JAMB UTME - Mathematics - 2009

Find the value of \( \sin 45^\circ - \cos 30^\circ \)

A regular polygon has \(150^\circ\) as the size of each interior angle. How many sides does it have?

If s = (2 + 3t)(5t - 4), find \( \frac{dy}{dx} \) when t = \( \frac{4}{5} \) sec

i. \(S \cap T \cap W = S\)
ii. \(S \cup T \cup W = W\)
ii. \(T \cap W = S\)

If \(S \subset T \subset W\). Which of the above statements are true?

If \(P = \begin{bmatrix} x+3 & x+2 \\ x+1 & x-1 \end{bmatrix}\) evaluate x if \(|P| = -10\)

Simplify \( \frac{5+\sqrt{7}}{3+\sqrt{7}} \)

The probability of a student passing any examination is \( \frac{2}{3} \). If the student takes three examinations, what is the probability that he will not pass any of them?

Find the range of values of \(x\) for which \(3x - 7 \le 0\) and \(x + 5 > 0\)

The distribution above shows the number of days a group of 260 students were absent from school in a particular term. How many students were absent for at least four days in the term

The cumulative frequency curve above shoes the distribution of the scores of 50 students in an examination. Find the 36th percentile scores

In the figure above, TS//XY and XY = TY,

Evaluate \( \int \sec^2 \theta \, d\theta \)

Find to infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3, \ldots\)

The histogram above represents the number of candidates that sat for Mathematics examination in a school. How many candidate scored more than 50 marks?

Find the value of x in the diagram.

The distribution above shows the number of days a group of 260 students were absents from school in a particular term. How many students were absent for at least four days in the term

A binary operation \(plus\) defined on the set of integers is such that m \(plus\) n = n + mn for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0.

Find the infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3, ...\)

Find the acute angle between the straight lines \(y = x\) and \(y = \sqrt{3x}\)

Evaluate \(\frac{81.81+99.44}{20.09+36.16}\) correct to 3 significant figures.

If \( p = \begin{pmatrix} x + 3 & x + 2 \\ x + 1 & x - 1 \end{pmatrix} \) evaluate x if \(|p| = -10\)

A student spent \( \frac{1}{5} \) of his allowances on books, \( \frac{1}{3} \) of the remainder on food and kept the rest for contingences. What fraction was kept?

If \(m * n = n-(m + 2)\) for any real numbers m and n, find the value of \(3 * (-5)\)

I.S∩T∩W=S II. S∪T∪W=S

III. T∩W=S

If S⊂T⊂W, which of the above statements are true?

If \(y = 3 \cos 4x\), \(\frac{dy}{dx}\) equals

Simplify \(4\frac{3}{4} - 6\frac{1}{4}\)

The table above shows the distribution of marks of students in a test. Find the probability of passing the test if the pass mark is 5.

A cliff on the bank of a river is 300 meter high. if the angle of depression of a point on the opposite side of the river is \(60^\circ\), find the width of the river.