment, calculate the take- home pay of the employee.

(a) A = {1, 2, 5, 7} and B = {1, 3, 6, 7} are subsets of the universal set U = {1, 2, 3,...., 10}. Find (i) \(A'\) ; (ii) \((A \cap B)'\) ; (iii) \((A \cup B)'\) ; (iv) the subsets of B each of which has three elements.
(b) Write down the 15th term of the sequence, \(\frac{2}{1 \times 3}, \frac{2}{2 \times 4}, \frac{4}{3 \times 5}, \frac{5}{4 \times 6},...\).
(c) An Arithmetic Progression (A.P) has 3 as its first term and 4 as the common difference, (i) write an expression in its simplest form for the nth term ; (ii) find the least term of the A.P that is greater than 100.

The marks obtained by 40 students in an examination are as follows :
85 77 87 74 77 78 79 89 95 90 78 73 86 83 91 74 84 81 83 75 77 70 81 69 75 63 76 87 61 78 69 96 65 80 84 80 77 74 88 72.
(a) Copy and complete the table for the distribution using the above data.

Class Boundaries	Tally	Frequency
59.5 - 64.5
64.5 - 69.5
69.5 - 74.5
74.5 - 79.5
79.5 - 84.5
84.5 - 89.5
89.5 - 94.5
94.5 - 99.5

(b) Draw a histogram to represent the distribution.
(c) Using your histogram, estimate the modal mark.
(d) If a student is chosen at random, find the probability that the student obtains a mark greater than 79.

In the diagram, PQT is a straight line and SQ // RT.

(a) Join QR and show that : (i) < RPS = < QRT ; (ii) < PRS = < QTR.
(b) ABC is a triangle. The sides AB and AC are produced to D and E respectively such that < DBC = 132° and < ECD = 96°. Show that \(\Delta\) ABC is isosceles.