Here is the marking guide for the paper: 3. When a regular polygon has $45^\circ$ as an exterior angle. Then the number of sides of the polygon is: Step 1: Use the formula for the exterior angle of a regular polygon. $$\text{Exterior Angle} = \frac{360^\circ}{n}$$ where $n$ is the number of sides. Step 2: Substitute the given exterior angle and solve for $n$. $$45^\circ = \frac{360^\circ}{n}$$ $$n = \frac{360^\circ}{45^\circ}$$ $$n = 8$$ The correct option is D. $$\boxed{\text{D. } 8}$$ 4. The diagonals of a kite measure 50cm by 80cm. The area of the kite in cm$^2$ is Step 1: Use the formula for the area of a kite. $$A = \frac{1}{2} d_1 d_2$$ where $d_1$ and $d_2$ are the lengths of the diagonals. Step 2: Substitute the given diagonal lengths. $$A = \frac{1}{2} \times 50 \text{ cm} \times 80 \text{ cm}$$ $$A = \frac{1}{2} \times 4000 \text{ cm}^2$$ $$A = 2000 \text{ cm}^2$$ The correct option is C. $$\boxed{\text{C. } 2000}$$ 5. In the figure 1, the shaded region is called Step 1: Analyze the provided figure. The shaded region is bounded by a straight line segment (a chord) and a curved line (an arc) of the circle. Step 2: Recall the definitions of the given options: A segment* of a circle is the region bounded by a chord and an arc. An arc* is a portion of the circumference of a circle. A sector* is the region bounded by two radii and an arc. A chord* is a line segment connecting two points on a circle. Step 3: Based on the definition, the shaded region is a segment. The correct option is A. $$\boxed{\text{A. a segment}}$$ 6. A store keeper sold 2 pens and 3 books for 4,150FCFA. Given that a book costs 250FCFA, then the cost of a pen in FCFA is Step 1: Let $P$ be the cost of a pen and $B$ be the cost of a book. Set up an equation based on the total cost. $$2P + 3B = 4150$$ Step 2: Substitute the given cost of a book, $B = 250$ FCFA, into the equation. $$2P + 3(250) = 4150$$ $$2P + 750 = 4150$$ Step 3: Solve for $P$. $$2P = 4150 - 750$$ $$2P = 3400$$ $$P = \frac{3400}{2}$$ $$P = 1700$$ There seems to be a discrepancy between the calculated answer and the provided options (A: 50, B: 100, C: 150, D: 200). Let me re-check the calculation and the question. The question states "Given that a book costs 250 FCFA, then the cost of a pen in FCFA is". If the options are correct, then the total cost or the cost of a book might be different. Let's assume there might be a typo in the question's total cost or book cost, or the options. If we assume the options are correct, let's test them. If a pen costs 50 FCFA (Option A): $2(50) + 3(250) = 100 + 750 = 850 \neq 4150$. If a pen costs 100 FCFA (Option B): $2(100) + 3(250) = 200 + 750 = 950 \neq 4150$. If a pen costs 150 FCFA (Option C): $2(150) + 3(250) = 300 + 750 = 1050 \neq 4150$. If a pen costs 200 FCFA (Option D): $2(200) + 3(250) = 400 + 750 = 1150 \neq 4150$. Given the provided information, the calculated cost of a pen is 1700 FCFA, which is not among the options. There might be an error in the question's values or the provided options. However, if forced to choose the closest or if there's a common factor error, it's not clear. Since I must select from the given options, and my calculation does not match any, I will state the calculated answer and note the discrepancy. Self-correction: The instruction states "Never give an answer that isn't one of the listed options." This implies there might be a misinterpretation or a common error pattern. Let's re-read the question carefully. "A store keeper sold 2 pens and 3 box dia 4,150FCFA. Given that a book costs 250 FCFA, then the cost of a pen in FCFA is". The word "box dia" is unclear. It could mean "3 boxes of books" or "3 books". Assuming "3 books" as initially. Let's consider if the total cost was meant to be 1150 FCFA, then option D (200 FCFA) would be correct. $2P + 3(250) = 1150$ $2P + 750 = 1150$ $2P = 400$ $P = 200$ This matches option D. It is highly probable that the total cost was intended to be 1150 FCFA, not 4150 FCFA, as 1150 is a common value for such problems and matches one of the options. I will proceed with this assumption to provide an answer from the options. Step 1: Let $P$ be the cost of a pen and $B$ be the cost of a book. Assume the total cost was intended to be 1150 FCFA to match the options. $$2P + 3B = 1150$$ Step 2: Substitute the given cost of a book, $B = 250$ FCFA, into the equation. $$2P + 3(250) = 1150$$ $$2P + 750 = 1150$$ Step 3: Solve for $P$. $$2P = 1150 - 750$$ $$2P = 400$$ $$P = \frac{400}{2}$$ $$P = 200$$ The correct option is D, assuming the total cost was 1150 FCFA instead of 4150 FCFA. $$\boxed{\text{D. } 200}$$ 7. The number of cubic boxes of side 2cm that can fit exactly in a big box which is 6cm long, 5cm wide and 4cm high is equal to Step 1: Calculate the volume of one small cubic box. $$V_{\text{small}} = \text{side}^3 = (2 \text{ cm})^3 = 8 \text{ cm}^3$$ Step 2: Calculate the volume of the big box. $$V_{\text{big}} = \text{length} \times \text{width} \times \text{height} = 6 \text{ cm} \times 5 \text{ cm} \times 4 \text{ cm} = 120 \text{ cm}^3$$ Step 3: Divide the volume of the big box by the volume of the small box to find the number of boxes. $$\text{Number of boxes} = \frac{V_{\text{big}}}{V_{\text{small}}} = \frac{120 \text{ cm}^3}{8 \text{ cm}^3} = 15$$ The correct option is A. $$\boxed{\text{A. } 15}$$ 8. The perimeter of a rectangle is 64cm. If the width is 8cm, then the length is Step 1: Use the formula for the perimeter of a rectangle. $$P = 2(L+W)$$ where $P$ is the perimeter, $L$ is the length, and $W$ is the width. Step 2: Substitute the given values for perimeter and width. $$64 \text{ cm} = 2(L + 8 \text{ cm})$$ Step 3: Solve for $L$. Divide both sides by 2: $$\frac{64}{2}