Question 2 a) Solve the following system of equations simultaneously (10 marks)
2x + y - 3z = -1
6x - 2y + z = 17
-x - 2y - 2z = 0
b) Solve the equation, |3x + 5| = 5x + 4 (6 marks).
Question 3
a. Evaluate the following (12 marks)
i. 45 - (23 - 32)
ii. (45 - 23) - 32
iii. 32 x 15 + 32 x 24
iv. 32 x (15 + 24)
What conclusion can you give to the pairs of operations in (i) and (ii); (iii) and (iv)? (3 marks)
b. If the average of four consecutive even integers is 123, find the numbers (10 marks)
Question 4
a. If the two roots of a quadratic function, f(x), are -2 and 5, find the function, f(x) (5 marks)
b. Find the truth set of the quadratic equation, x^2 + 5x + 6 = 0 (8 marks)
c. If the function f(x) = 5x^2 - 10x - 15 is expressed in the form f(x) = a(x - h)^2 + k, find the values of a, h, and k (8 marks)
ii. Find the minimum point and the axis of the parabola (4 marks)
Question 5
a. Evaluate the following:
i. x^4 - 5x^3 + 9x^2 - 6x (3 marks)
ii. (7 marks)
b. Differentiate the function, y = 2x^6 + 7x^5 - 2x^3 - 5x + 4 (5 marks)
c. Given the function, y = x^2 + 2x, differentiate from the first principle