# Year 10 — Maths (Higher)

### Term 1: Expressions, Calculations 1, Angles and polygons

Simplifying expressions

Indices

Expanding and factorising

Algebraic fractions

Place value and rounding

Multiplying and dividing

Systematic listing and the product rule

Angles and parallel lines

Properties of, and angles in, triangles and quadrilaterals

Angles in polygons

Congruency and similarity

Test on: Expressions, Calculations 1, Angles and polygons

### Alternate angles

Alternate angles in parallel lines are equal

### Polygon

A 2D shape with straight sides

A four sided 2D shape

### Expand

Multiply out the brackets

### Factorise

Put an algebraic expression into brackets

### Congruence

Two shapes are congruent if they are exactly the same shape and size

Power

### Similar shapes

Two shapes are similar if one is an enlargement of the other

### Simplify

To gather all the like terms together into a single term

### Corresponding angles

Corresponding angles in parallel lines are equal

• Spiritual
• Moral
• Social
• Cultural

#### Develop the individual:

Skills such as confidence with numeracy and rounding benefit our students’ functioning in society. Algebra provides opportunities for students to develop a sense of “awe and wonder” by using letters to represent variables. Students are encouraged to question “why”; they compose proofs and arguments and make assumptions when analysing a problem. For example, students develop algebraic fluency throughout the curriculum. Algebra is a uniquely powerful language that enables students to describe and model situations. Students learn geometrical reasoning through knowledge and application of angle rules and coditions for similarity and congruency. Students develop algebraic fluency throughout the curriculum.

#### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 2: Data handling 1 & 2, Fractions, Decimals & Percentages

Sampling.

Organising data.

Representing data: pie charts, frequency diagrams, box plots, cumulative frequency graphs, histograms.

Averages and spread (including quartiles and the interquartile range).

Scatter graphs and correlation, including correlation vs causation.

Time series.

Fractions and percentages.

Calculations with fractions.

Converting between fractions, decimals and percentages.

Recurring decimals.

Test on: T1 topics and Data handling 1 & 2, Fractions, Decimals & Percentages

### Random sample

A sample where everyone in the population has an equal chance of being chosen

### Mean

An average found by totalling the numbers and dividing by how many there are

### Median

An average found by listing the numbers in order and finding the middle number

### Interquartile range

The difference between the upper quartile and the lower quartile

### Range

The difference between the greatest and least values

### Stratified sample

A sample where different groups (e.g. boys and girls) are represented in sample in the same proportion as the population

### Mode

An average found by finding the item that occurs the most often

### Biased sample

A sample where everyone in the population does not have an equal chance of being chosen

### Cumulative frequencies

The total of all the frequencies in a set of data

### Positive correlation

As one quantity increases so does the other

### Negative correlation

As one quantity increases the other decreases

• Spiritual
• Moral
• Social
• Cultural

#### Develop the individual:

Student’s understanding of statistics is developed to a depth that will equip them to identify when statistics are meaningful or when they are being used inappropriately (eg in newspapers or on social media). The skill of interpreting data will benefit students’ functioning in society. Students will understand how to interpret graphs and charts, and be able to compare statistical distributions. Competance with percentages benefits our students’ functioning in society: sales, interest rates, taxes.

#### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 3: Formulae & Functions & Working in 2D (bearings, area and transformations)

Substitution into a formula and rearranging formulae.

Functions, including composite and inverse.

Algebraic expressions, identities and formulae.

Expanding and factorising double brackets, including difference of two squares.

Algebraic fractions.

Measuring lengths and angles.

Bearings.

Area of 2D shapes: triangle, parallelogram, trapezium and compound shapes.

Transformations (rotations, reflections, translations and enlargements)

Test on: T1 and T2 topics, Formulae & Functions & Working in 2D

### Formula

A mathematical relationship or rule expressed in symbols

### Function

A relation between a set of inputs and a set of permissible outputs

### Inverse function

A mathematical operation or function that exactly reverses another operation or function

### Transformation

The act of moving or changing a shape

### Reflection

A reflection is an image that you can see in a mirror line

### Rotation

The action of rotating about an axis or centre

### Enlargement

The action of enlarging a shape or solid

### Translation

The action of moving a shape along and up or down

### Tessellation

Repeating a shape to cover an area with no gaps and no overlapping

### Area

The amount of surface that a shape has

• Spiritual
• Moral
• Social
• Cultural

#### Develop the individual:

Students will learn about transformations of shapes. They will enlarge shapes by different scale factors. Algebra provides opportunities for students to develop a sense of “awe and wonder” by using letters to represent variables. Students are encouraged to question “why”; they compose proofs and arguments and make assumptions when analysing a problem. For example, students develop algebraic fluency throughout the curriculum. Algebra is a uniquely powerful language that enables students to describe and model situations.

#### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 4: Probability, Measures & Accuracy, Equations 1

Probability experiments and relative frequency

Theoretical probability

Mutually exclusive events

Probability tree diagrams

Estimation and approximation

Calculator methods

Measures and accuracy, including upper and lower bounds

Solving linear equations

Solving quadratic equations using factorisation, completing the square and the quadratic formula

No assessment this term - Revision of all material covered in this term and previous terms ready for Y10 examination in T5

### Relative frequency

Experimental probability

### Theoretical probability

The likeliness of an event happening based on all the possible outcomes

### Probability space diagram

A list of all possible probability events

### Mutually exclusive events

Two or more events are said to be mutually exclusive if they cannot occur at the same time

### Independent events

Two events are independent if the occurrence of one does not affect the occurrence of the other

### Estimate

An approximate calculation

### Upper bound

The upper limit of a calculation

### Lower bound

The lower limit of a calculation

### Error interval

The margin of error when rounding, usually expressed as an inequality

• Spiritual
• Moral
• Social
• Cultural

#### Develop the individual:

The topic of probability provides opportunities for students to consider whether situations are fair or biased and discuss gambling, betting, lotteries, raffles and games of chance. A knowledge of probability will benefit students’ functioning in society as they will understand bias and the chance of an event happening. By exploring upper and lower bounds students will be able to understand limits of accuracy. This skill will benefit students’ functioning in society.

#### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 5: Year 10 examination, Equations 2, Ratio and proportion, Factors, powers and roots, Circles

Solving simultaneous equations

Proportion

Ratio and scales

Percentage change and reverse percentages

Factors and multiples

Powers and roots including laws of indices

Surds

Area and circumference of a circle

Calculate arc lengths and areas of sectors

Year 10 examination: Assessment of T1, T2, T3 and T4 topics including Equations

### Equation

A mathematical statement where the values of two mathematical expressions are equal (indicated by the sign =)

### Inequality

The relation between two expressions that are greater or less then each other

### Surd

An expression containing one or more irrational roots of numbers, such as 2√3, 3√2 + 6

### Circumference

The distance round the outside of a circle

The distance from the centre to the edge of a circle

### Diameter

The distance across a circle through the centre

### Chord

A chord is a straight line drawn through a circle which divides the circle into two parts. The line can be drawn anywhere in the circle EXCEPT the center where it becomes the diameter

### Sector

The sector of a circle is a portion of the circle enclosed by two radii and an arc

### Segment

The segment of a circle is a part of the circle bounded by a chord and an arc

### Tangent

A line that touches a circle

• Spiritual
• Moral
• Social
• Cultural

#### Develop the individual:

All mathematics has a rich history and a cultural context in which it was first discovered or used, for example, students will consider how pi was first discovered. Numerical fluency and an understanding of proportion will benefit students’ functioning in society. For example to be able to convert between units, or state which is the better value for money? When solving mathematical problems students will develop their creative skills. When solving mathematical problems students will develop their creative skills. Students develop algebraic fluency throughout the curriculum. Algebra is a uniquely powerful language that enables students to reflect on experiences in order to describe and model situations.

#### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 6: Year 10 end of year Exams, Approximate solutions and iterations, inequalities, Constructions & Loci

End of year 10 exams.

Approximate solutions and iteration

Solving inequalities

Representing inequalities on a number line

Representing inequalities as regions

Ruler and compass constructions

Solving problems involving loci

Test on: All material covered throughout Year 10.

1 non-calculator paper and 1 calculator paper

### Iteration

The repetition of a mathematical process applied to obtain successively closer approximations to the solution of a problem

### Inequality

The relation between two expressions that are greater or less then each other

### Perpendicular bisector

A line which cuts a line segment into two equal parts at 90°

### Angle bisector

A line which cuts an angle into two equal parts

### Loci

The set of all points that satisfy given conditions

### Factor

A number that divides exactly into a given number e.g. the factors of 12 are 1 & 12, 2 & 6, 3 & 4

### Multiple

A multiple is a number made by multiplying together two numbers

### Prime factorisation

To express a number as the product of its prime factors

• Spiritual
• Moral
• Social
• Cultural

#### Develop the individual:

Algebra provides opportunities for students to develop a sense of “awe and wonder” by using letters to represent variables. Students are encouraged to question “why”; they compose proofs and arguments and make assumptions when analysing a problem. For example, students develop algebraic fluency throughout the curriculum. Algebra is a uniquely powerful language that enables students to describe and model situations.

#### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .