gce model questions vol1 2017 mathematics | Essay

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Question 1 View Details
A company manufactures widgets. In a particular week the number of widgets produced each day is given below: Monday: 1,235 Tuesday: 1,480 Wednesday: 1,350 Thursday: 1,415 Friday: 1,590 The total production for the week is the sum of these five days.
Question Parts
(a)
Write the total number of widgets produced in the week in standard form (a × 10ⁿ).
(b)
The company wants to package the weekly production into boxes each containing the same number of widgets, with no widgets left over. Determine the greatest possible number of widgets per box and the number of boxes required.
(c)
Express Monday's production as a percentage of the weekly total, rounded to one decimal place.
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Question 2 View Details
A school is planning a field trip. The total cost per student consists of a transport fee and an entry fee. The transport fee is three‑fifths of the total cost, while the entry fee is the remaining amount. The school has allocated a budget of ₦48,000 for the trip, which will cover exactly 28 students.
Question Parts
(a)
Determine the total cost per student in Naira, giving your answer as a decimal to two decimal places.
(b)
The entry fee per student is to be paid in advance. If the school decides to round the entry fee up to the nearest whole Naira, calculate the total amount that will be collected in advance and the amount of over‑payment that will need to be refunded.
(c)
After the trip, the school receives a 12 % discount on the transport fee from the transport company, applied to the total transport cost for all students. Calculate the amount saved by the school, to the nearest Naira.
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Question 3 View Details
A manufacturing company produces two products, A and B. The cost of producing one unit of product A is $2^{n}$, where $n$ is a positive integer. The cost of producing one unit of product B is $5^{,n-1}$. A batch consisting of 35 units of A and 16 units of B costs a total of $\$2,560$.
Question Parts
(a)
Determine the value of $n$.
(b)
Express the ratio of the square‑root of the cost of one unit of A to the square‑root of the cost of one unit of B in its simplest surd form.
(c)
If the selling price per unit of A is three times its cost and the selling price per unit of B is four times its cost, calculate the total profit obtained from the batch.
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Question 4 View Details
A school surveyed 200 students about their participation in three clubs: Mathematics (M), Physics (P) and Chemistry (C). The results are shown in the Venn diagram.
Question Parts
(a)
How many students are members of exactly two clubs?
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Question 5 View Details
Consider the algebraic expression E = \frac{2x^{3} - 6x^{2} - 8x + 24}{x^{2} - 4}, where x is a real number and x \neq \pm 2.
Question Parts
(a)
Simplify E completely.
(b)
Hence find the set of all real values of x for which E > 0.
(c)
Given that 0 < x \le 10, find the sum of all integer values of x that satisfy the inequality in part (b).
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Question 6 View Details
A school is planning a field trip. The total cost C (in naira) of the trip for n students is modelled by the linear equation C = 1200n + 15000, where the fixed cost of \(15\,000\) naira covers transportation and the variable cost of \(1200\) naira per student covers meals and entry fees.
Question Parts
(a)
If the school has a budget of 180 000 naira, what is the maximum number of students that can attend the trip?
(b)
The school decides to reduce the per‑student contribution by a constant amount k naira, keeping the total budget unchanged at 180 000 naira, so that the number of students can increase by 5. Determine the value of k (to the nearest naira).
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Question 7 View Details
A ball is thrown vertically upwards from ground level. Its height (in metres) after t seconds is given by h = -5t^2 + vt, where v is the initial speed in metres per second. The ball passes a window that is 12 m above the ground on its way up and again on its way down. The time interval between the two passages of the ball past the window is 3 seconds. Using this information, determine:
Question Parts
(a)
The quadratic equation that gives the times at which the ball is at a height of 12 m.
(b)
The value of the initial speed v (in m s⁻¹).
(c)
The two instants (in seconds) when the ball is at the height of 12 m.
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Question 8 View Details
Determine all real values of the parameter k for which the inequality 3x^2 – 12x + k > 0 holds for every real number x.
Question Parts
(a)
State the condition on the discriminant of the quadratic expression that guarantees the quadratic is always positive.
(b)
Find the range of k that satisfies the condition identified in part (a).
(c)
Verify your result by checking the inequality for a value of k within the obtained range and for a value outside the range.
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Question 9 View Details
A sequence {a_n} is defined by a_1 = 2 and for n \ge 1, a_{n+1} = 3a_n + 4.
Question Parts
(a)
Derive an explicit formula for a_n in terms of n.
(b)
Using the formula from part (a), find the sum of the first five terms of the sequence.
(c)
Determine the smallest integer n for which a_n exceeds 500.
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Question 10 View Details
The time T (in seconds) required for a group of workers to complete a fixed job varies directly as the square of the number of workers n and inversely as the efficiency e of each worker. The efficiency e varies inversely as the square root of the amount of training h (in hours) each worker receives.
Question Parts
(a)
Write the combined variation formula that relates T, n and h, and determine the constant of variation K using the data: when n = 5 workers, h = 4 hours, the time taken is T = 120 s.
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Question 11 View Details
The graph below shows the monthly revenue (in thousands of naira) of a small enterprise over a twelve‑month period.
Question Parts
(a)
Find the equation of the straight line that joins the points for month 3 and month 6.
(b)
Using the equation from part (a), estimate the month (to one decimal place) at which the revenue will reach 20 000 naira.
(c)
State the average rate of change of the revenue between month 1 and month 12.
(d)
Approximate the area under the revenue curve from month 1 to month 12 using the trapezium rule with the data points shown on the graph.
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Question 12 View Details
In the diagram, triangle ABC is drawn in a Cartesian plane. Vertex A is placed at the origin O and side AB lies along the positive x‑axis. ∠A = 40°, ∠B = 70° and AB = 8 cm.
Question Parts
(a)
Calculate the length of side BC. Give your answer correct to two decimal places.
(b)
Determine the coordinates of vertex C. Express each coordinate to two decimal places.
(c)
Find the equation of the line through B and C in the form y = mx + c. Give m and c correct to two decimal places.
(d)
Using the results above, calculate the area of triangle ABC. Give your answer to two decimal places.
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Question 13 View Details
In triangle ABC, ∠A = 40°, ∠B = 70° and side AB = 8 cm. Point D lies on side BC and divides it internally in the ratio BD : DC = 1 : 2.
Question Parts
(a)
Calculate the length of side BC.
(b)
Determine the length of side AC.
(c)
Find the lengths of BD and DC.
() Length of BD.
() Length of DC.
(d)
Calculate the area of triangle ABC.
(e)
Determine the length of the altitude from A to BC.
() Length of the altitude.
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