Question 1 

A conic with equation

ax² + by² = c

has two focus points, where a = 9, b = 27 and c = 51. One of those focus points has a positive x-coordinate. To two decimal places, what is the value of that positive x-coordinate?

Question 2 

What is the value of the Fibonacci number F_n, where n = 35?

Question 3

A conic has equation

ax² + by² = c

where a = 6, b = -17 and c = 33.

To two decimal places what is the gradient of the asymptote that has a positive gradient?

Question 4

Suppose a second-order difference equation is of the form ay_n+2 + by_n+1 + Cy_n = d

where a = 2, b = 2, c = 13 and d = 14

In radians and to two decimal places, what is the value of

θ

in the complementary function?

Question 5

A conic M, in standard or reflected standard form, is rotated through an angle r about the origin to obtain the conic N with equation ax2 bxy

ax² + bxy² + cy² = d

cy² = d

where a= 12, b = 4, c = 49 and d = 35.

To two decimal places, what is the absolute value of the angle r in degrees? As usual, do not give any units in your answer. Do not include a minus sign in your answer.

Question 6

To two decimal places, what is the value of the eccentricity of the conic with equation

ax² + by² = c

where a = 6, b= 30 and c = 36?

Question 7

A sequence Ln is such that L₁ = 0.2, L₂ = al and

L_n = 2L_n-1 - 1.5L_n-2 (n≥ 3).

Use Mathcad to determine the value of L₄₃, giving your answer to 2 decimal places.

Question 8

If you rationalise the denominator in the expression

1/a√(b-c)

where a = 72, b = 150 and c = 22, and you do not simplify your answer (i.a do not divide top and bottom by some number), then what is the absolute value of the new denominator? There should not be a negative sign in your answer.

Question 9

To two decimal places, what is the value of the eccentricity of the conic with equation

ax² + y² = c

where a = 10 b =-13 and c = 63?