c1 sample paper


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C1 sample exam paper
. The paper is 1 hour 30 minutes long.
. Calculators maynot
Calculators may be be
1 2 p
1. Express p in the form a b 2: (4 marks)
3À 2
2. (a) Solve the inequality 5(y 2) 5 3 À 7(2 À y) (3 marks)
(b) Solve the inequality (x À 4)(x À 6) < 0 (2 marks)
3. The curve C has equation y 2x 3 À x 2 . The points A and B both lie on the
curve C having coordinates (1, 1) and (2, 12) respectively.
(a) Show that the gradient of C at B is 5 times the gradient of C at A. (5 marks)
(b) Find an equation for the tangent to C at B. (3 marks)
4. The points A(À4, À2), B(6, 4) and C(4, À4) are the vertices of triangle ABC.
Point D is the mid point of AB.
(a) Find an equation for the line passing through A and B in the form
ax by c 0, where a, b and c are integers to be found. (4 marks)
(b) Show that CD is parallel to the line with equation 10x 6y 7 0. (4 marks)
5. xm ym
(y 1) m
The diagram represents the floor plan of an attic room which consists of a
square of side x m and a right-angled triangle of sides x m, y m and (y 1) m.
The perimeter of the room is 10 m.
(a) Show that 3x 2y 9. (2 marks)
The area of the floor is 5.5 m2 .
11 À 2x 2
(b) Show that y (4 marks)
(c) Using parts (a) and (b) find the value of x and the value of y. (5 marks)
AS Core for AQA # Pearson Education Ltd. 2004 1

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C1 Sample exam paper
6. y
In the figure the coordinates of points A, B and C are (5, 5), (8, 5) and (5, 1)
(a) Show that AB 2 AC 2 BC 2 . (2 marks)
A circle is drawn which passes through the points A, B and C.
(b) Find the coordinates of the centre of the circle and the radius
of the circle. (2 marks)
(c) Write down an equation of the circle.…read more

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C1 Sample exam paper
8. y
1 O 2 3
The diagram shows part of the curve C with equation y x 3 À 4x 2 x 6. The
points A and B are stationary points on the curve. The curve C crosses the x-
axis at À1, 2 and 3.
(a) Find .…read more


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