Algebra

For independent events, the probability of their intersection is the product of their individual probabilities, calculated as 0.4 * 0.5 = 0.2. Option D is incorrect because 0.9 is the sum of the probabilities, which represents the union of mutually exclusive events rather than their intersection.

The word 'MATH' consists of four unique letters, meaning the number of unique permutations is 4 factorial, which equals 24. Option A is incorrect because 12 only accounts for arranging two of the letters, while option B incorrectly assumes a power of two rather than a factorial calculation.

According to Vieta's formulas, the sum of the roots of a quadratic equation is given by -b/a. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Many students confuse the sum of the roots with the product of the roots, which is given by c/a, or they incorrectly apply the formula by not considering the sign of the coefficients.
• !Option B is incorrect because 6 represents the product of the roots, given by c/a, rather than their sum.
• !Option A is incorrect because 12 only accounts for arranging two of the letters, while option B incorrectly assumes a power of two rather than a factorial calculation.
• !Option A is incorrect because it only represents the upper bound, incorrectly allowing negative values like -10 which do not satisfy the original inequality.
• !Option D is incorrect because 0.9 is the sum of the probabilities, which represents the union of mutually exclusive events rather than their intersection.

Answer each from memory — you'll see instantly whether you're right and why.

Run a focused 10-question mini-mock on Algebra and see it stick.