ark globe academy remote learning pack phase v 10... · geometry. converting between metric units...

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Year 10 Maths Higher

Ark Globe Academy Remote Learning Pack

Phase V Monday 29 June – Friday 10 July

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Year 10 Higher Maths Session Title Work to be completed Resource

provided Outcome On-Line

Support 1 Geometry See Narrated PPT on week 1

Topics:

Parallel and perpendicular

lines

Higher Phase V Booklet

All tasks completed to a high standard.

Hegarty maths Students’ VLE Mathswatch

2 Geometry Midpoints Higher Phase V Booklet



3 Algebra Drawing quadratic graphs Higher Phase V Booklet



4 Geometry Converting between metric units of area and volume




5 Mixed Independent Learning task – Corbett Maths




6 Number See Narrated PPT on week 2

Topics:

Bounds




7 Geometry Area of sectors Higher Phase V Booklet



8 Geometry Length of an arc Higher Phase V Booklet



9 Probability &

Statistics

Frequency trees Higher Phase V Booklet



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 practice 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

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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.

Day 1: Parallel and perpendicular lines

View Week 1 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) but only when y is the subject of the equation.

• Parallel lines have the same gradient which means that they have the same steepness and are always equidistant (the same distance apart) and never intersect (cross).

• You can tell if lines are parallel if, when they are rearranged into the form y=mx+c, they have the same value of m. For example, line 1, y=2x+5, and line 2, 2y=4x+12, are parallel, as line 2 can be rearranged to y=2x+6. Both equations have the same gradient (2) and so are parallel.

• To find the equation of line that is parallel to another and that passes through a given coordinate, first find the equation of the first line. For example, in y=3x-4, the gradient is 3. This means you know that any line parallel to it will have the form y=3x+c, where c could take any value. If you know the parallel line passes through a particular point, such as (4, 17), you can then substitute these x and y values into y=3x+c to find the value of c. In this case, 17=3(4) +c, so 17 = 12 + c, so c = 5. Therefore, the parallel equation is y=3x+5.

• Perpendicular lines cross each other at right angles. • The gradients of perpendicular lines are negative reciprocals of one another. • Two numbers are reciprocals of each other if they multiply together to make 1. This

means that the reciprocal of 𝒂𝒂 is 𝟏𝟏𝒂𝒂 and the reciprocal of 𝒂𝒂

𝒃𝒃 is 𝒃𝒃

𝒂𝒂 (the fraction ‘flips’).

• Negative reciprocals multiply together to make -1. The negative reciprocal of 𝒂𝒂 is −𝟏𝟏𝒂𝒂

and the reciprocal of -𝒂𝒂𝒃𝒃 is 𝒃𝒃

𝒂𝒂.

• This means a line perpendicular to 𝒚𝒚 = 𝟑𝟑𝟑𝟑 − 𝟓𝟓 will be in the form 𝒚𝒚 = −𝟏𝟏𝟑𝟑𝟑𝟑 + 𝒄𝒄. If you are

given a coordinate that the perpendicular line passes through, you can substitute it into the perpendicular line equation to find the value of c.


CLIP NUMBER: 214, 215 & 216

https://corbettmaths.com/5-a-day/gcse/

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OR If you do not have access to Hegarty Maths, you can use the Corbett maths videos on the next page. Parallel lines Perpendicular lines

Scan the QR code above with your mobile phone or click on the QR code to follow the hyperlin

Day 1 Pracice: Parallel and perpendicular lines View Week 1 Narrated Powerpoint Lesson/Video

Question 1: Write down the equation of a line parallel to each of the following

Question 2: Write down the equation of each of the following lines

Question 3: Write down the equation of each of the following lines

Question 4: Write down the negative reciprocal of each of the following numbers

http://www.hegartymaths.com/

https://videopress.com/v/08hKgcPb

https://videopress.com/v/1annT6to

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Question 5: Write down each of the following lines

Question 6:

Extend Question 1: Write down the equations of the lines, from the box, that are:

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Progress check

You should now complete quiz numbers 214 and 215 on Hegarty Maths to show your teacher that you have understood this topic

Record your percentage scores below:

Quiz 214

Score:

%

Date completed:

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Quiz 215

Score:

%

Date completed:

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Day 2: Midpoints


Key points

• A line segment is a line that starts and ends at fixed points, such as A B, where A

and B are known as end points of the line segment. • The midpoint of a line segment is the point that is half-way along a line segment. • When you know the coordinates of the end points of the line segment, you can use them

to calculate the midpoint. • You do this by finding the x-coordinate in each end point and calculating the mean

average of them. You then calculate the mean average of the y-coordinates of the end points. The coordinates of the midpoint = (‘mean of x’, ‘mean of y’).

• This can be written as a formula that you can learn: if Point 1 has coordinates (x1, y1) and Point 2 has coordinates (x2, y2) then the midpoint is (𝟑𝟑𝟏𝟏+𝟑𝟑𝟐𝟐

𝟐𝟐, 𝒚𝒚𝟏𝟏+𝒚𝒚𝟐𝟐

𝟐𝟐).

• For example, if the end points of the two coordinates are (-3, 8) and (7, 4) then the midpoint is (−𝟑𝟑+𝟕𝟕

𝟐𝟐, 𝟖𝟖+𝟒𝟒

𝟐𝟐) = (𝟒𝟒

𝟐𝟐, 𝟏𝟏𝟐𝟐𝟐𝟐

) = (2, 6).


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

Scan the QR code above using your mobile phone

or click on the QR code to follow the hyperlink

CLIP NUMBER: 200


https://videopress.com/v/aruLzLGx

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Day 2 Practice: Midpoints


Question 1: Find the coordinates of the midpoints of the following line segments:

Question 2: Fine the midpoint of the line connecting these pairs of points

Question 3: M is the midpoint of PQ in each diagram below.

Find the coordinates of Q in each diagram.

Extend

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Progress check

You should now complete quiz number 200 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 3: Drawing quadratic graphs


Key points

• Quadratic functions always have x2 as the highest power of x. • The graphs of quadratic functions are always the same shape, called a parabola. • If the coefficient of x2 is positive, the parabola is u-shaped. • If the coefficient of x2 is negative, the parabola is n-shaped. • To draw the graph we need coordinates, generate these by substituting values into the

quadratic equation. • Ensure you join the points with a smooth curve.


OR If you do not have access to Hegarty Maths, you can use the Corbett maths videos below Drawing quadratic graphs



CLIP NUMBER: 251


https://videopress.com/v/7we47Prr

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Day 3 Practice: Drawing quadratic graphs


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Extend

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Progress check

You should now complete quiz number 251 on Hegarty Maths to show your teacher that you have understood this topic


Quiz 251

Score:

%

Date completed:

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Day 4: Convert metric units – Area and Volume


Key points

• Area is measured in units squared (e.g. m2, cm2, mm2). • To convert between different units of area, multiply or divide by the square of the ‘length’

conversion factor. • Volume is measured in units cubed (e.g. m3, cm3, mm3). • To convert between different units of volume, multiply or divide by the cube of the ‘length’

conversion factor. • When converting from a larger unit to a smaller unit (e.g. m2 to cm2), you multiply. • When converting from a smaller unit to a larger unit (e.g. mm2 to cm2), you divide. • 100cm2 = 10cm x 10cm • 1000km2 = 100km x 100km • 1000cm3 = 10cm x 10cm x 10cm


OR If you do not have access to Hegarty Maths, you can use the Corbett maths videos below Converting areas Converting volumes

CLIP NUMBERS: 700 & 702


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https://videopress.com/v/DLTjMO0n

https://videopress.com/v/WGj0AqWc

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Day 4 Practice: Convert metric units – Area and Volume View Week 1 Narrated Powerpoint Lesson/Video

Extend

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Progress check



Quiz 700

Score:

%

Date completed:

Quiz 702

Score:

%

Date completed:

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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: Bounds


Key points

• Lower bound – the smallest value that a number (given to a specified accuracy) can be. • Upper bound – the largest value that a number (given to a specified accuracy) can be. • A quick way to calculate the lower and upper bounds is to halve the degree of accuracy

specified, then subtract it from the rounded value for the lower bound and add this to the rounded value for the upper bound.

• When written as an inequality the lower bound can be ‘equal to’, however the upper bound cannot be ‘equal to’.


OR If you do not have access to Hegarty Maths, you can use the Corbett maths videos below Lower and upper bounds





https://videopress.com/v/ERpv9nEK

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Day 1 Practice: Bounds


Extend

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Progress check



Quiz 137

Score:

%

Date completed:

Quiz 138

Score:

%

Date completed:

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Day 2: Area of sectors


Key points

• The area of a sector of a circle is a fraction of the whole area of the circle • The area of a circle is calculated by using:

r is the length of the radius

• To find the area of the sector of a circle we use:


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

CLIP NUMBER: 546 & 547


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https://videopress.com/v/mDTce89Z

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Day 2 Practice: Area of sectors


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Extend

Question 7:

Question 8:

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Progress check

You should now complete quiz number 546 & 547 on Hegarty Maths to show your teacher that you have understood this topic


Quiz 546

Score:

%

Date completed:

Quiz 547

Score:

%

Date completed:

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Day 3: Length of an arc


Key points

• The arc length of a circle is a portion of the circumference of the whole circle • The circumference of a circle is calculated by using:

r is the length of the radius of the circle

• To find the length of an arc of the circle we use:

r is the length of the radius of the circle x is the angle of the sector


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


CLIP NUMBER: 544 & 545


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Day 3 Practice: Length of an arc


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Extend

Question 11:

Question 12:

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Progress check

You should now complete quiz number 544 & 545 on Hegarty Maths to show your teacher that you have understood this topic


Quiz 544

Score:

%

Date completed:

Quiz 545

Score:

%

Date completed:

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Day 4: Frequency trees


Key points

• A frequency tree is used to display how a group of people or items can be divided up into various categories. For example, how a school can be divided into students/teachers and by gender.

• Unlike probability trees, we used ‘frequencies’ on the frequency trees which means we use actual quantities as opposed to probabilities as fractions or decimals.

• We can use a frequency tree to calculate missing quantities or probabilities.


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

Scan the QR code above with your mobile phone




https://videopress.com/v/IQkTEMa6

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Day 4 Practice: Frequency trees


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Extend

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Progress check

You should now complete quiz numbers 368 and 369 on Hegarty Maths to show your teacher that you have understood this topic.

Record your percentage scores below:

Quiz 368

Score:

%

Date completed:

Quiz 369

Score:

%

Date completed:

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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/


ark globe academy remote learning pack phase v 10... · geometry. converting between metric units...

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