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)

Subject: Maths Year: 10 Term: 1 Topic: Graphs Unit 6 (part 2) Topic:

Lesson Sequence Quadratic Graphs Cubic Graphs Reciprocal Graphs Interpreting Graphs Graph of a circle

Key Assessments

Core Texts

Key Words Quadratic equation An equation that contains a term in x2

but no higher power of x Cubic equation An equation that contains a term in x3 but no

higher power of x.

Parabola The curved shape of a quadratic equation

Reciprocal function A function in the form k/x where k is a number

Maximum point The highest point on the graph. It’s where the graph turns.

Asymptotes A line that a graph gets very close to, but never actually touches

Minimum point The lowest point on the graph. It’s where the graph turns.

Key Points – Reciprocal graphs

The x and y axes are asymptotes to the curve

Positive reciprocal graph Negative reciprocal graph

Key Points – Quadratic graphs

Quadratic graphs must be drawn with a smooth curve

A quadratic equation can have 0, 1 or 2 solutions

Positive quadratic graph Negative quadratic graph

Key points – Cubic graphs

A cubic graph can alsohave terms in x2 and x.

A cubic equation can have 1, 2 or 3 solutions

Positive reciprocal graph Negative reciprocal graph

Key points – Graph of a circle

The equation of a circle with centre (0,0) and radius r is x2 + y2 = r2

Subject: Maths Year: 10 Higher Term: 2 Topic: Volume & Area

Lesson Sequence 1. Perimeter & Area 2. Units of accuracy 3.Prisms 4. Circles 5. Sectors of circles 6. Cylinders and spheres 7. Pyramids and cones

Previous Formulae:

Key Words: Prism A 3D solid that has the same cross-

section all through its length Sector A fraction of a circle

Cross Section A cross section is the shape we get

when cutting straight through an object Arc A fraction of the circumference

Trapezium A quadrilateral with one pair of sides parallel

Hectare (ha) Area of a square 100m by 100m

Subject: Transformations & solids Year: 10 Term: 2 Topic: Unit 8 Topic:

Lesson Sequence 1. 3-D Solids 2. Reflection 3. Rotation 4. Enlargement 5. Translation 6.Combinations of transformations

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:

Lesson Sequence 1. Bearings 2. Scale drawings 3. Constructions 4. Loci

Key Words: Perpendicular Bisector Cuts a line in half at right angles Equidistant Equally distant from

Construct Draw accurately using ruler and compass

Locus A set of points that obey a certain rule (often a continuous path)

Angle bisector Cuts an angle exactly in half

Subject: Maths Year: 10 Term: 3 Topic: Equations and Inequalities Unit 9 Topic: Lesson Sequence 1. Solving quadratic equations 2. Completing the square 3. Solving simultaneous equations 4. Solving linear & quadratic simultaneous equations 5. Solving inequalities

Formulae:

Key Words: The roots of a quadratic function are its solutions when it is equal to zero

When there are two unknowns you need two equations to find their values. These are called simultaneous equations.

Expressions such as (x+2)2 and (x+1)2 are called perfect squares

Subject: Maths Year: 10 Term: 3 Topic: Multiplicative Reasoning Topic:

Lesson Sequence 1. Growth & Decay 2. Compound measures 3. Ratio & proportion

Key Words: Depreciate To decrease in value Velocity Speed in a given direction

Compound interest

The interest earned each year is added to money in the account and earns interest the next year.

Initial velocity

Speed in a given direction at the start of the motion

Compound measures

Interest earned each year is Density The mass of substance in contained in a certain volume usually measured as grams per cm3 (g/cm3)

Acceleration The rate of change in velocity. Pressure The force in newtons applied over an area. Usually measured in (N/m2) or (N/cm2

Subject: Maths Year: 10 Higher Term: 4 Topic: Congruence & Similarity Topic: Lesson Sequence 1. Congruence 2. Geometric proof 3. Similarity 4. Similarity in 3-D solids Key points:

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.

Transforming Trigonometric graphs:

Key Points: