bece model questions vol1 2019 mathematics | Essay

Prepare for your exams with bece model questions vol1 questions? Reviewing past/model questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2019 mathematics (Essay) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1 View Details
A five‑digit integer N satisfies the following conditions: (i) The digit in the thousands place is twice the digit in the hundreds place. (ii) The sum of all its digits is 27. (iii) When N is divided by 9, the remainder is equal to the digit in the units place. (iv) The digit in the ten‑thousands place is the greatest digit among all the digits of N. Answer the following questions.
Question Parts
(a)
Determine the value of N.
(b)
State the remainder when N is divided by 11.
(c)
Write N in the form 1000 k + r, where 0 ≤ r < 1000. Give the values of k and r.
Detailed Essay Solution & Marking Scheme Available

Get the step-by-step mathematical proofs, key points required by examiners, and a comprehensive breakdown from our AI Tutor.

Reveal Answer
Question 2 View Details
A school has 240 students who are to be placed into equal groups for a competition. The groups must satisfy the following conditions: 1. Each group must contain more than 10 but fewer than 30 students. 2. The number of groups formed must be a whole number. 3. The number of groups must also be a divisor of 180. Answer the questions that follow.
Question Parts
(a)
List all possible numbers of students that a group can contain.
Detailed Essay Solution & Marking Scheme Available

Get the step-by-step mathematical proofs, key points required by examiners, and a comprehensive breakdown from our AI Tutor.

Reveal Answer
Question 3 View Details
A rectangular garden is to be planted with two different vegetables. The length of the garden is 3 1/2 metres and the width is 2 2/3 metres. The gardener wants to allocate the garden into two sections such that the area of the first section is \(\frac{3}{5}\) of the total area and the second section occupies the remaining area. The first section will be used for carrots and the second for lettuce. Carrot seeds are required at a rate of 1 1/4 kg per square metre, while lettuce seeds are required at a rate of 0.8 kg per square metre. Determine:
Question Parts
(a)
The total area of the garden in square metres, expressed as an improper fraction reduced to lowest terms.
(b)
The amount of carrot seeds and lettuce seeds required, each expressed as a mixed number in kilograms.
Detailed Essay Solution & Marking Scheme Available

Get the step-by-step mathematical proofs, key points required by examiners, and a comprehensive breakdown from our AI Tutor.

Reveal Answer
Question 4 View Details
A school is purchasing textbooks. The cost of a textbook is ₦2,350.75. The school receives a bulk discount of 12.5 % on the total purchase if it buys at least 40 textbooks. After the discount, a value‑added tax (VAT) of 5 % is applied to the discounted total. The school has a budget of ₦100,000. Determine:
Question Parts
(a)
The maximum number of textbooks the school can buy without exceeding the budget, assuming it must purchase at least the minimum quantity for the discount.
(b)
The total amount payable (including VAT) for that number of textbooks, expressed to the nearest kobo.
Detailed Essay Solution & Marking Scheme Available

Get the step-by-step mathematical proofs, key points required by examiners, and a comprehensive breakdown from our AI Tutor.

Reveal Answer
Question 5 View Details
A digital watch is sold at a price that includes a 5% sales tax. The final price paid by the customer is ₦12,500. The shopkeeper marks the watch up by a profit that is 25% of the cost price before tax is added.
Question Parts
(a)
Calculate the cost price of the watch.
(b)
Determine the amount of profit earned by the shopkeeper.
(c)
Find the amount of sales tax that was added.
(d)
If the sales tax were increased to 8% while the shopkeeper kept the same profit percentage (25% of cost), what would be the new selling price (including tax)?
Detailed Essay Solution & Marking Scheme Available

Get the step-by-step mathematical proofs, key points required by examiners, and a comprehensive breakdown from our AI Tutor.

Reveal Answer
Question 6 View Details
A farmer has 40 L of a fertilizer mixture that contains 15% nitrogen. He wishes to increase the nitrogen concentration to 20% by adding a second fertilizer that contains 35% nitrogen. After achieving the desired concentration, he will divide the mixture into two equal parts. One of the parts will then be diluted with water (0% nitrogen) so that its nitrogen concentration becomes 12%.
Question Parts
(a)
How many litres of the 35% nitrogen fertilizer must be added to obtain a 20% nitrogen mixture?
(b)
State the volume of each of the two equal parts after the addition.
(c)
How many litres of water must be added to one part so that its nitrogen concentration becomes 12%?
(d)
Give the final volume of the diluted part after the water has been added.
Detailed Essay Solution & Marking Scheme Available

Get the step-by-step mathematical proofs, key points required by examiners, and a comprehensive breakdown from our AI Tutor.

Reveal Answer
Question 7 View Details
A rectangular water tank can hold 1200 litres of water. Pipe P₁ can fill the tank in 8 hours, while pipe P₂ can fill it in 12 hours. Because of a restriction, pipe P₁ is opened alone for the first 3 hours, after which both pipes are opened together until the tank is full.
Question Parts
(a)
Write an expression for the volume of water supplied by pipe P₁ during the first 3 hours and evaluate it.
(b)
Determine the additional time required after the first 3 hours for the tank to become full.
(c)
If, after the tank is full, the water is emptied by a drain that removes water at 30 L per minute, calculate the total time required to empty the tank completely. Express your answer in hours and minutes.
Detailed Essay Solution & Marking Scheme Available

Get the step-by-step mathematical proofs, key points required by examiners, and a comprehensive breakdown from our AI Tutor.

Reveal Answer
Question 8 View Details
A small business intends to increase its monthly production by 3 % each month. The current monthly output is 5 000 units.
Question Parts
(a)
Using the binomial approximation (1 + x)ⁿ ≈ 1 + nx for small x, estimate the production after 5 months. Show the steps of your calculation.
(b)
The exact production after 5 months is given by (1.03)⁵ × 5 000. Calculate the exact value (to the nearest unit) and determine the absolute error of the approximation obtained in part (a).
Detailed Essay Solution & Marking Scheme Available

Get the step-by-step mathematical proofs, key points required by examiners, and a comprehensive breakdown from our AI Tutor.

Reveal Answer
Question 9 View Details
Consider the expression E = \frac{2^{x}\,\cdot\,5^{2x}}{10^{\,x-2}}. Answer the following questions.
Question Parts
(a)
Simplify E so that it is expressed as a single power of 2 multiplied by a single power of 5.
(b)
It is given that E = 12 500. Using your result from part (a), determine the value of x.
(c)
Using the value of x found in part (b), evaluate F = 8^{\,x-2}\;\cdot\;25^{\,1-x}.
Detailed Essay Solution & Marking Scheme Available

Get the step-by-step mathematical proofs, key points required by examiners, and a comprehensive breakdown from our AI Tutor.

Reveal Answer
Question 10 View Details
Let P(x)=ax^{2}+bx+c be a quadratic expression. It is known that: - When P(x) is divided by (x-1) the remainder is 5. - When P(x) is divided by (x+2) the remainder is -3. - P(0)=7. Answer the following questions.
Question Parts
(a)
Determine the exact values of the coefficients a, b and c.
Detailed Essay Solution & Marking Scheme Available

Get the step-by-step mathematical proofs, key points required by examiners, and a comprehensive breakdown from our AI Tutor.

Reveal Answer

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub:
Chat with Support