# Grade 8 and 9 Maths Problems

In this lesson there are five grade 8 and 9 maths problems for higher ability students.  Each of the questions require students to connect multiple high-level topics within a single problem.

## Grade 8 and 9 Maths Problems

The five questions connect the following topics:

• Solving quadratic equations arising from algebraic fractions
• Deriving the equation of a tangent to a circle using circle theorems.
• Using the Cosine rule, special triangles and surds to calculate a perimeter of a triangle.
• Calculating the volume, mass and density of a composite solid involving a frustum and hemisphere
• Using interpolation to compare a histogram with a box plot.

Fully worked solutions are provided for every question as well as a student handout

Here is a sample of three questions from the five.

## Histograms, Interpolation and Box Plots

In this question students make a comparison between two crops of beans. To make this comparison they will need to use interpolation to estimate the interquartile range and median from the histogram.

Their comparison should use these values to comment on the spread and measure of central location for each crop.

## Volume, Density and Mass of Composite Solids

Students are asked to work out the average density of the composite solid.  To do this they begin by working out the individual volumes of the frustum and hemisphere.

Should the students need further prompts I encourage them to present the information within a table as shown below.

By laying out the information in this way the majority of the students were able to go on and calculate the total volume and mass of the composite solid.

## Teach this lesson

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.

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