Alevel_C1C2

3
Exam-style mark scheme
Quadratic functions
Question Scheme Marks
Number
1. (a) Completing the square of the L.H.S. or expand the bracket of
the R.H.S. and compare the coefficients of the x 2 and x.
2 2 2
( x + 3) − 3 + 4 = ( x + 3) − 5 ⇒ a = 3,
b = −5
A2 (2)
(b) (x + 3) 2 - 5 = 0 B1
(x + 3) 2 = 5
x + 3 = ± 5
x = −3 ± 5 ⇒
B1
p = -3 and q = 1 A2 (4)
6
2. (a) Using the quadratic formula:
x =
2
2 ± ( −2) − 4 × 4 × ( −1)
2 × 4
=
2 ± 20
8
=
1 ± 5
4
B1 A1 (2)
( ) = B1
2
x −
1
( ) −
1
−
1
= 0 B1
4 16 4
( x − 1
2
−
5
) = a = −
1
b = −
5
2
(b) 4 x −
1
x −
1
0
2 4
4
16
0, , A2 (4)
4 16
6
3. (a)
y
O
4
x
B2 (2)
y = x(x – 4)
(b) (0, 0), (4, 0) B2 (2)
(2, -4) minimum B2 (2)
6
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Core C1