Alevel_C1C2
Alevel_C1C2
Alevel_C1C2
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15<br />
Exam-style mark scheme<br />
Integration<br />
Question Scheme Marks<br />
Number<br />
1. (a) y = 2x 3 + 3x 2 – x + c A2<br />
2 = -16 + 12 + 2 + c Þ c = 4 A1<br />
y = 2x 3 + 3x 2 – x + 4 B1 (4)<br />
3 2<br />
2<br />
(b) ( 2x + 3x − x]<br />
1 = 26 − 4 = 22<br />
B1 A1 (2)<br />
6<br />
2. (a) 2x 2 – 9x + 4 = 0<br />
(2x – 1)(x – 4) = 0 M1oe<br />
x = 1 , x = 4 A2 (3)<br />
2<br />
(b)<br />
(c)<br />
dy<br />
dx<br />
= −4x<br />
+ 9 = 0 M2<br />
x = 9 4<br />
2<br />
d y<br />
4<br />
2<br />
dx = − < 0, therefore max. point 9 ,<br />
49<br />
4 8<br />
y<br />
A1<br />
( ) B1 A1 (5)<br />
–4<br />
O<br />
1<br />
2<br />
4<br />
x<br />
B2 (2)<br />
4 ⎛ −<br />
3 2<br />
2<br />
⎤<br />
(d) Area = ∫1<br />
( − 2x + 9x − 4)<br />
d x =<br />
2x<br />
+<br />
9x<br />
−<br />
⎝<br />
⎜<br />
4x<br />
3 2 ⎥<br />
M3<br />
2<br />
⎦ 1<br />
= 40 3<br />
4<br />
2<br />
23<br />
24<br />
+ = 14.29 units 2 (2 dp.) A2 (5)<br />
15<br />
© Oxford University Press 2008<br />
Core C2
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