Year 10 Maths Work Pack IV Higher 10 Maths...Week 2 Topics Trigonometry: finding missing angles Higher Phase IV Booklet All tasks completed to a high standard. Hegarty maths Students’

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Year 10 Maths

Higher Ark Globe Academy

Remote Learning Pack Phase IV

Monday 8 June- Friday 19 June

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Year10HigherMaths

Session Title Worktobecompleted

Resourceprovided

Outcome On-LineSupport

1 Number See Narrated PPT on week 1 Topics: Multiplying fractions and Dividing fractions

Higher Phase IV Booklet

All tasks completed to a high standard.

Hegarty maths Students’ VLE Mathswatch

2 Geometry Interior and exterior angles in polygons




3 Geometry Pythagoras’ theorem Higher Phase IV Booklet



4 Geometry Trigonometry: finding missing sides




5 Mixed Independent Learning task – Corbett Maths




6 Geometry See Narrated PPT on Week 2 Topics Trigonometry: finding missing angles




7 Geometry Gradient of a line Higher Phase IV Booklet



8 Geometry Finding the equation of a line




9 Numbers Percentage increase and decrease




10 Mixed Independent Learning task – Corbett Maths




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Introduction

What is included in this home learning pack? It is not easy to learn at home without the support from your teacher that you are used to. This means that this pack includes some topics that you have already covered in Year 10 so that you get a chance to go back over them and remember them. It also includes some new topics that you would have been taught in the spring and summer terms. This new content is not everything and the topics have been chosen carefully as ones we think you can study on your own at home with the help of the resources in this pack. How should I use this pack effectively? You should make sure that you use the video tutorials for each topic to ensure you have fully understood the topic. This should then be followed by completing the practice questions and attempting the ‘extend’ questions to really make you think. Mark your own mark using the answers to check you are eon the right track. To finish, complete the progress check quizzes on Hegarty Maths to show your teacher that you are understanding the topics. They will be keeping an eye on your progress over the summer term. How is this booklet structured? Key points Precise bullet points which outline the key knowledge you need to

know in each topic Examples – Video tutorials

Videos that explain each topic and go through key examples

Practice A series of questions to give you the opportunity to practise and

demonstrate you have understood the topic fully Extend Some more challenging and stretching questions to make you think

a little bit more. Rise to the challenge and have a go at these questions!

Answers A full set of answers for the practice questions so that you can

check your work and assess your progress as you work through the booklet

Progress check Quizzes on Hegarty Maths to show your teacher that you have

understood the topic fully

Weekly ‘Corbett Maths 5-a-day’ check ins Each week, you will have one lesson which provides you with a Corbett Maths 5-a-day challenge which covers a variety of topics. These questions are based around the essential topics we would expect Year 10 students to be confident with. You should complete them use the answers to these foundation plus questions at https://corbettmaths.com/5-a-day/gcse/ to check how you are getting on and make any corrections.

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Day 1: Multiplying and Dividing Fractions

View Week 1 Narrated Powerpoint Lesson/Video

Key points

• Unlike when adding or subtracting fractions, when multiplying fractions, you do not

need common denominators. • We multiply the numerators together and then we multiply the denominators

together. • When giving our answers, we need to make sure they are given in simplest form. • We can ‘cross simplify’ fractions before multiplying. This makes it easier to calculate

with larger numbers and means we should not have to simplify at the end.

Examples – Video tutorials

OR If you do not have access to Hegarty Maths, you can use the Corbett maths videos below Multiplying fractions

Scan the QR code using your mobile phone

or click on the QR code to follow the hyperlink

CLIP NUMBERS: 68 & 69

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Day 1 Practice: Multiplying Fractions


Extend

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Progress check

You should now complete quiz numbers 68 and 69 on Hegarty Maths to show your teacher that you have understood this topic.

Record your percentage scores below:

Quiz 68

Score:

%

Date completed:

Quiz 69

Score:

%

Date completed:

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Day 1: Dividing Fractions


Key points

• Unlike when adding or subtracting fractions, when dividing fractions, you do not need

common denominators. • The reciprocal of 2 is !" . The reciprocal of #" is "#. When you multiply a number by its

reciprocal, the result is always 1. • To divide two fractions, we take the following steps:

• Find the reciprocal of the second fraction • Change the division calculation to a multiplication calculation • Multiply the first fraction by the reciprocal of the second

• When giving our answers, we need to make sure they are given in simplest form.


OR If you do not have access to Hegarty Maths, you can use the Corbett maths videos below Dividing fractions



CLIP NUMBERS: 70

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Day 1 Practice: Dividing Fractions


Extend

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Progress check

You should now complete quiz number 70 on Hegarty Maths to show your teacher that you have understood this topic.

Record your percentage score below:

Score:

%

Date completed:

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Day 2: Interior and exterior angles in polygons


Key points

• The sum of the exterior angles in any polygon is 360o. • The sum of interior angles in any polygon can be calculated using the formula

(n – 2) × 180 where n is the number of sides of the polygon. • An exterior angle and interior angle lie on a straight line and total 180o.


OR If you do not have access to Hegarty Maths, you can use the Corbett maths videos below Angles in polygons



CLIP NUMBERS: 561, 562, 563 & 564

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Day 2 Practice: Interior and exterior angles in polygons


Extend

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Progress check



Quiz 561

Score:

%

Date completed:

Quiz 563

Score:

%

Date completed:

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Day 3: Pythagoras’ theorem


Key points

• We can use Pythagoras’ theorem to find a missing side on a right-angled triangle when given two other sides.

• The side opposite the right-angle is called the hypotenuse. It is always the longest side of the triangle. We label this side c.

• The two shorter sides are labelled a and b. • Pythagoras’ theorem states: c2 = a2 + b2


OR If you do not have access to Hegarty Maths, you can use the Corbett maths videos below Pythagoras’ theorem

Scan the QR code above with your mobile phone



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Day 3 Practice: Pythagoras’ theorem


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Extend

Progress check



Quiz 498

Score:

%

Date completed:

Quiz 499

Score:

%

Date completed:

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Day 4: Trigonometry – Finding missing sides


Key points

• We can use trigonometry to find missing lengths of triangles. • Trigonometry uses three functions, these are called:

Sine (shortened to Sin and pronounced “sign”) Cosine (shortened to Cos) Tangent (shortened to Tan)

• We use the trig ratios given below to find unknown angles and sides:


OR If you do not have access to Hegarty Maths, you can use the Corbett maths videos below Trigonometry – Missing sides

CLIP NUMBER: 508, 509 & 510

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Scan the QR code above using your mobile phone


Day 4 Practice: Trigonometry – Finding missing sides


Question 1: Find the lengths of the sides labelled x below:

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Extend

Question 2:

Question 4:

Progress check

You should now complete quiz number 508, 509 & 510 on Hegarty Maths to show your teacher that you have understood this topic


Quiz 508

Score:

%

Date completed:

Quiz 509

Score:

%

Date completed:

Quiz 510

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Score: %

Date completed:

Day 5: Independent Learning Task

Corbett Maths 5-a-day challenge

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Answers to these foundation plus questions can be found at https://corbettmaths.com/5-a-day/gcse/

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Day 1: Trigonometry – Finding missing angles View Week 2 Narrated Powerpoint Lesson/Video

Key points

• We can use trigonometry to find missing lengths of triangles. • Trigonometry uses three functions, these are called:

Sine (shortened to Sin and pronounced “sign”) Cosine (shortened to Cos) Tangent (shortened to Tan)

• We use the trig ratios given below to find unknown angles and sides:


OR If you do not have access to Hegarty Maths, you can use the Corbett maths videos below Trigonometry – Missing Angles


CLIP NUMBER: 511 & 512

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Day 1Practice: Trigonometry – Finding missing angles


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Extend

Question 2:

Question 3:

Question 4:

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Progress check

You should now complete quiz numbers 511 and 512 on Hegarty Maths to show your teacher that you have understood this topic


Quiz 511

Score:

%

Date completed:

Quiz 512

Score:

%

Date completed:

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Day 2: Gradient of a line


Key points

• The gradient of a line is its steepness. • To calculate the gradient of a line, we need to consider two coordinates on the line. • To calculate the gradient of a line: Gradient = %&'()*,(-%&'()*,(. • A line sloping from bottom left to top right has a positive gradient. • A line sloping from top left to bottom right has a negative gradient.


OR If you do not have access to Hegarty Maths, you can use the Corbett maths videos below Gradient of a line

Scan the QR code above with your mobile phone



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Day 2 Practice: Gradient of a line


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Extend

Progress check



Quiz 201

Score:

%

Date completed:

Quiz 202

Score:

%

Date completed:

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Day 3: Finding the equation of a straight line View Week 2 Narrated Powerpoint Lesson/Video

Key points

• The equation of a straight line can be written in the form y=mx+c where m is the

gradient and c is the y-intercept (where the graph cuts the y-axis). • This means that the gradient is the value of the coefficient of x (number in front of

the x), and the y-intercept is the constant term (number on its own), but only when y is the subject of the equation.

• If the gradient is positive, the line will slope upwards, and if it is negative it will slope downwards.

• The equation of a straight line can be found if two coordinates that lie on the line are known. This is done by first finding the value of the gradient, and then finding the value of the y-intercept.

• To find the gradient, take the 2 known pairs of coordinates that lie on the graph and calculate the difference between the y-coordinates and divide this number by the difference between the x-coordinates.

• This can be written as a formula, where, for 2 coordinates (x1,y1) and (x2,y2), the gradient, /,= -"2-!."2."

• Once the gradient is found, rewrite y = mx+c with the calculated m. For example, if

you work out that the gradient is 5, you write y=5x+c. • Then substitute one of the two known coordinates into the formula to find c. For

example, if one of the two coordinates were (4, 17), you can then substitute these into y=5x+c à 17=5(4) +c, so 17 = 20 + c, so c = -3. So, the equation of the line is y= 5x - 3.


OR If you do not have access to Hegarty Maths, you can use the Corbett maths videos below Finding the equation of a line

CLIP NUMBERS: 211, 212 & 213

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Day 3 Practice: Finding the equation of a straight line


Question 1: Find the equations of each line below

Question 2: Find the equation of the straight line that passes through the points

Question 3: Find the equations of the straight line that:

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Question 4: Find the equations of the lines below

Extend

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Progress check

You should now complete quiz number 213 on Hegarty Maths to show your teacher that you have understood this topic


Score:

%

Date completed:

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Day 4: Percentage increase and decrease

View Week 2 Narrated Powerpoint Lesson/Vide

Key points

• To increase an amount by a percentage, calculate the percentage then add it to

the original amount. • To decrease an amount by a percentage, calculate the percentage then subtract it

from the original amount. • To work out the multiplier, first add or subtract the percentage from 100, then

convert to a decimal.


OR If you do not have access to Hegarty Maths, you can use the Corbett maths videos below Percentage increase and decrease Using multipliers

Scan the QR code above using your mobile phone


CLIP NUMBERS: 88, 89 & 90

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Day 4 Practice: Percentage increase and decrease

View Week 2 Narrated Powerpoint Lesson/Vide

Extend

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Progress check

You should now complete quiz numbers 88, 89 & 90 on Hegarty Maths to show your teacher that you have understood this topic


Quiz 88

Score:

%

Date completed:

Quiz 89

Score:

%

Date completed:

Quiz 90

Score:

%

Date completed:

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Day 5: Independent Learning Task

Corbett Maths 5-a-day challenge

Answers to these foundation plus questions can be found at https://corbettmaths.com/5-a-day/gcse/

Documents

Year 10 Maths Work Pack IV Higher 10 Maths...Week 2 Topics Trigonometry: finding missing angles Higher Phase IV Booklet All tasks completed to a high standard. Hegarty maths Students’