Mathematics Mock Examination 2022

Solve the equation: $x^2 - 4x + 4 = 0$ (04 marks)

Given that $tan(θ) = 1$ and that $180° ≤ θ ≤ 360°$, without using a calculator or mathematical tables, find the value of $sin(θ) - cos(θ)$. (04 marks)

A woman has children whose ages in years are 2, 4, 6, 6, 8, 13, 17, 20, and 23. Determine the (i) median age of the children (ii) mean age of the children (04 marks)

Find the values of $x$ and $y$ in $3x + 2y = 10$ and $2x + 3y = 7$ (04 marks)

A basket contains 6 mangoes and 4 tomatoes. If two fruits are selected at random without replacement, find the probability that the two fruits selected are mangoes. (04 marks)

Given that $a * b = a + b + ab$ (i) Evaluate $3 * 5$ (ii) Find if $7 * a = 23$ (04 marks)

An object at $(0, 0)$ undergoes a translation $(x, y) = (x + 5, y - 12)$, then followed by translation $(x, y) = (x + 3, y + 6)$. (i) Find a single translation equivalent to the two translations. (ii) How far is the object from $(0, 0)$? (04 marks)

Factorise; $4x^2 - 5x - 6$, and hence solve $4x^2 - 5x - 6 = 0$. (04 marks)

Solve the inequality: $\frac{2x}{3} - \frac{5}{2} < 3$ (04 marks)

Form a quadratic equation in terms of $x$ for the roots 3 and 2. (04 marks)