Category Archives: Algebra

Annuity and superannuation

Posted on June 9, 2024 by Sumant Sumant

Natalie’s family has decided that in three months they will start depositing $160 every 3 months for 3 years. The account will earn interest 5.7% /a, compounded quaterly. Then 3 months after the last deposit they plan to withdraw money … Continue reading →

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Two pulleys sinusoidal function

Posted on June 7, 2024 by Sumant Sumant

Two pulleys are connected by a belt. Pulley A has a radius of 3 cm and Pulley B has a radius of 6cm. As pulley A rotates, a drop of paint on the circumference of Pulley B rotates around the … Continue reading →

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An easy question for teaching exponents

Posted on June 2, 2024 by Sumant Sumant

Given and . Determine the possible values of $x^2y2z^2$

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Fixed piece of wire bent into square and rectangle. For minimum total area what should be the perimeter of each.

Posted on June 2, 2024 by Sumant Sumant

A 30 cm piece of wire is cut into two. One piece is bent into the shape of a square, the other piece into the share of a rectangle with a length to width ratio of 2:1. What are the … Continue reading →

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Two parabolas passing through their corresponding vertices

Posted on June 2, 2024 by Sumant Sumant

The parabola has vertex and the parabola has vertex where and are distinct points. The two parabolas intersect at and . Prove that .

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Find max area of inscribed rectangle in an isosceles triangle

Posted on June 2, 2024 by Sumant Sumant

An isosceles triangle has a base of 6m and height 4m. Find a rectangle of max area inscribed in that triangle.

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IB Math Modelling tide using sine function

Posted on May 28, 2024 by Sumant Sumant

In a busy harbor, the time difference between successive high tides is about 12.3 hrs. The water level varies by 2.4 meters between high and low tide. Tomorrow, the first high tide will be 4.7 meters at this time. a). … Continue reading →

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A problem on when one arithmetic sequence has a term twice the other arithmetic sequence term ?

Posted on May 28, 2024 by Sumant Sumant
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Precalculus Simple Interest

Posted on May 28, 2024 by Sumant Sumant

Sara’s parents decide to invest $500 on each of her birthday from the day she is born until she becomes 25. Each investment earns 6.4% /a simple interest. What will be the total amount of the investments when Sara is … Continue reading →

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IB Math question on intersection between ln(2x-7) and 2 ln(x)

Posted on May 28, 2024 by Sumant Sumant

The function f and g are defined by where and where . State the equation of the vertical asymptote to the graph .

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