GCSE Secondary Maths Age 13-17 - Algebra: Solving Equations 2 - Explained

The video tutorial explains solving a problem involving two right angle triangles with given tangent ratios. It covers setting up the equation, solving it through cross-multiplication, and factorizing a quadratic equation. The solution is validated by considering the context of the problem, and the marks allocation is discussed.

What is the relationship between the tangents of angles E and F in the given problem?

• tan E is greater than tan F

• tan E is less than tan F

• tan E is not related to tan F

• tan E is equal to tan F

What is the first step in solving the equation after setting up the tangent ratios?

• Add the equations

• Cross multiply the equations

• Subtract the equations

• Divide the equations

Which method is used to factorize the quadratic equation in the problem?

• Completing the square

• Trial and error

• Graphical method

• Mechanical method

What is the correct factor pair used to split the middle term in the quadratic equation?

• 15 and 4

• 10 and 7

• 20 and 3

• 18 and 2

What is the valid value of X obtained from solving the factorized equation?

• 3/4

• 1/2

• -1/4

• 5/3

Why is the value -1/4 rejected as a solution for X?

• It is not a real number

• It is greater than 1

• It results in a negative length in the triangle

• It does not satisfy the original equation

How many marks are awarded for correctly setting up the equation where tan E equals tan F?

• Three marks

• Two marks

• One mark

• Four marks