J maths 15

Given that \(A = \{3, 4, 1, 10, \tfrac{1}{3}\}\)
\(B = \{4, 3\tfrac{1}{3}, \tfrac{1}{3}, 7\}\).

Find \(A \cap B\).

Simplify 1(x+1)+1(x−1)

The volume of a cylinder whose height is 4cm and whose radius 5cm is equal to (π = 3.14)

The area of a circle of radius 4cm is equal to (Take π = 3.142 )

Factorize x²-2x-15

The area of an ellipse is 132cm². The length of its major axis is 14cm. Find the length of it minor axis.

If an investor invest ₦450,000 in a certain organization in order to yield X as a return of ₦25,000. Find the return on an investment of ₦700,000 by Y in the same organization.

If \((159.75)_{10} = (x)_{6}\). Find \(x\).

Simplify (0.09)² and give your correct answer to four significant figures.

Simplify 4 √[(390695T− 8)½)]

Simplify 6(1/12) − 2(¾) +1(½)

A man bought a car for ₦800 and sold it for ₦520. Find his loss per cent

Simplify 2.04 × 3.7 (Leave your answer in 2 decimal place)

Simplify \([1 \div (x^2 + 3x + 2)] + [1 \div (x^2 + 5x + 6)]\)

Find the value of \(x\) if \(\big[ 1 \div 64^{(x+2)} \big] = \big[ 4^{(x-3)} \div 16^x \big]\)

Find the simple interest on ₦325 in 5years at 3% per annum.

The probability of an event A is 1/5. The probability of B is 1/3 . The probability both A and B is 1/15. What is the probability of either event A or B or both?

The extension of a stretched string is directly proportional to its tension. If the extension produced by a tension of 8 Newtons is 2cm, find the extension produced by a tension of 12 Newtons.

Rationalize 5 ÷ (2 − √3)

A pipe made of metal 10cm thick has an external radius of 11cm. find the area of metal in making 2.4cm of pipe

Integral \(\int (5x^3 + 7x^2 - 2x + 5)\, dx\)

Given that S and T are sets of real numbers such that S = {x:0 ≤ x≤ 5} and T = {x :− 2 < x < 3} Find S ∪ T

A man sells his new brand car for ₦420,000 at a gain of 15%. What did it cost him?

Evaluate \(\int x^2 \sin x \, dx\)

The probability of an outcome A is 1/6. The probability of the B outcome is 1/4. If the probability of A or B or both is 1/12, what is the probability of both outcomes A and B?

One bag contain 3 blue and 5 red balls, another bag contain 2 blue and 4 red balls respectively. One ball is drawn for each bag. What is the probability both balls are blue

Calculate the value of \(x\) and \(y\) if \( 27^x \div 81^{x+2y} = 9, \; x + 4y = 0 \)

Evaluate \( \log_{5}\left(\dfrac{y^2 x^5}{125 b^{1/2}}\right) \)

Find the area of the curved surface of a cone whose base radius is 3cm and whose height is 4cm (π = 3.14)

If duty is levied at 25%, find the duty to be added to a bill of ₦80.

Find the derivatives of (2 + 3x)(1 - x) with respect to x

Add \(1101_2, 10111_2 \text{ and } 111_2\)

Factorize a² - b² -4a+4

Find the distance between the points (-2,-3) and (-2,4)

Solve:
\(5^{(x-2)} = \left(\frac{1}{125}\right)^{(x+3)}\)

How many sides has a regular polygon whose interior angles are 120 degrees each?

Find the range of the value of x satisfying the inequalities 5+x≤ 8 and 13 + x ≥ 7

A public car dealer marked up the cost of a car at 30% in an attempt to make 20% gross profit. Due to the value of dollar, he now placed 20% discount on the car. What profit or loss will he make?

If √(2x + 2) − √x = 1, find x

If A = (−3,5) and B = (4,−1) find the co-ordinate of the mid point

Evaluate: \(\log_{7}{17}\)

Given that Z = {1,2,4,5} what is the power of set Z?

The volume of a cone (s) of height 6cm and base radius 5cm is

Determine the third term of a geometrical progression whose first and second term are 2
and 14 respectively

Simplify √30 × √40

The sum of two numbers is 5; their product is 14. Find the numbers.

In the Venn diagram, the shaded region is?

Given that \(\tan x = \tfrac{2}{3}\), where \(0^\circ < x < 90^\circ\), find the value of \(2 \sin x\).

Find \(x\) if \(132_x = 70_8\).

Solve x² - 2x - 3 =0