Maths Kiran Publication: Arithmetic

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Questions and Answers

A line segment has endpoints A(2, -5) and B(6, 3). Determine the coordinates of point P that divides the segment AB in the ratio 3:1.

The coordinates of point P are (5, 1). Use the section formula: $P(x, y) = (\frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2})$, where $m_1 = 3$, $m_2 = 1$, $A(x_1, y_1) = (2, -5)$, and $B(x_2, y_2) = (6, 3)$.

Given that $\sin(\theta) = \frac{5}{13}$ and $\theta$ is an acute angle, find the value of $\tan(\theta) + \sec(\theta)$.

$\frac{17}{12}$. First, find $\cos(\theta)$ using the Pythagorean identity $\sin^2(\theta) + \cos^2(\theta) = 1$, then calculate $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$ and $\sec(\theta) = \frac{1}{\cos(\theta)}$, and finally add them together.

A pie chart represents the expenditure of a family on different items. If the central angle corresponding to education is 72°, and the total monthly income of the family is $45,000, calculate the amount spent on education.

$9,000. The amount spent on education is calculated by: $(\frac{72}{360}) \times 45000$.

The heights of 5 students are 160 cm, 165 cm, 170 cm, 175 cm and 180 cm. Determine both the mean and the median height.

The Mean is 170cm, and the Median is also 170cm. The mean is calculated by summing all the heights and dividing by 5. As there are an odd number of data points, the median is the middle value, which is 170cm. Signup and view all the answers

From the top of a cliff 20 m high, the angle of depression of a boat is 60°. Find the distance of the boat from the foot of the cliff.

$\frac{20}{\sqrt{3}}$ meters or $20\frac{\sqrt{3}}{3}$ meters. Use the tangent function: $\tan(60°) = \frac{20}{d}$, where d is the distance of the boat from the foot of the cliff. Signup and view all the answers

A shopkeeper marks up an item by 20% and then offers a discount of 10%. What is the overall percentage profit or loss for the shopkeeper?

8% profit Signup and view all the answers

Two numbers are in the ratio 3:5. If 9 is subtracted from each, the new ratio becomes 12:23. Find the smaller number.

33 Signup and view all the answers

If $a + b = 7$ and $ab = 12$, then what is the value of $a^2 + b^2$?

25 Signup and view all the answers

A train 150 meters long is running with a speed of 68 km/hr. In what time will it pass a man who is running at 8 km/hr in the same direction?

9 seconds Signup and view all the answers

A sum of money becomes double in 6 years at simple interest. In how many years will it become four times itself at the same rate of interest?

18 years Signup and view all the answers

If the angles of a triangle are in the ratio 2:3:4, determine the measure of the largest angle.

80 degrees Signup and view all the answers

A rectangular field has a length of 20 meters and a width of 14 meters. What is the area of the field and the length of the diagonal?

Area: 280 square meters. Diagonal: $\sqrt{596}$ meters or approximately 24.41 meters. Signup and view all the answers

Simplify the following expression: $(x^2 - 4) / (x + 2)$

$x-2$ Signup and view all the answers

Flashcards

Distance Formula

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane.

Section Formula

Formulas to find the coordinates of a point dividing a line segment internally or externally in a given ratio.