Graphs
Muhtasari
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.
Malengo
- 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
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Kadi za kumbukumbu
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Maelezo ya Somo
Dokezo Kamili la Somo Linapatikana kwenye Programu ya Green Bridge
Pata programu ya Green Bridge CBT kwenye simu au kompyuta yako kwa maktaba kamili ya IGCSE: mitihani ya miaka iliyopita, miongozo ya usahihishaji, ramani za mawazo, kadi za marudio na masomo ya sauti.
Tathmini ya Somo
Hongera kwa kukamilisha somo la Graphs. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.
Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.
Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.
- 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
Fanyia kazi maswali haya kwenye programu
Fanyia kazi maswali haya kwenye programu
Vitabu Vinavyopendekezwa
Jifunze zaidi kutoka vyanzo huria
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Sehemu ya kitabu
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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Sehemu ya kitabu
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
Vimechapishwa na mashirika mengine chini ya leseni huria na vinatajwa kama wanavyoomba. Viungo hufungua tovuti zao.
Fanya Mazoezi ya Maswali ya Majaribio
Ungependa kufanya mazoezi ya maswali ya majaribio kuhusu Graphs? Pakua programu ya Green Bridge CBT ili kupata maswali ya majaribio na tathmini kamili za mazoezi kuhusu mada hii.
Pakua Programu Kwenye Google Playstore
Kila kitu unachohitaji ili kufaulu katika JAMB, WAEC & NECO.
