Graphs
Gbogbo ọrọ náà
Graphs give you a way to see algebra. Every equation you write down corresponds to a curve or a line on a set of axes, and reading that picture tells you things the algebra alone can hide: where a quantity reaches its maximum, how fast something is changing, or where two conditions are satisfied at once.
This topic starts with the coordinate system itself and builds up through straight-line graphs to quadratics and, at Higher tier, cubics, reciprocals, and trigonometric curves. You will learn to find gradients, write equations of lines, and apply transformations to function graphs.
Ebumnobi
- Interpret information presented in a range of linear and non-linear graphs
- Understand and use conventions for rectangular Cartesian coordinates
- Plot points (x, y) in any of the four quadrants or locate points with given coordinates
- Determine the coordinates of points identified by geometrical information
- Determine the coordinates of the midpoint of a line segment, given the coordinates of the two end points
- Draw and interpret straight line conversion graphs
- Find the gradient of a straight line
- Recognise that equations of the form y = mx + c are straight line graphs with gradient m and intercept on the y-axis at the point (0, c)
- Recognise, generate points and plot graphs of linear and quadratic functions
- [Higher] Recognise, plot and draw graphs with equation y = Ax^3 + Bx^2 + Cx + D and related reciprocal and trigonometric forms
- [Higher] Apply to the graph of y = f(x) the transformations y = f(x) + a, y = f(ax), y = f(x + a), y = af(x) for linear, quadratic, sine and cosine functions
- [Higher] Interpret and analyse transformations of functions and write the functions algebraically
- [Higher] Find the gradients of non-linear graphs by drawing a tangent
- [Higher] Find the intersection points of two graphs, one linear and one non-linear, and recognise that the solutions correspond to the solutions of the combined equation
- [Higher] Calculate the gradient of a straight line given the coordinates of two points
- [Higher] Find the equation of a straight line parallel to a given line; find the equation of a straight line perpendicular to a given line
Maapụ uche
E seela isiokwu a ka ị hụ otu echiche si ejikọta.
Mepee maapụ uche na ngwa
Kaadị ncheta
Omume ncheta ngwa ngwa n'ihe a na-anwale n'isiokwu a.
Mee omume kaadị ndị a na ngwa
Akwụkwọ Ọmụmụ
Ndetu Nkuzi Zuru Ezu di na Ngwa Green Bridge
Nweta ngwa Green Bridge CBT na ekwenti gi ma o bu kompiuta maka ulo akwukwo IGCSE zuru oke: akwukwo ule ndi gara aga, usoro nyocha, eserese uche, kaadi omumu na nkuzi olu.
Nnyocha Ọmụmụ
Ekele diri gi maka imecha ihe karịrị na Graphs. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- What is the gradient of the line y = -4x + 7? A) 7 B) -4 C) 4 D) -7 Answer: B
- What is the midpoint of the segment from (2, 8) to (6, 2)? A) (4, 5) B) (8, 10) C) (3, 4) D) (4, 10) Answer: A
- In which quadrant does the point (-3, 5) lie? A) First B) Second C) Third D) Fourth Answer: B
- The line y = 2x + 1 is parallel to which of the following? A) y = -2x + 3 B) y = 2x - 5 C) y = 0.5x + 1 D) y = -0.5x + 1 Answer: B
- A line has gradient 3. What is the gradient of a line perpendicular to it? A) 3 B) -3 C) 1/3 D) -1/3 Answer: D
Rue ajuju ndi a n'ime ngwa ahu
Rue ajuju ndi a n'ime ngwa ahu
Akwụkwọ A Na-atụ Aro
Mụtakwuo ihe site na isi mmalite mepere emepe
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Akụkụ akwụkwọ
Graph Linear Equations in Two Variables
Plot points in a rectangular coordinate system
"Intermediate Algebra: Graph Linear Equations in Two Variables" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/intermediate-algebra/pages/3-1-graph-linear-equations-in-two-variables. Access for free at https://openstax.org/books/intermediate-algebra/pages/1-introduction
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Akụkụ akwụkwọ
Slope of a Line
Find the slope of a line
"Intermediate Algebra: Slope of a Line" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/intermediate-algebra/pages/3-2-slope-of-a-line. Access for free at https://openstax.org/books/intermediate-algebra/pages/1-introduction
Ndị otu ndị ọzọ bipụtara ha n'okpuru ikike mepere emepe, anyị na-ekele ha dị ka ha si chọọ. Njikọ na-emepe saịtị ha.
Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Graphs? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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Ihe nile ichoro iji nwee ihe ịga nke ọma na JAMB, WAEC & NECO.
