Full Grade 9 test

The quadratic trinomial x² − sx + p can be factorised into two factors:

(x − a)(x − b).

Find two numbers a and b that satisfy both conditions:

• their sum equals s: a + b = s;
• their product equals p: a · b = p.

First list the factor pairs of p, then select the pair whose sum equals s.

You can check the result by expanding the brackets: (x − a)(x − b) = x² − (a + b)x + ab.

At x = 0, all terms containing x vanish, so the y-intercept value is the constant term. In a linear cost formula it is the fixed fee; total cost = fixed fee + unit price × quantity. For a quadratic, the intercept is (0, c).

Substitute the given nonzero x. Calculate the full numerator ax + b first, then divide by x. Parentheses mean the entire sum is divided by x.

A central angle equals its intercepted arc measure in degrees. An inscribed angle over the same arc is half the central angle.

Find m and n whose sum is the x coefficient and whose product is the constant. Then x² + (m + n)x + mn = (x + m)(x + n). Check by expanding.

tan α = opposite leg / adjacent leg. Tangent relates both legs directly without using the hypotenuse. Use inverse tangent to find the angle.

A central angle intercepting the same arc as an inscribed angle is twice as large:

central angle = 2 · inscribed angle.

Multiply the given inscribed angle by 2. The resulting angle cannot exceed 360°.

Recall the special-angle values: sin 30° = 1/2, cos 60° = 1/2 and tan 45° = 1. Select the matching identity.