using the technique and layout - New College, Pontefract · 2020. 5. 15. · Task 3 :Additional...
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Mathematics Y11 to Y12 Further Mathematics Summer Independent Learning
June to August 2020
There are three tasks to work through. Please read the following instructions very carefully and ensure you label and collate all your work ready for checking in September.
For your first maths lesson please bring
A large A4 folder with five subject dividers.
These instructions with the tables filled in (print out/copy the tables onto A4 paper).
Dated and titled work done on each of the topics listed in Task 1 & 3.
The two practice initial tests (Task 2), fully marked and reviewed.
A list of questions you need to ask prior to doing your initial test.
Task 1: Preparation Work
1. For each topic, work through video.
2. Complete worksheet using the technique and layout used in the video.
3. Make sure you title and date your work.
4. Mark and correct work.
5. Do improvement work as necessary.
6. Repeat for each topic.
7. Keep track by filling in the following table.
8. Collate your work for each topic together so it is easy to check in September. (See point 3!)
Topic Video(s)
(Tick)
Worksheet (Tick)
Details of Improvement Work Completed
B1 Indices
B2 Surds
B3 Quadratics
B4 Simultaneous
Equations
B5 Inequalities
E1 Triangle
Geometry
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Task 2 1. Do Practice Initial Test 1 under exam conditions.
2. Mark and correct your test and identify any improvement work necessary.
3. Fill in the review sheet below.
4. Revisit relevant videos and worksheets.
5. Update review sheet with details of work completed.
Topic Score Improvement Work to Do Tick
B1 Indices
11
B2 Surds
10
B3 Quadratics
49
B4 Simultaneous Equations
11
B5 Inequalities
11
E1 Triangle Geometry
12
Total
114
6. Do Practice Initial Test 2 under exam conditions.
7. Mark and correct your test and identify any improvement work necessary.
8. Fill in the review sheet below.
9. Revisit relevant videos and worksheets.
10. Update review sheet with details of work completed.
11. Make a list of questions you need to ask prior to doing your initial test for real!
Topic Score Improvement Work to Do Tick Questions to ask…
B1 Indices
11
B2 Surds
10
B3 Quadratics
49
B4 Simultaneous Equations
11
B5 Inequalities
11
E1 Triangle Geometry
12
Total
114
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Task 3 :Additional Further Mathematics Preparation Work
1. For each topic section, work through the examples.
2. Complete the exercise, showing well-structured algebraic methods. You do not need to complete every question in the exercise, but should make sure you get enough practice with both the skills themselves, and with setting out your reasoning clearly and logically.
3. Mark and correct your work.
Topic Exercise
(Tick)
Areas for Improvement
2.1 Trigonometric Equations
2.2 Other Trigonometric Methods
3.1 Straight Line Graphs
3.2 Basic Shape of Curved Graphs
3.3 Factors
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Video hyperlinks
B1 Indices
https://youtu.be/1lThXgU08S0
https://youtu.be/v5bn4HZrmQs
https://youtu.be/W0h4rHj88ys
B2 Surds
https://youtu.be/jHelde32YtI
B3 Quadratics
https://youtu.be/Pziws8ojnlk
https://youtu.be/sn_joGVj15w
https://youtu.be/kk7p6hjn7hQ
https://youtu.be/toIqbX_NXHo
B4 Simultaneous Equations
https://youtu.be/4SRtwS5unwE
B5 Inequalities
https://youtu.be/wDut-In_7Wg
E1 Triangle Geometry
https://youtu.be/uVl6TAb0vBg
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Topic: B1 Indices Basic Skills videos: https://youtu.be/1lThXgU08S0
https://youtu.be/v5bn4HZrmQs https://youtu.be/W0h4rHj88ys
Mathematics Department
Advanced Skills
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TASK 1
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Exam Questions (OCR/MEI C1 Questions)
1. Jan 05 Q5
2. June 05 Q6
3. June 06 Q9
4. Jan 07 Q6
5. June 07 Q5
Answers – Basic Skills
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Topic: B2 Surds Basic Skills https://youtu.be/jHelde32YtI
Mathematics Department
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Exam Questions (AQA Questions)
1. Jan 05 Q5
2. June 05 Q5
3. Jan 06 Q1
4. June 06 Q4
5. Jan 07 Q3
6. June 07 Q7
Answers – Basic Skills
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Topic: B3 Quadratics Basic Skills https://youtu.be/Pziws8ojnlk https://youtu.be/sn_joGVj15w https://youtu.be/kk7p6hjn7hQ https://youtu.be/toIqbX_NXHo
Mathematics Department
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…include points of intesection with the x-axis
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Advanced Skills
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Exam Questions (AQA C1 Questions)
1. Jan 2011 Q7
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2. June 11 Q4
3. Jan 12 Q2
4. June 12 Q5
5. Jan 13 Q4
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6. June 13 Q5
Answers – Basic Skills
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Answers – Advanced Skills
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Topic: B4 Simultaneous Equations
Basic Skills
https://youtu.be/4SRtwS5unwE
Mathematics Department
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Exam Questions (AQA C1 Questions)
1. Jan 011 Q7
2. Jan 13 Q8
Answers – Basic Skills
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Topic: B5 Inequalities Basic Skills
Mathematics Department
https://youtu.be/wDut-In_7Wg
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Exam Questions (AQA C1 Questions)
1. Jan 11 Q7
2. June 11 Q7
3. Jan 12 Q6
4. June 12 Q7a
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Answers – Basic Skills
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Topic: E1 Triangle Geometry (Trigonometry) Basic Skills
https://youtu.be/uVl6TAb0vBg
Mathematics Department
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Advanced Skills
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Exam Questions (AQA C2 Questions)
1. June 2006 Q2
2. Jan 2007 Q4 (adapted)
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3. June 2008 Q4
4. Jan 2011 Q3
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5. Jan 2013 Q3
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TASK 2 Year 12 Initial Test for Mathematics
Write out the solutions to each of the following questions.
Show full working, without the use of a calculator.
Your initial test for mathematics will look exactly like this so use the videos and worksheets to ensure you are able to
do the following skills with the layout expected.
Practice 1 (No Calculator)
B3 Quadratics
1. Solve the following quadratic equations by factorising and use your solutions to sketch the related quadratic graph, labelling all intersections with the coordinate axis.
(a) (i) 𝑥2 + 3𝑥 − 28 = 0 (b) (i) 𝑥2 − 6𝑥 + 9 = 0 (c) (i) 2𝑥2 − 21𝑥 + 27 = 0
(a) (ii) Sketch 𝑦 = 𝑥2 + 3𝑥 − 28 (b) (ii) Sketch 𝑦 = 𝑥2 − 6𝑥 + 9 (c) (ii) Sketch 𝑦 = 2𝑥2 − 21𝑥 + 27
2. Solve the following quadratic equations by completing the square and use your solutions to sketch the
related quadratic graph, labelling all intersections with the coordinate axis and turning point.
(a) (i) 𝑥2 + 4𝑥 − 7 = 0 (b) (i) 11 + 8𝑥 − 𝑥2 = 0 (c) (i) 3𝑥2 − 12𝑥 + 2 = 0
(ii) Write 𝑦 = 𝑥2 + 4𝑥 − 7 in the form 𝑦 = 𝑎(𝑥 + 𝑏)2 + 𝑐
(ii) Write 𝑦 = 11 + 8𝑥 − 𝑥2in the form 𝑦 = 𝑎(𝑥 + 𝑏)2 + 𝑐
(ii) Write 𝑦 = 3𝑥2 − 12𝑥 + 2 in the form 𝑦 = 𝑎(𝑥 + 𝑏)2 + 𝑐
(iii) Sketch 𝑦 = 𝑥2 + 4𝑥 − 7 (iii) Sketch 𝑦 = 11 + 8𝑥 − 𝑥2 (iii) Sketch 𝑦 = 3𝑥2 − 12𝑥 + 2
3. Evaluate the equation of the following quadratics, giving your answer in the form 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐
(a)
(b)
(c)
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B4 Simultaneous Equations
1. Solve 3𝑥 + 3𝑦 = −4 5𝑥 − 2𝑦 = 5
2. Solve 𝑦 = 𝑥 − 6
1 𝑥 − 𝑦 = 4
2
3. Solve 3𝑥2 − 𝑥 − 𝑦2 = 0
𝑥 + 𝑦 = 1
B5 Inequalities
Find the set of values for which…
1. 3(1 − 2𝑡) ≤ 𝑡 − 4 2. 2𝑥2 − 9𝑥 + 4 ≤ 0 3. 2𝑦 + 3 < 3𝑦(𝑦 − 2)
E1 Triangle Geometry (Calculator)
1. Calculate the length AB
A
23cm
72o
B C 17cm
2. Calculate the angle 𝜗
C
53o
A 𝜗
6.2cm
5.7cm
B
3. Calculate the length AB and the obtuse angle 𝜗
B
A
𝜗
5.8m
11m
31o
C
4. Calculate the area of the triangle ABC
B
A 72o
12.1cm
10.7cm
C
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Year 12 Initial Test for Mathematics
Write out the solutions to each of the following questions.
Show full working, without the use of a calculator.
Your initial test for mathematics will look exactly like this so use the videos and worksheets to ensure you are able to
do the following skills with the layout expected.
Practice 2 (No Calculator)
B3 Quadratics
1. Solve the following quadratic equations by factorising and use your solutions to sketch the related quadratic graph, labelling all intersections with the coordinate axis.
(a) (i) 𝑥2 − 13𝑥 + 40 = 0 (b) (i) 𝑥2 + 5𝑥 = 0 (c) (i) 6𝑥2 + 5𝑥 − 4 = 0
(a) (ii) Sketch 𝑦 = 𝑥2 − 13𝑥 + 40 (b) (ii) Sketch 𝑦 = 𝑥2 + 5𝑥 (c) (ii) Sketch 𝑦 = 6𝑥2 + 5𝑥 − 4
2. Solve the following quadratic equations by completing the square and use your solutions to sketch the
related quadratic graph, labelling all intersections with the coordinate axis and turning point.
(a) (i) 𝑥2 + 2𝑥 − 20 = 0 (b) (i) −11 + 8𝑥 − 𝑥2 = 0 (c) (i) 3𝑥2 − 18𝑥 + 2 = 0
(ii) Write 𝑦 = 𝑥2 + 2𝑥 − 20 in the form 𝑦 = 𝑎(𝑥 + 𝑏)2 + 𝑐
(ii) Write 𝑦 = −11 + 8𝑥 − 𝑥2in the form 𝑦 = 𝑎(𝑥 + 𝑏)2 + 𝑐
(ii) Write 𝑦 = 3𝑥2 − 18𝑥 + 2 in the form 𝑦 = 𝑎(𝑥 + 𝑏)2 + 𝑐
(iii) Sketch 𝑦 = 𝑥2 + 2𝑥 − 20 (iii) Sketch 𝑦 = −11 + 8𝑥 − 𝑥2 (iii) Sketch 𝑦 = 3𝑥2 − 18𝑥 + 2
3. Evaluate the equation of the following quadratics, giving your answer in the form 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐
(a)
(b)
(c)
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B4 Simultaneous Equations
1. Solve 3𝑥 − 4𝑦 = 16 2𝑥 + 12𝑦 = 7
2. Solve 3𝑦 = 2𝑥 − 8 4𝑥 + 𝑦 = −5
3. Solve 3𝑥2 − 𝑥𝑦 + 𝑦2 = 36
𝑥 − 2𝑦 = 10
B5 Inequalities
Find the set of values for which…
1. 4(5 − 2𝑦) ≥ 3(7 − 2𝑦) 2. 2𝑥2 − 5𝑥 − 3 > 0 3. 𝑥(2𝑥 + 1) ≤ 𝑥2 + 6
E1 Triangle Geometry (Calculator)
1. Calculate the length AB
A
37o
69o
B C 11.6cm
2. Calculate the angle 𝜗
C
5.9m
A 𝜗
5.3m
4.9m
B
3. Calculate the length AB and the obtuse angle 𝜗
B
29o A
𝜗
7.6cm
13.2cm
C
4. Calculate the area of the triangle ABC
B
12.5m
A 49o
10.6m
C
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TASK 3
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