Subject: Year: 10 Term: 1 Topic: Graphs Unit 6 (Part 1) Lesson Sequence Linear graphs: Rearrange linear equations Sketch graphs Graphing rates of change Real life graphs Line segments Key Assessments Core Texts Key Words Gradient How steep a graph is Distance-time graph Represents a journey Y-intercept Where the line crosses the y-axis (x=0) Velocity The speed of something in a given direction. Linear equation An equation that generates a straight line Acceleration The increase in speed or rate X-intercept Where the line crosses the x-axis (y=0) Direct Proportion The relationship between quantities whose ratio is constant. Rearrange Change the subject of the equation Line segment A part of a line that is bounded by two distinct end points Key Points Linear Graphs The equation for a straight line (linear equation) can be written as y=mx+c where m is the gradient and c is the y- intercept. To compare the gradients and y-intercepts of two straight lines, make sure their equations are in the form y = mx+c Formula: y = mx+c Key Points Graphing rates of change and Real-life graphs On a distance-time graph, the vertical axis represents the distance from the starting point. The horizontal axis represents the time taken. A velocity-time graph has time on the x-axis and velocity on the y-axis The gradient of a straight line graph is the rate of change On a distance-time graph, the gradient is the speed The gradient is the velocity, or acceleration Deceleration is negative acceleration. It means an object is slowing down. Formula: Average speed = total distance Acceleration= change in velocity . total time time When two quantities are in direct proportion: Their graph is a straight line through the origin When one variable is multiplied by n, so is the other Key points - Line segments You can use pythagoras theorem to find the length of a line segment Formula: Lines with the same gradient are parallel When two lines are perpendicular, the product of the gradients are -1 When a graph has gradient m, a graph perpendicular to it has gradient -1/m (negative reciprocal)
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Lesson Sequence Linear graphs: Rearrange linear equations Sketch graphs Graphing rates of change Real life graphs Line segments
Key Assessments
Core Texts
Key Words Gradient How steep a graph is Distance-time graph Represents a journey
Y-intercept Where the line crosses the y-axis (x=0)
Velocity The speed of something in a given direction.
Linear equation
An equation that generates a straight line
Acceleration The increase in speed or rate
X-intercept Where the line crosses the x-axis (y=0)
Direct Proportion The relationship between quantities whose ratio is constant.
Rearrange Change the subject of the equation
Line segment A part of a line that is bounded by two distinct end points
Key Points
Linear Graphs
The equation for a straight line (linear equation) can be written as y=mx+c where m is the gradient and c is the y-intercept.
To compare the gradients and y-intercepts of two straight lines, make sure their equations are in the form y = mx+c
Formula: y = mx+c
Key Points
Graphing rates of change and Real-life graphs
On a distance-time graph, the vertical axis represents the distance from the starting point. The horizontal axis represents the time taken.
A velocity-time graph has time on the x-axis and velocity on the y-axis
The gradient of a straight line graph is the rate of change
On a distance-time graph, the gradient is the speed
The gradient is the velocity, or acceleration
Deceleration is negative acceleration. It means an object is slowing down.
Formula: Average speed = total distance Acceleration= change in velocity . total time time When two quantities are in direct proportion: Their graph is a straight line through the origin When one variable is multiplied by n, so is the other
Key points - Line segments
You can use pythagoras theorem to find the length of a line segment
Formula:
Lines with the same gradient are parallel
When two lines are perpendicular, the product of the gradients are -1 When a graph has gradient m, a graph perpendicular to it has gradient -1/m (negative reciprocal)
Other Key points: In an enlargement, the object and the image are SIMILAR In reflections, rotations and translations, the object and its image are CONGRUENT
Key Words: Plan View from above the solid
Transformation Moves a shape to a different position
Front elevation The view of the front of the solid Object The original shape
Side elevation The view of the side of the solid
Image When a shape has been transformed, the resulting shape is the image.
Resultant vector The vector that moves the original shape to its final position after a number of translations
Similar shapes Corresponding angles are equal. Corresponding sides are in the same ratio.
Congruent Shapes that are exactly the same.
Subject: Constructions, Loci, Bearings and scales. Year: 10 Term: 2 Topic: Unit 8 Topic:
1) Congruent triangles have exactly the same size and shape. Their angles are the same and corresponding sides are the same length.
2) To prove something, you write a series of logical statements that show the statement is true. Each statement must be supported by a mathematical reason.
3) Shapes are similar when one shape is an enlargement of the other. Corresponding angles are equal and corresponding sides are all in the same ratio.
You can use similarity to find missing side lengths.
Subject: Maths Year: 10 Term: 4 Topic: Circle Theorems Topic:
Lesson Sequence 1. Radii and Chords 2. Tangents 3. The Circle Theorems 4. Applying Circle Theorems
Key points: The angle between a tangent and the radius is 90◦ The perpendicular from the centre of a circle to a chord bisects the chord. The line drawn from the centre of a circle to the midpoint of a chord is at right angles to the chord
Circle Theorems:
Key Words:
Chord A straight line connecting two points on a circle.
Tangent A straight line that touches a circle at one point only.
Cyclic Quadrilateral A quadrilateral with all four vertices on the circumference of a circle.
Key points 2:
Subject: Maths Year: 10 Term: 5 Topic: More Trigonometry Topic: Lesson Sequence 1. Accuracy 2. Graph of the sine function 3. Graph of the cosine function 4. The Tangent function 5. Calculating areas & the sine rule 6.The cosine rule and 2D Trigonometric problems 7. Solving problems in 3D 8. Transforming Trigonometric graphs 9. 10. 11.