### 16/02/2021

Female Shinty Players

At a school students play one of three sports: Basketball; Cycling; Shinty. The school has 50% more boys than girls. Half the girls play shinty. The same number of boys play basketball as girls play shinty. There are 120 less female cyclists than male. Each of the 310 bicycles are used when the boys and girls go cycling.

If a student is picked at random, what is the probability that they are a female shinty player?

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### Solution to follow …

-oOo-

### 09/02/2021

Parallelogram or not?

OABC is a parallelogram, where $\stackrel{\rightharpoonup}{\mathrm{OJ}}=\frac{2}{3}\stackrel{\rightharpoonup}{\mathrm{OC}}$,
$\stackrel{\rightharpoonup}{\mathrm{OK}}=\frac{1}{4}\stackrel{\rightharpoonup}{\mathrm{OC}}$ and
$\stackrel{\rightharpoonup}{\mathrm{OL}}=\frac{8}{5}\stackrel{\rightharpoonup}{\mathrm{OA}}$

Show that $\mathrm{JKL}$ is a straight line. (note the figure is not to scale)

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### Solution

To solve this one we need to show that $\stackrel{\rightharpoonup}{\mathrm{JK}}$ is parallel to $\stackrel{\rightharpoonup}{\mathrm{JL}}$. If this is true and as they start from the same point they must be on a straight line.

To make the algebra simpler let's make $\stackrel{\rightharpoonup}{\mathrm{OA}}=\mathbf{a}$ and $\stackrel{\rightharpoonup}{\mathrm{OC}}=\mathbf{c}$.

Let's continue with determining $\stackrel{\rightharpoonup}{\mathrm{JK}}$.

We chose $J$ as the common point but we could have chosen any of the three. $K$ would be interesting as we would have to show that $\stackrel{\rightharpoonup}{\mathrm{KJ}}$ and $\stackrel{\rightharpoonup}{\mathrm{KL}}$ were antiparallel.

to be continued ...

-oOo-

### 08/12/2020

Sketching a Hill

Sketch the curve

$$y=4x-3-{x}^{2}$$.Find all the intersections and the co-ordinates of the vertex.

-oOo-

### Solution to follow …

-oOo-

### 10/11/20

All you need to know is three things about a triangle: part II (it turns out to be untrue)

Triangle ABC has lengths $\mathrm{AB}=\mathrm{10\; cm}$, $\mathrm{BC}=\mathrm{6\; cm}$ and $\mathrm{\angle BAC}=\mathrm{30\xb0}$. Find the possible areas of this triangle.

-oOo-

### Solution to follow ...

-oOo-

27/10/2020

All you need to know is three things about a triangle - part I?

A triangle has two angles of 60° and 90°, and an area of 10cm².

What is the perimeter?

Solution to follow ...