Shapes, Space, Measurements Flashcards
Acute Angle
What angle range?
0 - 90 degrees
Obtuse Angle
What angle range?
90 - 180 degrees
Relex Angle
What angle range?
180 - 360 degrees
Name the 3 angles
Acute
Obtuse
Reflex
What is a COMPLEMENTARY Angle?
Angles that add up to 90 degrees
What is a SUPPLEMENTARY angle?
Angles that add up to 180 degrees
ShaWhat is a PERPENDICULAR line?
Lines that meet at a right angle
What is the CIRCUMFERENCE?
The line (distance) around the outside of a circle
What is the RADIUS?
The line (distance) from the center of the circle to the circumference
What is a CHORD line?
In context of a circle, not an aerofoil
A line joining to different points of a circumference
What is the DIAMETER?
The chord line directly in the middle of a circle
The longest chord line
2x Radius
What is a TANGENT?
A line that touches a circle at one point
What is an ARC?
It is part of the circumference
What is a SECTOR?
A slice of the circle
(Like a pie slice)
What is a SEGMENT?
A section of the circle cut off by the chord line
C = 2兀R
What is C = 2 x pi x R
Calculate the circumference of a circle
Alternatively C = 兀 x D
A = 兀R^2
What is A = pi x R(squared)
Calculate the area of a circle
Millimeter (mm)
Centimeter (cm)
Meter (m)
Kilometer (km)
Metric or Imperial units?
Metric Units
How many millimeters in a meter?
1000mm = 1m
Milli means “thousandth”
How many centimeters in a meter?
100cm = 1m
Centi means “Hundredth”
How many meters in a kilometer?
1000m = 1km
Kilo means “thousand”
Kilogram (Kg)
Gram (g)
Milligram (mg)
Tonne
Metric or imerpail units?
Metric units
Milligram = thousandth of a gram
Kilogram = 1000 grams
1 Metric tonne = 1000kg
Litre (L)
Centilire (cL)
Millilitre (mL)
Metric or imperial units?
Metric units
1ml x 10 = 1cl
1cl x 10 = 1l
1ml x 1000 = 1l
How much is 1ml in centimeters?
1cm^3
(1 cubic centimeter)
1 foot = ?? inches
1 gallon = ?? pints
1 yard = ?? feet
1lb = ?? oz
1 mile = ?? yards
1 stone = ?? lbs
Imperial units
1 foot = 12 inches
1 gallon = 8 pints
1 yard = 3 feet
1lb = 16 oz
1 mile = 1760 yards
1 stone = 14 lbs
1 kg = ?? lbs
1 inch = ?? cm
1 foot = ?? cm
1 mile = ?? km
1 litre = ?? pints
1 Imp gal = ?? litre
1kg = 2.2 lbs
1 inch = 2.54 cm
1 foot = 30.5 cm
1 mile = 1.6 km
1 l = 1.75 pints
1 Imp gal = 4.5 L
What is a bearing, and where is it measured from?
The angle from 000 degrees north measured clockwise
Always measured with 3 numbers i.e. 045 = 45 degree bearing from 0 degree north
What is an ALTERNATE angle?
A line intersects 2x parallel lines.
The INNER angle of the “Z” pattern
These angles will be the same
What is a CORRESPONDING angle?
A line intersects 2x parallel lines.
The INNER angle of the “F” pattern
These angles will be the same
What is an EQUALATERAL triangle?
A triangle that has all sides the same length
REMEMBER: All sides EQUAL in EQUALateral
What is an ISOSCELES triangle?
Triangle that has 2 sides the same length
REMEMBER: 2 x Sides the same, 2 x S, iSoSceles
What is a SCALENE Triangle?
Triangle that has no sides the same length
REMEMBER: ANother triangle, scAleNe
REMEMBER: Scale LEANS means it is unbalanced = not equal
What is an EXTERIOR angle the sum of?
The exterior angle is equal to the sum of the 2 opposite interior angles
A + B + C = 180 degrees
C + D = 180 degrees
A + B = D
What are CONGRUENT shape?
Where 2 shapes are exactly the same shape and size
Calculate the area of a square or rectangle
Area = length x width
A = L x W
Calculate the area of a parallelogram
Area = base x perpendicular height
Calculate the area of a triangle
Area = (base x perpendicular height) / 2
Calculate the area of a trapezium
trapezium has 2 parallel sides
Area = 1/2(a + b)h
Area = 1/2 x (a + b) x height
((a + b) x h) / 2
What is a COMPOUND shape?
A shape made up of 2 or more simple shapes.
Example, a square and a triangle represents a house
What is the volume of a CUBOID?
Volume = Length x Width x Height
V = L x W x H
Unit is <unit>^3</unit>
What is a PRISM?
A solid that keeps the same shape all the way along
A constant cross section
Find the area of the cross section and multiple by the length of the shape
What is PYTHAGORAS’ Theorem equation?
a^2 + b^2 = c^2
In PYTHAGORAS’ theorem, what must C be?
C = Hypotenuse
Hypotenuse = Longest side
The side opposite the right angle
What is the hypotenuse of a triangle (side A to B) If;
Side B to C = 12
Side C to A = 5
a^2 + b^2 = c^2
(12 x 12) + (5 x 5) = C^2
144 + 25 = 169
Square root of 169 = 13
If side A = X (short side)
B = 9cm
C = 12cm (Hypotenuse)
What is X?
Use pythagoras’ theorem
a^2 + b^2 = c^2
x^2 + 9^2 = 12^2
x^2 + 81 = 144
x^2 = 144 - 81
x^2 = 63
Square root of 63 = 7.93
What is the formula for working out distance if given speed and time?
Distance = Speed x Time
S D T
REMEMBER: SPEEDy Dirt Track
What is the formula for working out density if given mass and volume?
Density = Mass / Volume
D M V
REMEMBER: Americans go to the D M V
What is the definition of a VECTOR?
Something that has both size and direction
EXAMPLE: Force is a vector. Has mass and acts in a direction
EXAMPLE: Velocity is a vector. Car has mass, and travels at speed in a direction
EXAMPLE: Acceleration is a vector. Car has mass, and speeds up in a direction
How does a column vector work?
(x
y)
X = horizontal movement
Y = vertical momvent
Positive X right, negative x left
Positive Y up, Negative Y down
Example:
(4
2) = 4 horizontally to the right. 2 vertically up
What forumula is used if C is a point in 3 dimensional space with coordinates (x,y,z) where a is the origin?
AC = Square root(x^2 + y^2 + z^2)
Pythagoras’ theoren ub 3D
You are given 2 sides of of a triangle, and the associated angle. Which formula should you use to determine the 3rd side?
Sine or Cosine?
Cosine
a^2 = b^2 + c^2 - 2bc cos A
b^2 = a^2 + c^2 - 2ac cos B
c^2 = a^2 + b^2 - 2ab cos C
If you are given 2 sides, and the included angle, and want the 3rd side, use the cosine rule
You are given 3 sides of a triangle. Which formula should you use to determine the angle?
Sine or Cosine?
Cosine
a^2 = b^2 + c^2 - 2bc cos A
b^2 = a^2 + c^2 - 2ac cos B
c^2 = a^2 + b^2 - 2ab cos C
If you are given 3 sides, and want to find anangle, use the cosine rule
You are given a side of a scalene triangle and its associated angle. Which formula should you use?
Sine or Cosine?
Sine
sin A / a = sin B / b = sin C / c
a / sin A = b / sin B = c / sin C
If you are given a side, and its associated angle, use the sine rule
The formula for the area of a triangle
1/2ab sin C
1/2 x a x b x sin C
if given a b, it is sin C
If given b c, it is sin A
If given a c, it is sin B
How to remember which formula;
Sin or Cosine
SIN is shorter than COSINE
Therefore;
SIN = Shorter formula;
a / sin A = b / sin B = c / sin C
COSINE = Longer formula
a^2 = b^2 + c^2 - 2bc cos A
REMEMBER: SIN is shorter than COSINE, use the shorter formula
What is an ASYMPTOTE?
In context of Tan (90)
Tan 90 when plotted on a graph never actually reaches 90 degrees. The curve goes off to infinity
Sine Curve - What is the AMPLITUDE?
Peaks or maximum value of the sine curve
Example; Sin = 5 sin3x
The amplitude is 5
Sine Curve - What is the PERIOD?
The length of one cycle
Example; Sin = 5 sin3x
The period is 360 degrees divided by 3 = 120 degrees
How many cycles in the Sine Curve
y = sin 2x
2 cycles in 360 degrees
y = sin 2x
What is the period (length) of the Sine Curve cycle
y = sin 1/2x
There is 1/2 cycle in 360 degrees
y = sin 1/2x
360 / 0.5 = 720 degrees
It takes 2 full rotations of 360 degrees to equal a total cycle, as there is only half a cylce in 360 degrees, it takes 720 degrees to have a full rotation
