Interesting quadratic patterns
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Lesson details
Key learning points
- In this lesson, we will explore different patterns related to quadratics and square numbers.
Licence
This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.
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6 Questions
Q1.
Select the words that best fill in the gaps in order: The __________ is where the curve crosses the y axis, when _______.
x intercept, x=0
x intercept, y=0
y intercept, y=0
Q2.
What are the coordinates of where y= x² + 14x + 24 crosses the y axis?
(0, 10)
(0, 14)
(24, 0)
24
Q3.
Where does y = x² - 3x - 10 cross the y axis?
(-3, -10)
(10, 3)
(3, 10)
Q4.
Which graph could be a sketch of y=(x+4)(x-3)?
Option A
Option B
Option C
Q5.
Which graph could be a sketch of -x² + 3x - 2? Hint Try out some coordinates to check!
Option A
Option B
Option D
Q6.
Zaki says y = x² + 1 will never cross either axes. Is that correct?
Zaki is correct, the curve will never cross either axes.
Zaki is incorrect the curve wil cross the x axis only.
Zaki is incorrect the curve will cross BOTH axes.
6 Questions
Q1.
Which of the following could represent 3 consecutive integers?
n, 2n, 3n
n, n+3, n+6
None of the above,
Q2.
I pick two consecutive integers. I square the bigger one and then subtract 4 of the smaller one. Which example could be my calculation?
(4 x 3)- 3²
(4 x 3)- 4²
3² - (4 x 3)
Q3.
I pick two consecutive integers. I square the bigger one and then subtract 4 of the smaller one. Write out some examples of these. What do you notice about the answers?
The answer is always a cube number.
The answer is always bigger than both of the original numbers.
The answer is always the square of one of the original numbers.
Q4.
I pick two consecutive integers. I square the bigger one and then subtract 4 of the smaller one. Which example could be an algebraic representation of this situation?
4(n+1)- n²
4n- (n+1)²
n² - 4(n+1)
Q5.
I pick two consecutive integers. I square the bigger one and then subtract 4 of the smaller one. Zaki writes a different algebraic expression to me but is still correct. Which one could he have written?
(n-1)² - 4(n+1)
(n-1)² - 4n
4n- (n-1)²
Q6.
I pick two consecutive integers. I square the bigger one and then subtract 4 of the smaller one. Alex and Steven have both tried to generalise my pattern. Who is correct?
Alex and Steven are both incorrect.
Just Alex is correct.
Just Steven is correct