Search results - Victorian Curriculum (2024)

Your search for 'x axis y axis' returned 118 results

Sort by

Relevance
Title
Type

Select a page

Result list

VCMMG261

Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries

Elaborations
- describing patterns and investigating different ways to produce the same transformation such as using two successive reflections to provide the same result as a translation
- creating and re-creating patterns using combinations of reflections and rotations, using digital technologies
VCMMG261 | Mathematics | Level 7 | Measurement and Geometry | Location and transformation
VC2M7SP03

describe the effect of transformations of a set of points using coordinates in the Cartesian plane, including translations, reflections in an axis, and rotations about the origin

Elaborations
- using digital tools to transform shapes in the Cartesian plane, describing and recording the transformations
- describing patterns and investigating different ways to produce the same transformation, such as using 2 successive reflections to provide the same result as a translation
- experimenting with, creating and re-creating patterns using combinations of translations, reflections and rotations, using digital tools
VC2M7SP03 | Mathematics | Mathematics Version 2.0 | Level 7 | Space
VCSSU061

Earth’s rotation on its axis causes regular changes, including night and day

Elaborations
- modelling the relative sizes and movement of the Sun, Earth and Moon
- describing timescales for the rotation of the Earth
- constructing sundials and investigating how they work
VCSSU061 | Science | Levels 3 and 4 | Science Understanding | Earth and space sciences
VC2M10AA10

experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns
See Also
6.7: Graph Quadratic Functions Using Transformations Quadratic-exponential functionals of Gaussian quantum processes

Elaborations
- applying a bisection algorithm to determine the approximate location of the horizontal axis intercepts of the graph of a quadratic function such as $f (x) = 2 x^{2} - 3 x - 7$
- applying transformations to the graph of $x^{2} + y^{2} = 1$
- identifying the coordinates of any points of intersection of the graph of a linear function with the graph of a quadratic function or a circle
- identifying intervals on the real number line over which a given quadratic function is positive or negative
- using a table of values to determine when an exponential growth or decay function exceeds or falls below a given value, such as monitoring the trend in value of a share price in a context of exponential growth or decay
VC2M10AA10 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra
VC2M9A07

experiment withthe effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns

Elaborations
- investigating transformations of the graph of $y = x$ to the graph of $y = a x + b$ by systematic variation of $a$ and $b$ and interpreting the effects of these transformations using digital tools; for example,
  $y = x \to y = 2 x$ (vertical enlargement as $a > 1$ ) $\to y = 2 x - 1$ (vertical translation) and
  $y = x \to y = \frac{1}{2} x$ (vertical compression as $0 < a < 1$ ) $\to y = - \frac{1}{2} x$ (reflection in the horizontal axis) $\to y = - \frac{1}{2} x + 3$ (vertical translation)
- investigating transformations of the parabola $y = x^{2}$ to the graph of $y = a {(x - h)}^{2} + b$ in the Cartesian plane using digital tools to determine the relationship between graphical and algebraic representations of quadratic functions, including the completed square form; for example,
  $y = x^{2} \to y = \frac{1}{3} x^{2}$ (vertical compression as $0 < a < 1$ ) $\to y = \frac{1}{3} {(x - 5)}^{2}$ (horizontal translation) $\to y = \frac{1}{3} {(x - 5)}^{2} + 7$ (vertical translation) or
  $y = x^{2} \to y = 2 x^{2}$ (vertical enlargement as $a > 1$ ) $\to y = - 2 x^{2}$ (reflection in the horizontal axis) $\to y = - 2 {(x + 6)}^{2}$ (horizontal translation) $\to y = - 2 {(x + 6)}^{2} + 10$ (vertical translation)
- experimenting with digital tools by applying transformations to the graphs of functions, such as reciprocal $y = \frac{1}{x}$ , square root $y = \sqrt[]{x}$ , cubic $y = x^{3}$ and exponential functions $y = 2^{x}, y = {(\frac{1}{2})}^{x}$ , identifying patterns
VC2M9A07 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra
VC2M9A05

identify and graph quadratic functions, solve quadratic equations graphically and numerically, and use null factor law to solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate

Elaborations
- recognising that in a table of values, if the second difference between consecutive values of the dependent variable is constant, then it is a quadratic
- graphing quadratic functions using digital tools and comparing what is the same and what is different between these different functions and their respective graphs; interpreting features of the graphs such as symmetry, turning point, maximum and minimum values; and determining when values of the quadratic function lie within a given range
- solving quadratic equations algebraically and comparing these to graphical solutions
- using graphs to determine the solutions of quadratic equations; recognising that the roots of a quadratic function correspond to the $x$ -intercepts of its graph and that if the graph has no $x$ -intercepts, then the corresponding equation has no real solutions
- relating horizontal axis intercepts of the graph of a quadratic function to the factorised form of its rule using the null factor law; for example, the graph of the function $y = x^{2} - 5 x + 6$ can be represented as $y = (x - 2) (x - 3)$ with $x$ -axis intercepts where either $(x - 2) = 0$ or $(x - 3) = 0$
- recognising that the equation $x^{2} = a$ , where $a > 0$ , has 2 solutions, $x = \sqrt[]{a}$ and $x = - \sqrt[]{a}$ (for example, if $x^{2} = 39$ then $x = \sqrt[]{39} = 6.245$ correct to 3 decimal places, or $x = - \sqrt[]{39} = - 6.245$ correct to 3 decimal places) and representing these graphically
- graphing percentages of illumination of moon phases in relation to Aboriginal and Torres Strait Islander Peoples’ understandings that describe the different phases of the moon
VC2M9A05 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra
VCHHK144

Different historical interpretations and contested debates about World War I and the significance of Australian commemorations of the war

Elaborations
- investigating the ideals associated with the Anzac tradition and how and why World War I is commemorated within Australian society
- evaluating the fairness of the post war treaties on Axis powers
VCHHK144 | The Humanities | History | Levels 9 and 10 | Historical Knowledge | The modern world and Australia | Australia at war (1914 – 1945): World War I
Science: Levels 3 and 4 achievement standards

By the end of Level 4, students describe situations where science understanding can influence their own and others’ actions. They explain the effects of Earth’s rotation on its axis. They distinguish between temperature and heat and use examples to illustrate how heat is produced and transferred...

Level description | Science | Levels 3 and 4
VC2M2ST02

create different graphical representations of data using software where appropriate; compare the different representations, and identify and describe common and distinctive features in response to questions

Elaborations
- collecting data from a limited list of choices, creating 2 different graphical representations of the data, and discussing and comparing the different representations; for example, asking the class to choose their favourite colour from a given set, then co-creating a picture graph with colours on the horizontal axis and comparing it to a column graph with colours on the horizontal axis and numbers on the vertical axis
- creating different data displays (for example, lists, tally charts, jointly created column graphs and picture graphs) to represent a data set, describing the information that each display represents and discussing how easy or hard they are to interpret and why
- using digital tools to create picture graphs to represent data using one-to-one correspondence, deciding on an appropriate title for the graph and considering whether the categories of data are appropriate for the context
- comparing picture graphs with one-to-one column graphs of the same data, interpreting the data in each and saying how they are the same and how they are different; for example, collecting data on the country of birth of each student and creating different pictographs to represent classroom data
- using dot plots, sticker charts, picture graphs, bar charts and column graphs to represent data
VC2M2ST02 | Mathematics | Mathematics Version 2.0 | Level 2 | Statistics
VC2M5SP02

construct a grid coordinate system that uses coordinates to locate positions within a space; use coordinates and directional language to describe position and movement

Elaborations
- understanding how the numbers on the axes on a grid coordinate system are numbers on a number line and are used to pinpoint locations
- discussing the conventions of indicating a point in a grid coordinate system; for example, writing the horizontal axis number first and the vertical axis number second, and using brackets and commas
- comparing a grid reference system to a grid coordinate system (first quadrant only) by using both to play strategy games involving location; for example, in playing the game Quadrant Commander, deducing that in a grid coordinate system the lines are numbered (starting from zero), not the spaces
- placing a coordinate grid over a contour line, drawing and listing the coordinates of each point in the picture, asking a peer to re-create the drawing using only the list of coordinates, and discussing the reasons for the potential similarities and differences between the 2 drawings
VC2M5SP02 | Mathematics | Mathematics Version 2.0 | Level 5 | Space
VC2M5ST02

interpret line graphs representing change over time; discuss the relationships that are represented and conclusions that can be made

Elaborations
- reading and interpreting different line graphs, discussing how the horizontal axis represents measures of time such as days of the week or times of the day, and the vertical axis represents numerical quantities or ordinal categorical variables such as percentages, money, measurements or ratings such as fire hazard ratings
- interpreting real-life data represented as a line graph showing how measurements change over a period of time, and make simple inferences
- matching unlabelled line graphs to the context they represent based on the stories of the different contexts
- interpreting the data represented in a line graph, making inferences; for example, reading line graphs that show the varying temperatures or ultraviolet (UV) rates over a period of a day and discussing when would be the best time to hold an outdoor assembly
VC2M5ST02 | Mathematics | Mathematics Version 2.0 | Level 5 | Statistics
VC2M9SP01

recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity

Elaborations
- understanding the terms ‘base’, ‘altitude’, ‘hypotenuse’, and ‘adjacent’ and ‘opposite’ sides to an angle, in a right-angled triangle, and identifying these for a given right-angled triangle
- investigating patternsto reason about nested similar triangles that are aligned on a coordinate plane,connectingideas of parallel sides and identifying the constancy of ratios of corresponding sides for a given angle
- establishing an understanding thatthe sine of an angle can be considered asthe length ofthe altitude of aright-angled trianglewith ahypotenuse of length one unitand similarly the cosine as the length of the base of the same triangle, and relating this to enlargement and similar triangles
- relating the tangent of an angle to the altitude and base of nested similar right-angled triangles, and connecting the tangent of the angle at which the graph of a straight line meets the positive direction of the horizontal coordinate axis to the gradient of the straight line
VC2M9SP01 | Mathematics | Mathematics Version 2.0 | Level 9 | Space
VC2M8A05

experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns

Elaborations
- using graphing software to investigate the effect of systematically varying parameters of linear functions on the corresponding graphs, making and testing conjectures; for example, making a conjecture that if the coefficient of $x$ is negative, then the line will slope down from left to right
- using graphing software to systematically contrast the graphs of $y = 2 x, - y = 2 x, y = - 2 x$ and $- y = - 2 x$ with those of
  $y < 2 x, - y < 2 x, y < - 2 x$ and $- y < - 2 x$ and those of $y > 2 x, - y > 2 x, y > - 2 x$ and $- y > - 2 x$ , making and testing conjectures about sign and direction of the inequality
- using digital tools to investigate integer solutions to equations such as $2 x + 3 y = 48$
VC2M8A05 | Mathematics | Mathematics Version 2.0 | Level 8 | Algebra
VC2M10A08

solve linear inequalities and graph their solutions on a number line

Elaborations
- representing word problems with simple linear inequalities and solving them to answer questions
- graphing regions corresponding to inequalities in the Cartesian plane (for example, graphing $2 x + 3 y < 24)$ and verifying using a test point such as (0,0)
VC2M10A08 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra
VCMNA311

Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations

Elaborations
- graphing parabolas, and circles connecting x-intercepts of a graph to a related equation
VCMNA311 | Mathematics | Level 9 | Number and Algebra | Linear and non-linear relationships
VC2M8A02

graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution

Elaborations
- recognising that in a table of values, if the first difference between consecutive values of the dependent variable is constant, then it is a linear relation
- graphing linear functions and relations of the form $x = a$ , $y = a$ , $x \leq a$ , $x > a$ , $y \leq a$ , $y > a$ on the Cartesian plane for known values of $a$
- completing a table of values, plotting the resulting points on the Cartesian plane and determining whether the relationship is linear
- graphing the linear relationship $a x + b = c$ for given values of $a, b$ and $c$ and identifying from the graph where $a x + b < c$ or where $a x + b > c$
- solving linear equations of the form $a x + b = c$ and one-variable inequalities of the form $a x + b < c$ or $a x + b > c$ where $a$ > 0 using inverse operations and digital tools, and checking solutions by substitution
- solving linear equations such as $3 x + 7 = 6 x - 9,$ representing these graphically, and verifying solutions by substitution
VC2M8A02 | Mathematics | Mathematics Version 2.0 | Level 8 | Algebra
Mathematics: Level 4 achievement standards

Number and Algebra
Students recall multiplication facts to 10 x 10 and related division facts. They choose appropriate strategies for calculations involving multiplication and division, with and without the use of digital technology, and estimate answers accurately enough for the context. Students...

Level description | Mathematics | Level 4
Mathematics: Level 4 description

In Level 4, students extend the number system to simple decimal fractions, and broaden their use of measures and scales.
Students model, represent and order numbers to tens of thousands, and extend place value to tenths and hundredths. They investigate odd and even numbers and explore number patterns...

Level description | Mathematics
VCVIU117

Recognise the sounds and tones of spoken Vietnamese, and notice how they are represented in words and symbols

Elaborations
- identifying the 29 letters of the Vietnamese alphabet by their names and sounds as well as the five tone markers
- building phonic awareness by recognising and experimenting with sounds and rhythms, focusing on letters that are similar in the English alphabet but produce different sounds in Vietnamese, for example, e and i, d and đ
- developing pronunciation, phrasing and intonation skills by singing, reciting and repeating words and phrases
- noticing that Vietnamese is a tonal language, and that pitch changes affect the meaning of words
- understanding that although Vietnamese and English use the same alphabet there are additional symbols/markers that create more letters in Vietnamese
- developing familiarity with similarities and differences in Vietnamese sound–letter correspondence, such as a, ă, â; e, ê; o, ô, ơ; u, ư; as well as c and k, i and y, s and x, and ch and tr
- noticing that the same word with different tone markers has different meanings, for example, ma, mà, má, mả, mã and mạ
- exploring Vietnamese spelling strategies such as grouping words according to initial letters that represent particular sounds, for example, h (hoa hồng, hát, học) or m (mẹ, má, mèo)
- using single and consonant clusters, vowels and vowel clusters with tone markers to form and spell words, for example, ta, la, tha, nga
- recognising and using lower and upper case letters
VCVIU117 | Languages | Vietnamese | F–10 Sequence | Foundation to Level 2 | Understanding | Systems of language
Turkish - F–10 Sequence: Foundation to Level 2 description

Students' familiarity with the spoken form of Turkish supports their introduction to the written form of the language. They become familiar with the Turkish alphabet and writing conventions, and are introduced to the sound–letter correspondence of the 21 consonants and eight vowels that...

Level description | Languages | Turkish | F–10 Sequence

Refine results by Area

All areas (118)
Languages (91)
Mathematics (24)
Science (2)
The Humanities (1)

Refine results by Subject

All subjects (118)
Auslan (14)
French (6)
German (5)
History (1)
Italian (2)
Japanese (1)
Mathematics (4)
Mathematics Version 2.0 (20)
Modern Greek (1)
Science (2)
Spanish (38)
Turkish (10)
Vietnamese (14)

Refine results by Level

All levels
Foundation level (13)
Level 1 (13)
Level 2 (14)
Level 3 (18)
Level 4 (20)
Level 5 (12)
Level 6 (10)
Level 7 (33)
Level 8 (32)
Level 9 (31)
Level 10 (26)
Level 10A (3)

Refine results by Type

All types (118)
Curriculum content (94)
Standards (14)
Level description (10)

Select a page

Search results - Victorian Curriculum (2024)

Result list

VCMMG261

Elaborations

VC2M7SP03

Elaborations

VCSSU061

Elaborations

VC2M10AA10

Elaborations

VC2M9A07

Elaborations

VC2M9A05

Elaborations

VCHHK144

Elaborations

Science: Levels 3 and 4 achievement standards

VC2M2ST02

Elaborations

VC2M5SP02

Elaborations

VC2M5ST02

Elaborations

VC2M9SP01

Elaborations

VC2M8A05

Elaborations

VC2M10A08

Elaborations

VCMNA311

Elaborations

VC2M8A02

Elaborations

Mathematics: Level 4 achievement standards

Mathematics: Level 4 description

VCVIU117

Elaborations

Turkish - F–10 Sequence: Foundation to Level 2 description

Refine results by Area

Refine results by Subject

Refine results by Level

Refine results by Type