## 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 ½ (N+!) th position of the ordered set. Mode may be one of several. Concepts of range, spread and skew. Discrete and continuous data types. Class boundaries.

This list below, which is also on the next page, Arithmetic, is the summary sheet often offered as a list of topics covered::

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 an 8-figure display 1/17=0.0588235, but 4/17=0.23529411, so the overlap can be seen, so if we look also at 7/17=0.4117647 and 11/17=0.64705882, we can see that 1/17 = 0.0588235294117647…. repeating from here.

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

Squares - learn all squares up to 30²

The NEXT square is made from adding to teh last known square the number itself and the next number.  (N+1)² = N² + N + (N+1).
Eg 41² = 40² + 40 + 41 = 1681, 13² = 12² + 12 + 13 = 144+25=169
Going down subtract: 19² = 20² - 20 - 19 = 400-39 = 361

Squares of numbers ending in a ½ are made in a similar way (N+½ )² = N * (N + 1) +¼
So 5 ½ ² = 5*6 + ¼ = 30 ¼     10 ½ ² = 10*11 + ¼ = 110 ¼..and the numbners ending in 5 go much the same way…  25² = 20*30 + 25 = 625,  multiply the 2 and 3 and stick a 25 on the end.  For  65²  take the  6*7=42 and put a 25 on the end;
65² = 4225

Fractions - equivalents    3/5 = 6/10 = 12/20 Multiply the top and the bottom by the same thing. Cancelling (reducing a fraction) is the same process, divide top and bottom by the same thing until there is no remaining common factor. factors are an important part of Y8 work.

Fractions - arithmetic.    Multiplication is the ONLY easy process with fractions

a  x b  =   ab     numerator                 adding and subtracting are much harder
c     d       cd     denominator

First decide what units to work in and at worst multiply the two denominators

a  ±  b  =   ad ± bc                     and then do any possible cancelling
c      d           cd

There was another page of this…. including the matrix work.

Email: David@Scoins.net      © David Scoins 2018