Rithvik's Blog GCSE

The function f(x) is defined as f(x) = 3x^2 - 2x + 5. Find the value of x when f(x) = 0.

The circle has equation x^2 + y^2 + 6x - 4y - 12 = 0 Find the centre and radius of the circle

In a right-angled triangle ABC, angle BAC is 90 degrees. The lengths of the other two sides are as follows: AB = 8 cm and BC = 15 cm. Find the length of side AC (the hypotenuse).

Solve the quadratic 3x^2 + 5x - 2 = 0

A rectangle has a length that is 3 cm more than its width. If the area of the rectangle is 40 cm^2, find the dimensions of the rectangle. Let the width of the rectangle be x cm.

The diagram shows a trapezium ABCD with AB parallel to DC. E is a point on AD such that DE is perpendicular to DC. The length of AD is x cm and the length of DE is y cm. Given that: The area of triangle AED is x²/4 The area of the trapezium ABCD is x² + 16cm^2 Find an expression for the length of BC in terms of x

A box contains red, blue, and green marbles. There are twice as many red marbles as blue marbles, and there are 5 more green marbles than blue marbles. If the total number of marbles is 37, how many of each colour marble are there?

A train travels a distance of 180 miles in 3 hours. If the train travels at a constant speed, how long will it take the train to travel 270 miles?

A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 cm, find the dimensions of the rectangle.