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2019-20 N. American Planner_DP Sample

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USEFUL INFORMATION<br />

MATHEMATICAL LAWS, FORMULAE, SYMBOLS<br />

SYMBOLS<br />

Equality and Inequality Signs<br />

..... is equal to<br />

..... is not equal to<br />

..... is less than<br />

..... is greater than<br />

..... is less than or equal to<br />

..... is greater than or equal to<br />

..... is not less than<br />

..... is not greater than<br />

..... is equivalent to<br />

..... is approximately equal to<br />

..... is congruent to<br />

..... is proportional to<br />

..... therefore<br />

..... percentage<br />

SET NOTATION<br />

..... the set of<br />

..... such that<br />

..... is an element of<br />

..... is not an element of<br />

..... is a subset of<br />

..... is not a subset of<br />

..... the Universal set<br />

..... the null or empty set<br />

..... the intersection of<br />

..... the union of<br />

..... is equivalent to<br />

SETS OF NUMBERS<br />

N ..... the set of natural numbers<br />

J ..... the set of integers<br />

J-J+ ... the sets of negative and<br />

positive integers<br />

Q ..... the set of rational numbers<br />

Q’ ..... the set of irrational numbers<br />

R ..... the set of real numbers<br />

R-R+... the sets of negative and<br />

positive real numbers<br />

GEOMETRY<br />

..... pi, approximately 3.142<br />

..... angle<br />

..... is parallel to<br />

..... is perpendicular to<br />

..... right angle<br />

..... the co-ordinates of a point<br />

..... the interval ST<br />

..... the ray ST<br />

..... the line ST<br />

..... the length of interval ST<br />

or<br />

..... the gradient of ST<br />

..... the sum of<br />

INDICES<br />

..... to the power ( )n<br />

..... square root<br />

INDEX LAWS<br />

1st Law a x x a y = a x+y<br />

2nd Law a x a y = a x-y<br />

3rd Law a° = 1<br />

4th Law (a x ) y = a xy<br />

5th Law (a x b) x = a x x b x<br />

6th Law a x a x<br />

b = b x<br />

7th Law a -n =<br />

a l n<br />

8th Law a p /q = q a p = ( q a) p<br />

LOG LAWS<br />

log mn = log m + log n<br />

log m n<br />

= log m - log n<br />

log m p = p log m<br />

log l = 0<br />

log ax = n x = a n<br />

log 10 x = n x = 10 n<br />

ln x =<br />

x<br />

log e = n e n = x<br />

PARALLEL LINES are shown by<br />

arrows on the lines. The line that<br />

cuts the parallel lines is called the<br />

Transversal.<br />

a b<br />

d c<br />

e f<br />

h g<br />

VERTICALLY OPPOSITE ANGLES<br />

a = c, b = d, e = g, h = f<br />

ALTERNATE ANGLES<br />

c = e, d = f<br />

CORRESPONDING ANGLES<br />

b = f, c = g, a = e, d = h<br />

COINTERIOR ANGLES<br />

c + f = 180°, d + e = 180°<br />

These angles only apply to parallel lines.<br />

STANDARD FORM is given by<br />

(a number between 1 and 10) x<br />

(Power of 10)<br />

Ex. 456.7 = 4.567 x 10 2<br />

STATISTICS<br />

Measures of Central Tendency<br />

Mean, x, is the average<br />

Mode is the most common value<br />

Median is the middle value when the<br />

data is put in order<br />

Frequency is how often a value occurs<br />

Standard Deviation, SD is the spread<br />

around the Mean<br />

Range is the difference from the largest<br />

to the smallest value<br />

Boxplots and Interquartile Ranges<br />

show the spread of data around the<br />

Median<br />

TYPE OF TRIANGLES<br />

3 sides and angles to 180°<br />

Scalene<br />

3 sides different<br />

3 angles different<br />

Isosceles<br />

2 sides equal<br />

2 angles equal<br />

Equilateral<br />

3 sides equal<br />

3 angles equal<br />

Right-angled<br />

has a 90° angle<br />

TYPES OF QUADRILATERALS<br />

4 sides and angles add up to 360°<br />

Irregular<br />

4 sides different<br />

4 angles different<br />

Kite<br />

2 pairs of sides equal<br />

1 pair of angles equal<br />

Rectangle<br />

4 right angles<br />

2 pairs of sides equal<br />

Rhombus<br />

4 sides equal<br />

2 pairs of sides equal<br />

Parallelogram<br />

Opposite sides equal<br />

and parallel<br />

2 pairs of angles equal<br />

Square<br />

4 right angles<br />

4 sides equal<br />

Trapezium<br />

1 pair of sides parallel<br />

CO-ORDINATE GEOMETRY<br />

For two point (a,b) and (e,d)<br />

gradient = m = d - b = rise = tan<br />

e - a run<br />

distance between points<br />

= (e-a) 2 + (d-b) 2 = rise 2 + run 2<br />

midpoint<br />

(a+e) , b+d)<br />

2 2<br />

y-intercept<br />

Gradient<br />

equation of a straight line y = mx + c<br />

Parallel Lines m 1 = m 2<br />

Perpendicular Lines m 1 = - l<br />

m 2<br />

VECTORS<br />

r = xi + yi + zk lrl = x 2 + y 2 + z 2<br />

r 1 -r 2 = r 1 r 2 cos = r = x 1 x 2 +y 1 y 2 +z 1 z 2<br />

155<br />

<strong>20</strong>18/19 Intl <strong>Planner</strong>_<strong>DP</strong>_REAR.indd 155 25/5/18 3:15 pm

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