00 CORE 1 MOCK TO June 10

C1 MOCK PAPER

1. Solve the inequality .
(3)

2. Find .
(4)
3. Find the value of (a) , (b) , (c) .
(1) (2) (1)

4. A sequence is defined by , where k is a constant.

(a) Write down an expression for a2 in terms of k.
(1)
(b) Find a3 in terms of k, simplifying your answer.
(2)
Given that a3 = 13, (c) find the value of k.
(2)

5. (a) Show that eliminating y from the equations 2x + y = 8, 3x2 + xy = 1 produces the equation x2 + 8x - 1 = 0. (2)

(b) Hence solve the simultaneous equations 2x + y = 8, 3x2 + xy = 1

giving your answers in the form a + bÖ17, where a and b are integers. (5)

6. .
(a) Show that f(x) can be written in the form ,

stating the values of the constants P, Q and R . (3) (b) Find f ¢(x). (3) (c) Show that the tangent to the curve with equation y = f(x) at the point where x = 1 is parallel to the line with equation 2y = 11x + 3. (3)

7. (a) Factorise completely x3 - 4x. (3) (b) Sketch the curve with equation y = x3 - 4x, showing the coordinates of the points where the curve crosses the x-axis.
(3)
(c) On a separate diagram, sketch the curve with equation y = (x - 1)3 - 4(x - 1),

showing the coordinates of the points where the curve crosses the x-axis. (3)

8. The straight line l1 has equation y = 3x - 6.

The straight line l2 is perpendicular to l1 and passes through the point (6, 2).

(a) Find an equation for l2 in the form y = mx +c, where m and c are constants. (3) The lines l1 and l2 intersect at the point C.

(b) Use algebra to find the coordinates of C. (3) The lines l1 and l2 cross the x-axis at the points A and B respectively.

(c) Calculate the exact area of triangle ABC. (4)

9. An arithmetic series has first term a and common difference d. (a) Prove that the sum of the first n terms of the series is n[2a + (n