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

Shapes, Space, Measurements Flashcards

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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
Q

1 foot = ?? inches
1 gallon = ?? pints
1 yard = ?? feet
1lb = ?? oz
1 mile = ?? yards
1 stone = ?? lbs

Imperial units

A

1 foot = 12 inches
1 gallon = 8 pints
1 yard = 3 feet
1lb = 16 oz
1 mile = 1760 yards
1 stone = 14 lbs

26
Q

1 kg = ?? lbs
1 inch = ?? cm
1 foot = ?? cm
1 mile = ?? km
1 litre = ?? pints
1 Imp gal = ?? litre

A

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
Q

What is a bearing, and where is it measured from?

A

The angle from 000 degrees north measured clockwise
Always measured with 3 numbers i.e. 045 = 45 degree bearing from 0 degree north

28
Q

What is an ALTERNATE angle?

A

A line intersects 2x parallel lines.
The INNER angle of the “Z” pattern
These angles will be the same

29
Q

What is a CORRESPONDING angle?

A

A line intersects 2x parallel lines.
The INNER angle of the “F” pattern
These angles will be the same

30
Q

What is an EQUALATERAL triangle?

A

A triangle that has all sides the same length

REMEMBER: All sides EQUAL in EQUALateral

31
Q

What is an ISOSCELES triangle?

A

Triangle that has 2 sides the same length

REMEMBER: 2 x Sides the same, 2 x S, iSoSceles

32
Q

What is a SCALENE Triangle?

A

Triangle that has no sides the same length

REMEMBER: ANother triangle, scAleNe
REMEMBER: Scale LEANS means it is unbalanced = not equal

33
Q

What is an EXTERIOR angle the sum of?

A

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
Q

What are CONGRUENT shape?

A

Where 2 shapes are exactly the same shape and size

35
Q

Calculate the area of a square or rectangle

A

Area = length x width
A = L x W

36
Q

Calculate the area of a parallelogram

A

Area = base x perpendicular height

37
Q

Calculate the area of a triangle

A

Area = (base x perpendicular height) / 2

38
Q

Calculate the area of a trapezium

trapezium has 2 parallel sides

A

Area = 1/2(a + b)h
Area = 1/2 x (a + b) x height
((a + b) x h) / 2

39
Q

What is a COMPOUND shape?

A

A shape made up of 2 or more simple shapes.
Example, a square and a triangle represents a house

40
Q

What is the volume of a CUBOID?

A

Volume = Length x Width x Height
V = L x W x H
Unit is <unit>^3</unit>

41
Q

What is a PRISM?

A

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

42
Q

What is PYTHAGORAS’ Theorem equation?

A

a^2 + b^2 = c^2

43
Q

In PYTHAGORAS’ theorem, what must C be?

A

C = Hypotenuse
Hypotenuse = Longest side
The side opposite the right angle

44
Q

What is the hypotenuse of a triangle (side A to B) If;
Side B to C = 12
Side C to A = 5

A

a^2 + b^2 = c^2
(12 x 12) + (5 x 5) = C^2
144 + 25 = 169
Square root of 169 = 13

45
Q

If side A = X (short side)
B = 9cm
C = 12cm (Hypotenuse)
What is X?

Use pythagoras’ theorem

A

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
Q

What is the formula for working out distance if given speed and time?

A

Distance = Speed x Time
S D T

REMEMBER: SPEEDy Dirt Track

47
Q

What is the formula for working out density if given mass and volume?

A

Density = Mass / Volume
D M V

REMEMBER: Americans go to the D M V

48
Q

What is the definition of a VECTOR?

A

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

49
Q

How does a column vector work?

A

(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

50
Q

What forumula is used if C is a point in 3 dimensional space with coordinates (x,y,z) where a is the origin?

A

AC = Square root(x^2 + y^2 + z^2)

Pythagoras’ theoren ub 3D

51
Q

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?

A

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

52
Q

You are given 3 sides of a triangle. Which formula should you use to determine the angle?

Sine or Cosine?

A

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

53
Q

You are given a side of a scalene triangle and its associated angle. Which formula should you use?

Sine or Cosine?

A

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

54
Q

The formula for the area of a triangle

A

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

55
Q

How to remember which formula;
Sin or Cosine

A

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

56
Q

What is an ASYMPTOTE?

In context of Tan (90)

A

Tan 90 when plotted on a graph never actually reaches 90 degrees. The curve goes off to infinity

57
Q

Sine Curve - What is the AMPLITUDE?

A

Peaks or maximum value of the sine curve

Example; Sin = 5 sin3x
The amplitude is 5

58
Q

Sine Curve - What is the PERIOD?

A

The length of one cycle

Example; Sin = 5 sin3x
The period is 360 degrees divided by 3 = 120 degrees

59
Q

How many cycles in the Sine Curve
y = sin 2x

A

2 cycles in 360 degrees
y = sin 2x

60
Q

What is the period (length) of the Sine Curve cycle
y = sin 1/2x

A

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

BGS - Maths and Physics (11 decks)

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