Free EJU Mathematics Questions and Answers

Question 1

Determine the amount of money in a money market account providing an annual rate of 7% compounded daily if Philips invested $2500 and left it in the account for 10 years.

Accepted Answer

$5034.04

Answer

Explanation:
The correct answer is $5034.04. To determine the amount of money in the money market account, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values, we have A = 2500(1 + 0.07/365)^(365*10) = $5034.04.

Question 2

Given that log 5 = 0.6990, evaluate log 5000.

Accepted Answer

3.6990

Answer

Explanation:
The logarithm of a number represents the exponent to which a base must be raised to obtain that number. In this case, we are given that log 5 = 0.6990. To evaluate log 5000, we need to find the exponent to which the base 5 must be raised to obtain 5000. Since 5^4 = 625, and 5^5 = 3125, we can conclude that 5000 is between these two values. Therefore, the exponent must be between 4 and 5. Since the answer choices are in the form of 0.6990, we can deduce that the correct answer is 3.6990, as it falls between 3 and 4.

Question 3

Differentiate y = ln(7x+2)

Accepted Answer

Dy/dx = 7 /(7x+2)

Answer

Explanation:
The correct answer is dy/dx = 7 /(7x+2). This is the correct differentiation of the given function y= ln(7x+2). The derivative of ln(u) with respect to x is du/dx divided by u. In this case, u = 7x+2, so du/dx = 7. Therefore, the derivative of ln(7x+2) with respect to x is 7/(7x+2).

Question 4

Someone wants to know the inclination angle of a street. He notices that the bricks in a fence are horizontal with respect to the street and that the horizontal distance from a point is 35 cm. From there, downward, the brick measures 6 cm of vertical distance toward the street. What is the inclination angle?

Accepted Answer

9°43´39.28”

Answer

Explanation:
The correct answer of 9°43´39.28” can be explained by using the concept of trigonometry. The problem provides the horizontal distance (35 cm) and the vertical distance (6 cm) of the brick from a point. By using the tangent function, we can calculate the angle of inclination. The tangent of an angle is equal to the ratio of the opposite side (vertical distance) to the adjacent side (horizontal distance). In this case, the tangent of the angle is 6 cm / 35 cm. By taking the inverse tangent (arctan) of this ratio, we can find the angle of inclination, which is approximately 9°43´39.28”.

Question 5

If you need to buy a rope for the flag pole and you notice that the shadow cast by the flagpole is 11.6m. While the elevation angle of the sun is 35° 40.’ What is the length of the rope you must buy?

Accepted Answer

16.65m

Answer

Explanation:
Given that the shadow cast by the flagpole is 11.6m and the elevation angle of the sun is 35° 40', we can use trigonometry to find the length of the rope. The shadow cast by the flagpole represents the adjacent side of a right triangle, while the height of the flagpole represents the opposite side. We can use the tangent function to find the length of the rope, which is the hypotenuse of the triangle. By using the formula tan(angle) = opposite/adjacent, we can calculate the length of the rope to be approximately 16.65m.

EJU - Examination for Japanese University Practice Test

EJU - Examination for Japanese University Practice Test

Free EJU Mathematics Questions and Answers