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mathematics UK Year 10 Mathematics (KS4)

Solved problems for the chapter:

Circle theorems

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Quadrilateral for KS4

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0.1. Properties of a parallelogram

0.2. Special types of Parallelograms

0.3. Perimeter of parallelogram

0.4. Area of Parallelogram

0.5. Properties of trapezium

0.6. Special types of Trapezium

0.7. Perimeter of Trapezium

0.8. Area of Trapezium

0.9. Properties of kite

0.10. Perimeter of Kite

0.11. Area of Kite

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Quadratic function

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1. Formats of the quadratic function

1.1. General form and meaning of the leading coefficient a

1.2. Zero shape and zero square functions

1.3. Top shape and quadratic function themes

1.3.1. Specify the peak shape

1.3.2. Determining the apex shape by completing it to a perfect square

2. Draw a graph of a quadratic function (parabola)

2.1. Drawing a parabola based on a general shape

2.2. Drawing a parabola based on the vertex shape

3. Mutual position of parabola and line

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Quadratic equation

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1. General form of the quadratic equation

1.1. Simplifying quadratic equations

1.1.1. Example of simplifying a quadratic equation

1.1.2. Generalisation of simplifying quadratic equation

2. Solving quadratic equations

2.2. Case D = 0

2.3. Case D < 0

2.4. Solving special forms of quadratic equations by factorisation

2.4.1. Case b = 0 (generalisation)

2.4.2. Case b = 0 (practical example)

2.4.3. Case c = 0 (generalisation)

2.4.4. Case c = 0 (example)

2.4.5. Case a = 1 (generalisation)

2.4.6. Case a = 1 (example)

3. Zero form of the quadratic equation

↓ Show theory [3] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:circle_theorems/5338/

The ratio of two angles of a cyclic-quadrilateral is 3:4. If one of its angles is . Calculate the remaining angles.

An exterior angle of a cyclic quadrilateral measures 100 °. If one of the interior angle is 15 ° greater than the other, find all interior angles of the quadrilateral.

In a semicircle of radius 10 cm, a triangle is drawn so that one of its sides is equal to the diameter of the circle. What is the length of the other two sides of the triangle if the area of the triangle is at maximum?

Two sides of a cyclic quadrilateral extend and meet at an external point. An interior angle of the quadrilateral is given as 75° and an exterior angle as 60°. If both angles lies on a side, calculate the angle formed at the meeting point of the extended two sides of the quadrilateral.

The diagram below shows a circumscribe triangle ABC:

Given that the angle is 31°, and the radius of the outlined circle is . Calculate side b.

Draw a rectangle in a circle with a radius of 30 cm, the sides of which differ by 12 cm. Calculate the sides of the rectangle.