Gradient Concept Variations
Explore different scenarios related to gradients including mathematical calculations, definitions, and visual comparisons. Learn about the concept of gradients in various contexts such as slopes, inclines, and changes in properties. Discover the significance of consistent gradients and engage in tasks to determine and compare gradient values within the provided content.
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Possible answers: 1 5,5, 1 5, 5 10 50= 50 10= 10 50 = 50 10 10 50 = = 50 10 = 10 50 = 50 10 = 50 10= 10 50= 10 50= 50 10= 50 10= 10 50 = 50 10 = 10 50= 10 50 = 50 10 =
Possible answers: 1 5,5, 1 5, 5 ? 10 50= ? ? 50 10= 10 50 = ? ? ? 50 10 10 50 = ? = 50 10 = ? ? ? ? 10 50 = 50 10 = ? 50 10= ? 10 50= ? ? ? 10 50= 50 10= ? ? 50 10= ? 10 50 ? = ? 50 10 = ? ? ? 10 50= ? 10 50 = 50 10 = ? ?
Word Gradient Word class Noun Definition 1. 2. an inclined part of a road or railway; a slope. an increase or decrease in the magnitude of a property (e.g. temperature, pressure, or concentration) observed in passing from one point or moment to another. Example The car has fail-safe brakes for use on steep gradients. Synonyms Slope, incline Origins From the Latin gradus , meaning step.
All of the blue lines have the same gradient. What might this mean?
Do all the blue lines still have the same gradient?
Do all the blue lines still have the same gradient?
Which blue lines have the same gradient? 12 12 3 120 3 12 3 30
Find the gradient of the blue line. ? ????????? ? ???? ? ????????? ? ???? 10 10 5 5 ?? 2 ? 1 ? ?
Find the gradient of the blue line. ? ????????? ? ???? ? ????????? ? ???? 100 100 50 50 ??? 2 ? 1 ? ??
Find the gradient of the blue line. ? ????????? ? ???? ? ????????? ? ???? 5 10 5 10 ? 1 2 ? ? 1 ? ??
Find the gradient of the blue line in each question. The lines have not been drawn accurately. 1) 2) 3) 4) 5) 120 12 12 120 12 40 4 8 30 3 8) 6) 7) 1 6 3 0.3 1.2 6 12 11) 10) 9) 1 6 1 6 1 3 1 3 3 6
Find the gradient of the blue line in each question. The lines have not been drawn accurately. 1) 2) 3) 4) 5) 120 12 3 2 12 120 12 3 3 4 4 40 4 8 30 3 1 36 1 4 1 4 8) 6) 7) 1 6 3 0.3 1.2 6 12 1 18 1 2 1 18 11) 10) 9) 1 6 1 6 1 3 1 3 3 6
Find the gradient of the blue line in each question. The lines have not been drawn accurately. 3) 1) 2) 1 6 3 0.3 1.2 6 12 6) 5) 4) 1 6 1 6 1 3 1 3 3 6 7) 8) 9) 10) 11) ? 12 ? 12 12?7 12? 12? ?3 3 3 ? 3 ?3 3? 3?
Find the gradient of the blue line in each question. The lines have not been drawn accurately. 1 36 3) 1) 2) 1 4 1 6 1 4 3 0.3 1.2 6 12 6) 1 18 1 2 5) 4) 1 6 1 18 1 6 1 3 1 3 3 6 7) 8) 9) 10) 11) ? 12 ? 12 12?7 1 ?6 36 12? 12? 4? ? 4?6 4 4?2 ?3 3 3 ? 3 ?3 3? 3?
Same measurements Different directions Down (-) Up (+) Right (+) Right (+) Consider our directions from vectors!
For each blue line, write down whether it has a positive or negative gradient. 1) 4) 3) 5) 2) 8) 6) 7) 11) 12) 10) 9) 13) 14)
For each blue line, write down whether it has a positive or negative gradient. Positive 1) 4) Negative 3) 5) Positive 2) Positive Negative 8) Positive 6) Positive 7) Positive 11) 12) Positive Positive 10) Negative 9) Negative 13) Positive 14) Negative
Find the gradient of the blue line. ?? 10 10 Negative gradient, therefore 2 5 5 +? ? ????????? ? ???? ? ????????? ? ???? ? ????????? ? ???? ? ????????? ? ???? 10 5 10 5 = 2 = 2
5 5 15 15 15 15 5 5 ? ????????? ? ???? ? ????????? ? ???? ? ????????? ? ???? ? ????????? ? ???? ? ????????? ? ???? ? ????????? ? ???? ? ????????? ? ???? ? ????????? ? ???? +15 +5 15 5 15 5 +15 +5 = 3 = 3 = 3 = 3
Find the gradient of the blue line in each question. The lines have not been drawn accurately. 4) 2) 3) 1) 5) 60 60 10 10 10 60 60 60 10 10 Find the missing length when given the gradient of the following lines: 7) 1 6) 19 19 12) 13) 7 7 ? 19 20 9) ? 10) 7? 7 8) 20 7 19? 7 20 19 20 ???????? =1 11) 1 7 ???????? = 2 2 7 19
Find the gradient on the blue line in each question. The lines have not been drawn accurately. 4) 2) 3) 1) 5) 60 1 1 6 60 10 10 1 6 10 60 6 6 6 60 60 10 10 Find the missing length when given the gradient of the following lines: 7 7) 1 6) 19 7 19 19 19 12) 13) 7 7 ? 7 40 19 20 19 9) 7 10 ? 10) 7? 7 7 8) 19 20 7 19 19? 7 20 19 7 7 20 ???????? =1 11) 19 1 7 ???????? = 2 7 2 7 19
Greg says that the gradients of the blue lines are the same because base and height of the triangles are the same. Explain his mistake. 24 24 7 7
Find the gradient of the blue line. ? ????????? ? ???? ? ????????? ? ???? 33 33 56 63 56 ?? 16 ??
In each case, find the gradient of the blue line as a fraction in its simplest terms. 15 24 20 7 15 15 24 24 20 20 7 7
In each case, find the gradient of the blue line as a fraction in its simplest terms. 3 4 15 4 3 24 7 24 20 7 15 15 7 24 24 24 24 7 20 20 7 20 15 24 7 7
