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BGS - Maths and Physics > Shapes, Space, Measurements > Flashcards

Shapes, Space, Measurements Flashcards

1
Q

Acute Angle

What angle range?

A

0 - 90 degrees

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2
Q

Obtuse Angle

What angle range?

A

90 - 180 degrees

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3
Q

Relex Angle

What angle range?

A

180 - 360 degrees

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4
Q

Name the 3 angles

A

Acute
Obtuse
Reflex

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5
Q

What is a COMPLEMENTARY Angle?

A

Angles that add up to 90 degrees

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6
Q

What is a SUPPLEMENTARY angle?

A

Angles that add up to 180 degrees

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7
Q

ShaWhat is a PERPENDICULAR line?

A

Lines that meet at a right angle

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8
Q

What is the CIRCUMFERENCE?

A

The line (distance) around the outside of a circle

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9
Q

What is the RADIUS?

A

The line (distance) from the center of the circle to the circumference

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10
Q

What is a CHORD line?

In context of a circle, not an aerofoil

A

A line joining to different points of a circumference

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11
Q

What is the DIAMETER?

A

The chord line directly in the middle of a circle
The longest chord line
2x Radius

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12
Q

What is a TANGENT?

A

A line that touches a circle at one point

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13
Q

What is an ARC?

A

It is part of the circumference

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14
Q

What is a SECTOR?

A

A slice of the circle
(Like a pie slice)

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15
Q

What is a SEGMENT?

A

A section of the circle cut off by the chord line

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16
Q

C = 2兀R
What is C = 2 x pi x R

A

Calculate the circumference of a circle
Alternatively C = 兀 x D

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17
Q

A = 兀R^2
What is A = pi x R(squared)

A

Calculate the area of a circle

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18
Q

Millimeter (mm)
Centimeter (cm)
Meter (m)
Kilometer (km)

Metric or Imperial units?

A

Metric Units

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19
Q

How many millimeters in a meter?

A

1000mm = 1m
Milli means “thousandth”

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20
Q

How many centimeters in a meter?

A

100cm = 1m
Centi means “Hundredth”

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21
Q

How many meters in a kilometer?

A

1000m = 1km
Kilo means “thousand”

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22
Q

Kilogram (Kg)
Gram (g)
Milligram (mg)
Tonne

Metric or imerpail units?

A

Metric units
Milligram = thousandth of a gram
Kilogram = 1000 grams
1 Metric tonne = 1000kg

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23
Q

Litre (L)
Centilire (cL)
Millilitre (mL)

Metric or imperial units?

A

Metric units
1ml x 10 = 1cl
1cl x 10 = 1l
1ml x 1000 = 1l

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24
Q

How much is 1ml in centimeters?

A

1cm^3
(1 cubic centimeter)

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25
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
26
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
27
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
28
What is an ALTERNATE angle?
A line intersects 2x parallel lines. The INNER angle of the "Z" pattern These angles will be the same
29
What is a CORRESPONDING angle?
A line intersects 2x parallel lines. The INNER angle of the "F" pattern These angles will be the same
30
What is an EQUALATERAL triangle?
A triangle that has all sides the same length ## Footnote REMEMBER: All sides EQUAL in **EQUAL**ateral
31
What is an ISOSCELES triangle?
Triangle that has 2 sides the same length ## Footnote REMEMBER: 2 x **S**ides the same, **2 x S**, i**S**o**S**celes
32
What is a SCALENE Triangle?
Triangle that has no sides the same length ## Footnote REMEMBER: **AN**other triangle, sc**A**le**N**e REMEMBER: Scale LEANS means it is unbalanced = not equal
33
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
34
What are CONGRUENT shape?
Where 2 shapes are exactly the same shape and size
35
Calculate the area of a square or rectangle
Area = length x width A = L x W
36
Calculate the area of a parallelogram
Area = base x perpendicular height
37
Calculate the area of a triangle
Area = (base x perpendicular height) / 2
38
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
39
What is a COMPOUND shape?
A shape made up of 2 or more simple shapes. Example, a square and a triangle represents a house
40
What is the volume of a CUBOID?
Volume = Length x Width x Height V = L x W x H Unit is ^3
41
What is a PRISM?
A solid that keeps the same shape all the way along ## Footnote A constant cross section Find the area of the cross section and multiple by the length of the shape
42
What is PYTHAGORAS' Theorem equation?
a^2 + b^2 = c^2
43
In PYTHAGORAS' theorem, what must C be?
C = Hypotenuse Hypotenuse = Longest side The side opposite the right angle
44
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**
45
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
46
What is the formula for working out distance if given speed and time?
Distance = Speed x Time S D T ## Footnote REMEMBER: **SPEED**y **D**irt **T**rack
47
What is the formula for working out density if given mass and volume?
Density = Mass / Volume D M V ## Footnote REMEMBER: Americans go to the **D M V**
48
What is the definition of a VECTOR?
Something that has both size and direction ## Footnote 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
49
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 ## Footnote Example: (4 2) = 4 horizontally to the right. 2 vertically up
50
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) ## Footnote Pythagoras' theoren ub 3D
51
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 ## Footnote If you are given 2 sides, and the included angle, and want the 3rd side, use the cosine rule
52
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 ## Footnote If you are given 3 sides, and want to find anangle, use the cosine rule
53
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 ## Footnote If you are given a side, and its associated angle, use the sine rule
54
The formula for the area of a triangle
1/2ab sin C 1/2 x a x b x sin C ## Footnote if given a b, it is sin C If given b c, it is sin A If given a c, it is sin B
55
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 ## Footnote REMEMBER: SIN is shorter than COSINE, use the shorter formula
56
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
57
Sine Curve - What is the AMPLITUDE?
Peaks or maximum value of the sine curve ## Footnote Example; Sin = 5 sin3x The amplitude is 5
58
Sine Curve - What is the PERIOD?
The length of one cycle ## Footnote Example; Sin = 5 sin3x The period is 360 degrees divided by 3 = 120 degrees
59
How many cycles in the Sine Curve y = sin 2x
2 cycles in 360 degrees y = sin **2**x
60
What is the period (length) of the Sine Curve cycle y = sin 1/2x
There is **1/2** cycle in 360 degrees y = sin **1/2**x 360 / 0.5 = 720 degrees ## Footnote 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

BGS - Maths and Physics (11 decks)

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