Formulas/info Flashcards

Question

Line of Best fit 5.3

Answer 1

Line of best fit: the straight line drawn through the centre of dots with an equal number of dots above and below lone. - The line can be used to predict values given one variable. LINE OF BEST FIT - REGRESSION LINE (least squares line of best fit)

Answer 2

AVERAGE SPEED = Distance travelled ÷ time taken Speed: rate at which something is moving/changing Fuel consumption: Rate at which a vehicle uses fuel measured in L/100km - depends on: driving urban, towing, using A/C

Answer 3

- express as fraction, then divide A car travels at 75km/h, how far to the nearest 0.1m will it travel in 5sec

Answer 4

- y = mx+c - m = r X standard deviation of y-scores ÷ standard deviation of x-scores - c = mean of y-scores - mean of x-scores Regression line: line of best fit, representing all points (gradient/y-intercept calculated using formula)

Answer 5

Life expectancy: average number of years of life remaining to a person of specific age

Answer 6

Graph = diagram of a network, containing vertices (points), joined by lines called edges (arcs) Loop = edge connecting a vertex to itself Directed network = arrows on edges, indicate direction Weighted network = numbers/weights on edges, distance same - WEIGHT = SUM OF ALL EDGES Degree: number of edges connected to vertices can be odd/even - SUM OF ALL DEGREES = TWICE NUMBER OF EDGES Walk: any route along edges that includes repeat vertexes/edges Closed: starts/ends at same vertex Trail: walk with no repeat edges, vertices may be reused Circuit: Closed trail with no repeat edges Path: no repeat vertices/edges Cycle: Closed path with no repeat vertices/edges Connected network: connected if path between 2 vertices Networks/tables: networks can be represented using matrix/table

Answer 7

Eulerian trail: uses every edge only once - TRAILS = 2 ODD VERTICES, START AND FINISH AT THOSE VERTICES Eulerian circuit: uses every edge only once, starts and ends at the same - CIRCUIT = VERTICES ARE EVEN

Answer 8

Tree: any 2 vertices are connected by one path, no cycles Spanning tree: tree connecting all vertices Minimum spanning tree: spanning tree with smallest weight KRUSKAL'S ALGORITHM 1. sort edges in increasing order of weight 2. Diagram of network with all vertices, no edges 3. Choose edge with smallest weight 4. Choose next edge with smallest weight 5. Continue process with no cycles and vertices PRIM'S ALGORITHM 1. choose any vertex in network 2. Choose edge with least weight and correlate to another 3. Use 2 vertices, select next edge with least weight 4. Choose next edge with least weight 5. Repeat step 4 until all connected

Answer 9

Shortest path: between 2 vertices, can be found by trial and error FINDING SHORTEST PATH 1. redraw network with circles at each except start 2. For all vertices from start write shortest distance 3. Continue until final vertex reached 4. Shortest path found by moving back from finish to start

Answer 10

Activity table: shows order/time of each project predecessor: previous activity needing to be completed Dummy activity: eliminate repeat edges, zero time/weight Critical path: longest time path start/finish vertices Forward scanning: calculates EST, depending on completion of predecessor 1. redraw network w/ empty box on vertex, with 0 at start 2. select highest point for each 1st box 3. Continue until end

Answer 11

- FLOAT TIME = LSTnext - ESTnext - FLOAT TIME = LSTnext - EST - activity time *where ESTnext is ESTof next activity (earliest end time), LSTnext is LST of next activity (latest end time) Backward scanning: calculates LST for each activity (take smallest distance) Float time: longest time activity can be delayed without decreasing completion

Answer 12

Source: start of network sink: end of flow network capacities: weights on edges representing amount it holds flow capacity: total flow through the network Inflow: total capacity of all edges entering the vertex outflow: total capacity of all edges leaving vertex maximum outflow: smaller of the inflow/outflow of vertex cut: line drawn through edges of flow network capacity of cut: amount of flow blocked by cut, found by summing the cut edges passing from source to sink

Answer 13

Maximum flow: capacity of the minimum cut TO FIND - calculate capacity of each cut and identify the cut that has the minimum capacity

Answer 14

Max heart rate: upper limit of what cardiovascular system handles - MHR MALES = 220 - AGE - MHR FEMALES = 226 - AGE Target heart rate: desired heart rate to better aerobic fitness - THR = I X (MHR - RHR) + RHR *RHR = resting heart rate, MHR = max heart rate, I = exercise intenity

Answer 15

ENERGY UNITS - 1 kilojoule (kj) = 1000 joules (j) - 1 megajoule (MJ) = 1 000 000 joules = 1000kj - 1 Calorie (cal) = 4.184kj

Answer 16

- WATT = 1w = 1000mW - KILOWATT = 1kW = 1000W - MEGAWATT = 1MW = 1000kW = 1000000W (10^6W) - GIGAWATT = 1GW = 1000MW = 10^9 Kilowatt hours: electricity usage measured in kWh Cents/kilowatt hours (c/kwh) = electricity usage given Domestic rate: electricity used during day Off-peak rate: electricity used late evenings/early morning, charges at cheaper rate

Answer 17

RUNNING COST = POWER USED (kWh) X ELECTRICITY COST ($/kWh)

Answer 18

Energy efficient: homes making most of natural heating/cooling Features considered - orientation: should face North to capture Winter sun - insulation: light-coloured roofing - wind/skylight: windows face North - Ventillation: cross-ventilation allowing air flow - Landscapes/shading: plants/trees can shade walls/windows - Building materials: materials that can absorb stone and heat

Answer 19

SOH CAH TOA - Sin 0 = opposite÷hypotenuse - Cos 0 = adjacent÷hypotenuse - Tan 0 = opposite÷adjacent Angle of elevation: angle looking up Angle of depression: angle looking down

Answer 20

Bearings: show direction of location from given point true bearing: (3 figures) between 000 + 360 measured clockwise from North Compass bearing: angles measured from North-South axis towards East or West

Answer 21

- SINE RULE - a÷sinA = b÷sinB = c÷sinC Sine rule: relationship between sides/opposite angles

Answer 22

- OBTUSE ANGLE ANSWERS = 180º0

Answer 23

c^2 = a^2+b^2 - 2abcosC

Answer 24

CosC = a^2+b^2-c^2 ÷ 2ab

Answer 25

A = 1/2abSinC

Answer 26

Triangle problems involving 2 sides and 2 angles opposite these sides - SINE RULE Triangle problems involving 3 sides and 1 angle - COSINE RULE

Answer 27

Scale drawing: reduction of real object Scale ratio: compares lengths in scale drawings to actual lengths - e.g. if scale is 1:3, actual lengths are 3x size scaled length

Answer 28

Scale = map: real life 1:1000 = 1mm:1000mm or 1cm : 1000cm or 1m : 1000m

Answer 29

House plan: drawings drawn to scale - the plan: diagram of the floor (floor plan) - the elevation: view of front/back/sides of house

Answer 30

Right angled triangles: use pythag theorem, the trigonometric ratios and - A=1/2bh Non right angled triangles: use sine/cosine rules and - A=1/2 Offset survey: used for irregular blocks of land e.g. surveyor chooses traverse line measuring offsets to each corner Compass radial survey: taking true bearing of each corner on field using compass placed in middle of field

Answer 31

TRAPEZOIDAL RULE - A=h/2 (df + dl) *h = distance between successive points, df = first measurement, dl = last measurement

Answer 32

THE PARABOLA y=ax^2+bx+c - if positive: concave up - if negative: concave down - y-intercept is c and vertex is (0,c)

Answer 33

maximum and minimum quadratic: represented by vertex of its graph, y-value of vertex - Concave down: maximum value - Concave up: minimum value (*answer is the y-value)

Answer 34

- EXPONENTIAL CURVE - y=a^x, y=a^-x - exponential curve always above x-axis - y-intercept is 1 - if a>1, y=a^x is increasing - if a>1, y=a^-x is decreasing Exponential growth: any quantity increasing y=b(a^x), where a>1 e.g. population size, investments, bushfire Exponential decay: any quantity decreasing y=b(a^-x), where a>1 or between 0 and 1 in y=b(a^x) e.g. radioactive decay EXPONENTIAL GROWTH AND DECAY - growth occurs when y=b(a^x) and a>1 - decay occurs when y=b(a^-x) and a>1, or when y=b(a^x) and a is between 0 and 1) - b is initial value of y (when x =0) - b is y-intercept of exponential curve

Answer 35

THE HYPERBOLA y=k÷x - 2 seperate branches in opposite quadrants - point symmetry (0,0) - asymptotes = x,y axis - if k is positive, hyperbola decreasing, branches in 1st/3rd quadrant - if k is negative, hyperbola increasing, branches in 2nd/4th quadrant - higher value of k, further hyperbola from x, y axis Reciprocal function: non-linear function, when x is denominator Hyperbola: graph of reciprocals function, 2 seperate functions

Answer 36

SOLVING INVERSE VARIATION PROBLEM 1. identify two variables and form variation equation 2. substitute given values of x/y to find k 3. rewrite equation y=k÷x using k value 4. sub value for x/y into equation to solve problem Direct variation: two variables change in same direction e.g. fuel consumption of car, viewing range/height of tower Inverse variation: two variables change in different directions e.g. time of journey and average speed, or temperature and altitude

Answer 37

Normal distribution: mean, median, mode are equal - bell shaped curve is smooth and symmetrical about the mean Frequency histogram: large small, bigger = normal curve

Answer 38

Z-SCORES = SCORE-MEAN ÷ STANDARD DEVIATION z-score: shows position of raw score relative to mean - e.g. z-score of 1.8 standard deviation is 1.8means, a score of -0.5 means is half standard deviation below the mean

Answer 39

since z-scores don't depend on value of mean, we use them to compare scores from different distributions

Answer 40

CENTRAL TENDENCY - MEAN = SUM OF SCORES NO. OF SCORES - MEDIAN = MIDDLE SCORE SPREAD - RANGE = HIGHEST SCORE - LOWEST - IQR = Q3-Q1 - STANDARD DEVIATION = USING STATISTICS MODE Measure of central tendency: an average used to indicate the centre of a data set Measures of spread: used to indicate spread of data

Answer 41

peaks: high points of distribution clusters: groups of scores bunched together + skew: tail right, mean higher than mode/median - skew: tail left, mean lower than mode/median symmetry: data balanced

Answer 42

OUTLIER - LESS THAN = Q1 - 1.5XIQR - MORE THAN = Q3 + 1.5 X IQR outlier: very high/low score, clearly seperate from data - mean is most affected by outlier - median can be affected but not much - mode is not affected

Answer 43

Back-to-back stem and leaf: compares 2 data sets Box plot: uses five-number summary to show data spread

Formulas/info Flashcards

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