bece model questions vol1 2021 mathematics | Essay

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Question 1 View Details
The number is written in words as “seven million five hundred two thousand thirty‑six”.
Question Parts
(a)
Write the number in standard form (digits).
(b)
State the value of the digit in the thousands place.
(c)
Round the number to the nearest ten thousand.
(d)
Express the number in scientific notation correct to three significant figures.
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Question 2 View Details
A certain number of beads is to be shared equally among 3, 4 and 5 friends. In each case there are 2 beads left over.
Question Parts
(a)
Find the smallest possible number of beads that is greater than 50 and satisfies the condition.
(b)
If the beads are arranged in rows of 6, how many beads will be left over?
(c)
If the beads are packed in boxes each containing 12 beads, determine the number of full boxes that can be made and the number of beads left over.
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Question 3 View Details
The diagram shows a solid formed by a right circular cylinder of radius r metres and height h_c metres, surmounted by a right circular cone of the same radius r and height h_k metres. The solid rests on a horizontal plane; the base of the cylinder is in contact with the ground and is not to be painted. The following data are given: - The total height of the solid (cylinder plus cone) is 12 m. - The ratio of the radius to the height of the cylinder is 1 : 3. - The ratio of the volume of the cone to the volume of the cylinder is 1 : 2. Using this information, answer the questions that follow.
Question Parts
(a)
Determine the numerical values of the radius r, the height of the cylinder h_c and the height of the cone h_k (in metres).
(b)
Calculate the total external surface area of the solid, including the curved surface of the cylinder, the curved surface of the cone and the circular top of the cone, but excluding the base of the cylinder. Give your answer to two decimal places (m²).
(c)
If the solid is to be painted at a cost of ₦250 per square metre, find the total painting cost. State your answer in naira, rounded to the nearest naira.
(d)
The solid is to be made from a material that costs ₦1,500 per cubic metre. Using the total volume of the solid, determine the material cost, rounded to the nearest naira.
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Question 4 View Details
A stationery shop sells two types of pens. - Type A costs ₦125.50 each. - Type B costs ₦89.75 each. A student buys a total of 23 pens and spends exactly ₦2,529.00. Answer the following:
Question Parts
(a)
Determine how many pens of each type were purchased.
(b)
Calculate the average cost per pen (to the nearest kobo).
(c)
Find the percentage of the total amount that was spent on Type A pens and on Type B pens (give each percentage to one decimal place).
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Question 5 View Details
A secondary school purchased 12 identical computers. The total amount paid was ₦1,800,000. The price paid includes a discount of 12% on the list price and a sales tax of 5% that was applied after the discount. Using this information, answer the following.
Question Parts
(a)
Determine the list price of one computer (to the nearest naira).
(b)
What is the percentage increase from the discounted price (before tax) to the final price per computer?
(c)
Express the amount of tax paid per computer as a percentage of the list price (to one decimal place).
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Question 6 View Details
A drink vendor prepares a fruit drink using water and concentrate in the ratio 4:1 by volume. The vendor wishes to produce a total of 45 litres of the drink and also wants to add a flavouring that must constitute 8% of the final volume. Answer the following questions.
Question Parts
(a)
Calculate the volumes (in litres) of water, concentrate and flavouring required.
(b)
The concentrate is sold only in containers of 3 L. Determine the number of containers the vendor must purchase and the amount of concentrate left over after filling the required 8.28 L.
(c)
Express the ratio of water to the total non‑water components (concentrate + flavouring) in its simplest whole‑number form.
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Question 7 View Details
A rectangular water tank can be filled by two inlet pipes, A and B. Pipe A can fill the tank in 6 hours when operating alone, while pipe B can fill it in 8 hours when operating alone. The tank, however, has a small leak that empties water at a constant rate of one‑twelfth (\(\frac{1}{12}\)) of the tank per hour. Both pipes are opened together while the leak remains open.
Question Parts
(a)
Calculate the total time, in hours, required to fill the tank completely when both pipes and the leak are operating together.
(b)
After the tank becomes full, the leak is closed but pipe B is switched off while pipe A continues to operate. How long will it take for pipe A alone to empty the full tank through the leak?
(c)
Explain, in a short paragraph, how the presence of the leak influences the overall efficiency of using both pipes together compared with using pipe A alone.
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Question 8 View Details
The binomial approximation \((1+x)^n \approx 1+nx\) is useful when \(|x|\) is small. Consider the expression \((1.03)^4\).
Question Parts
(a)
Using the linear (first‑order) binomial approximation, estimate the value of \((1.03)^4\).
(b)
Obtain a more accurate estimate by expanding \((1+0.03)^4\) using the binomial theorem up to the \(x^2\) term and ignoring higher‑order terms.
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Question 9 View Details
Consider the algebraic expression E = \frac{(2x^{3}y^{-2})^{2}\;\times\;(x^{-1}y^{5})}{4x^{k}y^{m}}. It is known that after simplifying, the value of E is exactly 1 for all non‑zero real numbers x and y. Answer the following:
Question Parts
(a)
Using the laws of indices, simplify the numerator of E and write the simplified form of E in terms of x, y, k and m.
(b)
Since E = 1 for all admissible x and y, determine the integer values of k and m.
(c)
Verify the result by evaluating the original (unsimplified) expression for x = 2 and y = 3 using the values of k and m you have found. Show that the value obtained is indeed 1.
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Question 10 View Details
Let F(x) = (x^{2} + a x + 9)(x - 3) - (x^{3} - 27). The expression F(x) is required to be a constant (i.e., independent of x). Answer the following:
Question Parts
(a)
Expand F(x) fully and collect like terms in powers of x.
(b)
Determine the value of the constant a for which F(x) is independent of x.
(c)
With the value of a found in part (b), state the constant value of F(x).
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