Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
Learning Objectives:
National curriculum:
Algebra: identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing
the square}
Kangaroo Maths
Stage 10:
Essential knowledge: Know the meaning of roots, intercepts and turning points
Algebraic proficiency: visualising 1
Key concepts: identify and interpret roots, intercepts, turning points of quadratic functions graphically
Possible success criteria: Identify (interpret) roots, intercepts and turning points of quadratic functions graphically
Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
Edexcel A11 New to 2015
identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically [U] and turning points by completing the square
[B]
Edexcel example:
Edexcel Higher-unit 15 -topic test
Q5. The same with the H1 calculator paper 2 (p.123)
The graph of y = f(x) is drawn on the grid.
(a) Write down the coordinates of the turning point of the graph.
Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
(..........................., ...........................)
(1)
(b) Write down the roots of f(x) = 2
...........................................................
(1)
(c) Write down the value of f(0.5)
...........................................................
(1)
(Total for question = 3 marks)
Q6.The expression x2 – 8x + 21 can be written in the form (x – a)2 + b for all values of x.
(a) Find the value of a and the value of b.
a=......................
b=......................
(3)
Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
The equation of a curve is y = f(x) where f(x) = x2 – 8x + 21
The diagram shows part of a sketch of the graph of y = f(x).
The minimum point of the curve is M.
(b) Write down the coordinates of M.
..............................................................................................................................................
(1)
(Total for Question is 4 marks)
This question was poorly answered. It was clear that only a small minority of candidates were well practised in the technique of completing the square.
Candidates who realised what was required often went on to carry out this technique but then spoiled their responses by writing a = −4, b = 5. Other
Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
candidates wrote (x + 4)2 +5 then a = 4, b = 5. This was clearly incorrect working and could not be awarded the marks. "8" and "21" were commonly
seen incorrect answers. Part (b) was answered correctly by only a small minority of candidates with many of the more able candidates failing to see the
connection between the two parts of the question.
between the two parts of the question.
Q8. Solve x2 > 3x + 4
...........................................................
(Total for question = 3 marks)
Q9. Solve the inequality x2 > 3(x + 6)
...........................................................
(Total for question = 4 marks)
Q10. (i) Sketch the graph of f(x) = x2 − 5x + 10, showing the coordinates of the turning point and the coordinates of any intercepts with the coordinate
axes.
(ii) Hence, or otherwise, determine whether f(x + 2) − 3 = 0 has any real roots.
Give reasons for your answer.
(Total for question = 6 marks)
Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
OCR
Year term
Wk No
GCSE
content
Ref.
DfE Ref
Specification Description
AO 1 Overview
11T2
11T2
5
5
7.01c
7.01c
A11, A12
Polynomial
functions
Identify intercepts and, using symmetry, the turning point of graphs of
quadratic functions.
E.g. y=x2 - 4x + 1 has line of symmetry through x=2 and y-intercept at
(0,1)
A11, A12
Polynomial
functions
Identify intercepts and, using symmetry, the turning point of graphs of
quadratic functions. Find the roots of a quadratic equation
algebraically.
Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
11T2
5
7.01c
A11, A12
Polynomial
functions
Sketch graphs of quadratic functions, identifying the turning point by
completing the square.
E.g. Rearrange y=x2- 8x + 9 to y=(x-4)2-7
AO 2 suggestions
Construct a chain of reasoning to change x2+ bx + c into (x-m)2 + n in order to identify max/min y value by completing the square.
Sketch graphs of quadratic functions, identifying the turning point by completing the square.
E.g. Rearrange y=x2- 8x + 9 to y=(x-4)2-7
OCR example paper
4H calculator
Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
OCR Higher Check In - 6.01 Algebraic expressions
Extension
Match each quadratic expression with its factorised form and completed square form.
There is one blank space in each column for you to fill in the missing expression to complete each set.
x 2  13 x  36
 x  11 x  7 
 x  3
2
 36
x 2  14 x  32
 x  6 x  8
 x  8
2
 36
x 2  18 x  77
 x  2 x  6
x 2  3 x  28
 x  7  x  12
x 2  14 x  48
 x  9 x  4
2
5  289

x  2  4


 x  4
2
4
Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
x 2  5 x  66
 x  2 x  14 
 x  7
2
 81
2
 x  3 x  9
3  121

x  2  4


x 2  6 x  27
 x  7 x  4
13 
25

x  2   4


x 2  16 x  28
 x  16  x  2
x 2  5 x  84
AQA
Higher 2 paper
2
 x  7
2
1
2
4
 x  9
Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
Understanding the Pedagogical Implication of Teaching Higher Level Mathematics through Peer Learning
Higher paper 3