The composite transformation qanbspo qbnbspcan be expressed

Question

Question 1

The composite transformation q_a O q_b can be expressed as the single transformation r_c, where a = 0.1, b = 1.9 and

0≤ c ≤ 2Π

To 2 decimal places, what is the value of c?

Question 2

f(x) = x² + bx + c, where b = -28 and c = 36. What is the coefficient of x² in the function f(f(x)).?

Question 3

f(x) = ax² + bx + c, where a = -25, b = 12 and c = 14. What is the gradient of the point, with x coordinate 19, on the graph of y = f(x)?

Question 4

To 2 decimal places, what is the coefficient of x⁸ in the expansion of

(ax³ + b/x)⁸

where a = 3.2 and b = 1.5?

Question 5

The composite transformation q_{a O} r_b can be expressed as the single transformation q_c where a = 0.8. b = 5.1 and 0 ≤ c < Π

To 2 decimal places, what is the value of c?

Question 6

f and g are linear transformations. The matrices for f and g are respectively

where a = -8, b = 4, c = 5, d = -8, m - 7, n = -7, p = -2 and q = 9.

What is the lower-left entry in the matrix that represents the composite transformation g o f?

Question 7

What is the area of the triangle with vertices at (a, h), (c, d) and (m, n) if

a = 7,b= -8, c = -13, d = 3, m = 17, and n = 11?

As usual, your answer should be a number only (with no units).

Question 8

f(x) = ax² + bx + c, where a = 6, h = -25 and c = -15. There are two fixed points at x₁ and x₂, where x₁ > x₂. To two decimal places what is the value of x₁?

Question 9

f(x) = ax³+ (b - ad)x² + (c - bd)x - cd, where a = 27, b = -11, c = 25 and d = 12.

What value of x satisfies the equation f(x) = 0?

Question 10

The composite of three translations given by

t_a, O t_c,d O t_h,k

is equivalent to the single translation t_m,n.

What is the value of m if a = -19, b = 12, c = 16, d = -10, h = -6 arid k = -4 ?