You're on a roll — here are the solutions to the problems: 50. If $f(x) = 2x^2 - 1$, then $f(3) = $ Step 1: Substitute $x=3$ into the function $f(x)$. $$ f(3) = 2(3)^2 - 1 $$ Step 2: Calculate the square. $$ f(3) = 2(9) - 1 $$ Step 3: Perform the multiplication. $$ f(3) = 18 - 1 $$ Step 4: Perform the subtraction. $$ f(3) = 17 $$ The correct option is (C). $$\boxed{\text{C) } 17}$$ 51. What is the gradient of the straight line $2y = -3x - 8$? Step 1: To find the gradient, rearrange the equation into the slope-intercept form $y = mx + c$, where $m$ is the gradient. $$ 2y = -3x - 8 $$ Step 2: Divide both sides of the equation by 2. $$ y = \frac{-3x}{2} - \frac{8}{2} $$ $$ y = -\frac{3}{2}x - 4 $$ The gradient $m$ is the coefficient of $x$. $$ m = -\frac{3}{2} $$ The correct option is (B). $$\boxed{\text{B) } -\frac{3}{2}}$$ 52. What is the measure of $\angle BAC$? Step 1: Analyze the construction description. "With centre A, an arc BC is drawn." This means that the distance from A to B is equal to the distance from A to C. So, $AB = AC$. "With centre B, and the same radius, the arc PCQ is drawn." This means the distance from B to A is equal to the distance from B to C. So, $BA = BC$. Step 2: Conclude the type of triangle. Since $AB = AC$ and $BA = BC$, it follows that $AB = AC = BC$. Therefore, triangle ABC is an equilateral triangle. Step 3: Determine the angle measure. In an equilateral triangle, all interior angles are equal to $60^\circ$. Thus, $\angle BAC = 60^\circ$. The correct option is (C). $$\boxed{\text{C) } 60^\circ}$$ 53. In the triangle, the value of $x$ is Step 1: Identify the properties of the triangle. The markings on two sides of the triangle indicate that it is an isosceles triangle, meaning those two sides are equal in length. Step 2: Apply the property of isosceles triangles. In an isosceles triangle, the angles opposite the equal sides are also equal. One of the base angles is given as $40^\circ$, so the other base angle must also be $40^\circ$. Step 3: Use the sum of angles in a triangle. The sum of the interior angles in any triangle is $180^\circ$. $$ x^\circ + 40^\circ + 40^\circ = 180^\circ $$ $$ x^\circ + 80^\circ = 180^\circ $$ Step 4: Solve for $x$. $$ x^\circ = 180^\circ - 80^\circ $$ $$ x^\circ = 100^\circ $$ The correct option is (C). $$\boxed{\text{C) } 100}$$ What's next?