Lesson details

Key learning points

  1. In this lesson, we will explore different patterns related to quadratics and square numbers.

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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
Correct answer: y intercept, x=0
y intercept, y=0
Q2.
What are the coordinates of where y= x² + 14x + 24 crosses the y axis?
(0, 10)
(0, 14)
Correct answer: (0, 24)
(24, 0)
24
Q3.
Where does y = x² - 3x - 10 cross the y axis?
(-3, -10)
Correct answer: (0, -10)
(10, 3)
(3, 10)
Q4.
Which graph could be a sketch of y=(x+4)(x-3)?
An image in a quiz
Option A
Option B
Option C
Correct answer: Option D
Q5.
Which graph could be a sketch of -x² + 3x - 2? Hint Try out some coordinates to check!
An image in a quiz
Option A
Option B
Correct answer: Option C
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.
Correct answer: Zaki is incorrect the curve will cross the y axis only.

6 Questions

Q1.
Which of the following could represent 3 consecutive integers?
n, 2n, 3n
Correct answer: n, n+1, n+2
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)
Correct answer: 4² - (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.
Correct answer: The answer is always the square of one less than one 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?
Correct answer: (n+1)² - 4n
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
Correct answer: n² - 4(n-1)
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?
An image in a quiz
Correct answer: Alex and Steven are both correct.
Alex and Steven are both incorrect.
Just Alex is correct.
Just Steven is correct

Lesson appears in

UnitMaths / Quadratic expressions (9.9)