Year Eight content

GeometryAngles: complementary, supplementary [c= 90º, s=180º] also (two parallel lines crossed by a straight line);  alternate (Z), allied, vertically opposite, corresponding. Allied are supplementary.

Acute, obtuse, reflex, right angle. Lines can be perpendicular. Triangles can be equilateral, isosceles, right or scalene. They have interior and exterior angles. the interior angles of  a triangle add to 180º, ie are supplementary. The exterior angles of a polygon add to 360º.


Constructions:

Joining points with a straight line, bisecting a line, an angle. Dropping a perpendicular, Creating 90º, 60º, 30º etc angles. Four centres of a triangle (three in line). Circle inside triangle, circle through point of triangle.


Calculators - Use of your calculator is your problem, but here are some useful techniques to practise:

Long Fractions – using a calculator, the remainder of long fractions can be revealed, e.g.  with only an 8 figure display, 1/17 = 0.0588235, but 4/17= 0.23529411, so the overlap can be seen; similarly 7/17=0.4117647 and11/17=0.64705882, so 1/17=0.0588235294117467….

Pythagoras: R-P and P-R or Rec() and Pol()… see the Maths folder on the intranet. Learn 3-4-5, 5-12-13, 7-24-25, 8-15-17, 9-40-41, 20-21-29

Arithmetic skills - see adjacent page

Number precision

The number two, implied precision one significant figure (1 sig.fig.) lies in the interval  1.5 ≤ two < 2.5  . Similarly

2.45 ≤ “”2.5” < 2.55, but the exception is where ten is to 1 sig.fig., 9.5 ≤ ten < 15 , although if ‘ten’ is to one decimal place, (1 d.p.) then 9.5 ≤ ‘ten’ < 10.5 as you would expect.


Algebra

a+a+a = 3a,   a*a*a = a3 ,      a*b=b*a

Factors and factorising and simplification

3pq + 6p = 3p (q+2)     Collecting like terms; minus times minus makes plus.

Especially notice this sort of example;

3 – 2 (x-5) = 3 – 2x + 10 = 13 – 2


Statistics

Mean, median, mode. Median is in (N+!)/2 th position of ordered set. Mode may be one of several. Concepts of range, spread and skew. Discrete and continuous data types. Class boundaries.



© David Scoins 2017