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Question 11:

The first and third terms of a geometric series are 9 and 1. The sum of the first five terms is...

Let the first term be $a$ and the common ratio be $r$. The general form of a geometric sequence is: $a, ar, ar^2, ar^3, \dots$ Given that the first term $a = 9$ and the third term $ar^2 = 1$, we can find $r$: $9r^2 = 1 \quad \Rightarrow \quad r^2 = \frac{1}{9} \quad \Rightarrow \quad r = \frac{1}{3}$

Now, we can use the sum formula for a geometric series: $S_n = a \frac{1 - r^n}{1 - r}$ For the first five terms: $S_5 = 9 \frac{1 - \left( \frac{1}{3} \right)^5}{1 - \frac{1}{3}} = 9 \frac{1 - \frac{1}{243}}{\frac{2}{3}} = 9 \times \frac{242}{243} \times \frac{3}{2} = \frac{3267}{243} = 13.45$

So, the closest answer is (A) $13 \frac{4}{9}$.

Question 12:

The diagram shows an isosceles trapezoid ABCD. The coordinates of point $C$ are asked in terms of $p$ and $q$, where the value of $p + 2q$ is sought.

For this question, you would typically need more details, like a clearer view of the trapezoid and any related points or coordinates.

Question 13:

The graph represents a line $k$, and you are asked to find $g(10)$, where the line represents the function $g$.

The line crosses the x-axis at $x = 0$ and appears to have a negative slope. The exact equation of the line would depend on its slope and intercepts, but without clear markings on the graph, it's hard to give an exact answer. If additional information is provided, such as the slope or intercepts, we could calculate $g(10)$.

Question 14:

Calculate the shaded area in the diagram.

The diagram shows a shaded parallelogram on a grid. The formula for the area of a parallelogram is: $\text{Area} = \text{base} \times \text{height}$ From the grid, the base and height can be visually estimated. The closest area value appears to be (B) 8.

Question 15:

Identify the coordinates on the line $k$.

You are asked to find which of the given coordinates lies on line $k$. By inspecting the graph, it's likely that the point is (B) (-1, 5), though verifying this requires knowing the equation of the line.

Would you like further explanations or details on any specific part? Here are some follow-up questions:

1. How do we determine the common ratio in a geometric progression from two terms?
2. What is the sum formula for a geometric series, and how is it applied to different values of $n$?
3. How can the coordinates of a point in a trapezoid be determined using geometric properties?
4. How do you calculate the area of a parallelogram when given base and height?
5. What is the method for determining the equation of a line from a graph?

Tip: In geometric series, finding the ratio between terms helps quickly solve for unknowns like the sum or a specific term in the series.