2026 COMPREHENSIVE EXAM SCRIPT FULL
QUESTIONS AND CORRECT ANSWERS
◉ Negative and Fractional indices. Answer: a^1/m = m√a
a^n/m = m√aⁿ
a^-n = 1/aⁿ
◉ Multiplying surds. Answer: √a x √b = √ab
◉ Dividing surds. Answer: √a ÷ √b = √a/b
◉ Rationalising denominators with surds. Answer: 1/√a x √a/√a
1/a+√b x a-√b/a-√b
◉ What is the form of a quadratic equation?. Answer: ax² + bx + c = 0
where a, b and c are real constants and a≠0
, ◉ What is the quadratic formula?. Answer: x = (-b±√b²-4ac)/2a
◉ completing the square. Answer: x² + bx = (x+b/2)² - (b/2)²
ax² + bx + c = a(x + b/2a)² + (c - b²/4a²)
◉ The discriminant. Answer: b²−4ac > 0 two real, distinct roots.
b²−4ac = 0 one repeated root.
b²−4ac < 0 no real roots.
◉ Gradient of a straight line. Answer: m = y₁ - y / x₁ - x
◉ Equation of a straight line. Answer: y = mx + c
OR
ax + by + c = 0
◉ Equation of a line using two known points.. Answer: y - y₁ = m(x -
x₁)
where m = gradient and (x₁,y₁) are the coordinates used.