bece model questions vol1 2017 mathematics | Essay

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Question 1 View Details
A number N is written as 342 in base 5. When N is expressed in base 10 it becomes a three‑digit integer.
Question Parts
(a)
Find the value of N in base 10.
(b)
State the sum of the digits of N (in base 10).
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Question 2 View Details
A school has 84 pupils who are to be arranged into equal teams for a sports competition. The number of teams formed is 7 more than the number of pupils in each team.
Question Parts
(a)
Determine the number of pupils in each team.
(b)
Find the total number of teams formed.
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Question 3 View Details
A school canteen sells two types of snack packs. Pack A contains 1/2 kg of peanuts and 1/3 kg of raisins. Pack B contains 1/3 kg of peanuts and 1/2 kg of raisins. The canteen wants to prepare a mixed snack pack that contains exactly 5/6 kg of peanuts and 5/6 kg of raisins by mixing only whole packs of type A and type B.
Question Parts
(a)
Let x be the number of Pack A and y be the number of Pack B required. Write a system of linear equations that represents the total amounts of peanuts and raisins needed.
(b)
Solve the system to find the whole‑number values of x and y. Show all reasoning steps.
(c)
Verify that the mixture obtained with the values of x and y satisfies the required amounts of peanuts and raisins.
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Question 4 View Details
A farmer records the daily yields (in tonnes) of his two fields over a week. Field X yields (tonnes): 1.25, 0.95, 1.10, 1.40, 0.85, 1.20, 1.05. Field Y yields (tonnes): 0.80, 1.15, 0.90, 1.30, 1.00, 0.75, 1.25.
Question Parts
(a)
Calculate the average daily yield for each field, showing all steps and keeping three decimal places in intermediate results.
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Question 5 View Details
A shop sells a particular fabric. The marked price per metre is unknown. The shop first gives a 20% discount on the marked price and then an additional 10% discount on the reduced price. After these two discounts a fixed overhead of ₦20 per metre is added. The final selling price per metre is ₦740. The shop reports that this selling price represents a profit of 25% on the cost price per metre.
Question Parts
(a)
Determine the cost price per metre of the fabric (in ₦).
(b)
Determine the original marked price per metre (in ₦).
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Question 6 View Details
A secondary school intends to allocate new textbooks to three of its classes – A, B and C. The numbers of books allocated to the classes are in the ratio 5 : 7 : 12. It is known that class B receives exactly 12 more books than class A. After the initial allocation, 20% of the books originally given to class A are transferred to class B because they are in better condition. No other changes are made.
Question Parts
(a)
Find the original number of books allocated to each class.
(b)
After the 20% transfer from class A to class B, state the new number of books in each class.
(c)
Show that, after the transfer, the combined total of books in classes A and B equals the number of books in class C.
(d)
State the total number of books that were originally allocated to the three classes together.
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Question 7 View Details
A water tank has a capacity of 1200 litres. Pipe A can fill the tank in 8 hours, while pipe B can fill it in 12 hours. Pipe C can empty the tank, and when opened together with pipe A the tank is filled in 10 hours. The tank is initially empty.
Question Parts
(a)
Find the rate at which pipe C empties the tank (in litres per hour).
(b)
If pipe A and pipe C are opened together from the empty tank, after how many hours will the tank be half full?
(c)
The tank is now half full. Pipe B is now opened together with pipe A and pipe C. How long will it take to fill the tank completely from this point?
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Question 8 View Details
A farmer wishes to estimate the length of the diagonal of a rectangular field whose length is 250 m and width is 150 m. Because he only has a ruler marked in centimetres and can read only to the nearest 0.5 cm, he decides to use approximation methods. Let the exact diagonal be D = √(250² + 150²) metres.
Question Parts
(a)
Using the linear approximation of f(x)=√x about x₀ = 250², find an estimated value of D.
(b)
Calculate the percentage error of this estimate compared with the exact diagonal (to two decimal places).
(c)
Using the binomial expansion √(1+u) ≈ 1 + u/2 – u²/8 for |u|<1, where u = (150²)/(250²), obtain a better approximation of D.
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Question 9 View Details
Two positive integers \(a\) and \(b\) satisfy the simultaneous conditions \[a^{2}\,b = 2592 \qquad\text{and}\qquad a\,b^{2} = 3888.\] Using the laws of indices, determine the values of \(a\) and \(b\). Then, using those values, find the numerical value of \(a^{3} b^{3}\).
Question Parts
(a)
Find the values of \(a\) and \(b\).
(b)
Using the values of \(a\) and \(b\) obtained in part (a), calculate \(a^{3} b^{3}\).
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Question 10 View Details
Consider the cubic algebraic expression \[E(x) = 2x^{3} - m x^{2} + n x - 12,\] where \(m\) and \(n\) are integers. It is known that \((x-2)\) and \((x+3)\) are factors of \(E(x)\).
Question Parts
(a)
Determine the values of \(m\) and \(n\).
(b)
Using the values of \(m\) and \(n\) found in part (a), find the remainder when \(E(x)\) is divided by \((x-1)\).
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