J maths 19

Make \(T\) the subject of the relation

\(P = \left(\frac{Q(R - T)}{15}\right)^{\tfrac{1}{3}}\)

Find the equation of a line perpendicular to the line 4y = 7x + 3 which passes through (-3, 1)

This table below gives the scores of a group of students in a Further Mathematics Test.

Calculate the mean deviation for the distribution.

Evaluate \(\dfrac{2 \log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625}\)

Find the value of \(x\) for \(\dfrac{2 + 2x}{3} - 2 \geq \dfrac{4x - 6}{5}\)

If the universal set is μ = {x : 1 ≤ x ≤ 20} and
A = {y : multiple of 3}
B = {z : odd numbers}
Find A ∩ B

In the circle above, with centre O and radius 7 cm. Find the length of the arc AB, when < AOB = 57°.

Find the value of k in the equation: √28+√112−√k=√175

In a committee of 5, which must be selected from 4 males and 3 females. In how many ways can the members be chosen if it were to include 2 females?

A bricklayer charges ₦1,500 per day for himself and ₦500 per day for his assistant. If a two bedroom flat was built for ₦95,000 and the bricklayer worked 10 days more than his assistant, how much did the assistant receive?

Points X and Y are 20km North and 9km East of point O, respectively. What is the bearing of Y from X? Correct to the nearest degree.

If the volume of a frustum is given as
\(V = \dfrac{\pi h}{3}(R^2 + Rr + r^2)\), find \(\dfrac{dV}{dR}\).

If M varies directly as N and inversely as the root of P. Given that M = 3, N = 5 and P = 25. Find the value of P when M = 2 and N = 6.

Find the value of \(x\) for \(\dfrac{2 + 2x}{3} - 2 \geq \dfrac{4x - 6}{5}\)

Differentiate 2x/(sinx) with respect to x.

Find the distance between the points C(2, 2) and D(5, 6).

Integrate \(\int (4x^{-3} - 7x^2 + 5x - 6)\,dx\).

If \(\sin x = \dfrac{4}{5}\), find \(\dfrac{1 + \cot^2 x}{\csc^2 x - 1}\).

Express (0.0439/3.62) as a fraction.

If \[
\begin{vmatrix}
2 & -5 & 3 \\
x & 1 & 4 \\
0 & 3 & 2
\end{vmatrix} = 132
\]
find the value of x.

In the diagram above, O is the centre of the circle ABC, < ABO = 26 ° and < BOC = 130 °. Calculate <AOC.

Find the value of x and y in the simultaneous equation: 3x + y = 21; xy = 30

Each of the interior angles of a regular polygon is 140 degrees. Calculate the sum of all the interior angles of the polygon.

If 2x^3 +x-3 divide by x-2. Find the remainder

The histogram above represents the number of candidates who did Further Mathematics examination in a school. How many candidates scored more than 40?

Given the matrix A=\(
\begin{pmatrix}
3 & -2 \\
1 & 6
\end{pmatrix}
\), fine the reverse of A

If y = 8x³ - 3x² + 7x - 1, find \(\frac{d^2y}{dx^2}\).

A factory worker earns ₦50,000 per month out of which he spends 15% on his children's education, ₦13,600 on Food, 3% on electricity and uses the rest for his personal purpose. How much does he have left?

Simplify (0.0839×6.381) / 5.44 to 2 significant figures.

The polynomial
\[
2x^{3} + 3x^{2} + qx - 1
\]
has the same remainder when divided by
\((x+2)\) and \((x-1)\).
Find the value of the constant \(q\).

A man bought a car newly for ₦1,250,000. He had a crash with the car and later sold it at the rate of ₦1,085,000. What is the percentage gain or loss of the man?

Find the probability that a number selected at random from 21 to 34 is a multiple of 3

Find the equation of the locus of a point A(x, y) which is equidistant from B(0, 2) and C(2, 1)

A binary operation Δ is defined by a Δ b = a+3b+2. Find (3 Δ 2) Δ 5

This table below gives the scores of a group of students in a Further Mathematics Test

\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
\text{Score} & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
\text{Frequency} & 4 & 6 & 8 & 4 & 10 & 6 & 2 \\
\hline
\end{array}
\]

Find the mode of the distribution.

Calculate the volume of the regular three dimensional figure drawn above, where < ABC = 90° (a right- angled triangle).

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Marks} & 1 & 2 & 3 & 4 & 5 \\
\hline
\text{Frequency} & 2y & 2y-1 & 3y-4 & 3-y & 6-2y \\
\hline
\end{array}
\]

The table above is the distribution of data with mean equal to 3.
Find the value of \(y\).

If the 3rd and 7th terms of a G.P are 9 and 1/9 respectively. Find the common ratio.

Evaluate
\[
\frac{2 \sin 30 + 5 \tan 60}{\sin 60},
\]
leaving your answer in surd form.

Determine the values for which
\[
x^{2} - 7x + 10 \leq 0
\]