bece model questions vol1 2020 mathematics | Essay

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Question 1 View Details
A school library wants to arrange its books in rows of equal length. If each row contains 12 books, the total number of books leaves a remainder of 9 when the books are arranged in rows of 15. Determine the smallest possible total number of books. Then state the remainder when this total is divided by 9.
Question Parts
(a)
Find the smallest total number of books that satisfies the two conditions.
(b)
State the remainder when the total found in part (a) is divided by 9.
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Question 2 View Details
A farmer plants three different crops – A, B and C – in separate fields. The total number of trees planted is 210. The number of trees of crop A is twice the number of trees of crop B. The number of trees of crop C is 30 fewer than the number of trees of crop A. Determine the number of trees of each crop. Then find the highest common factor (HCF) of the three numbers and the least common multiple (LCM) of the three numbers.
Question Parts
(a)
Find the number of trees of crops A, B and C.
(b)
Determine the highest common factor (HCF) of the three numbers obtained in part (a).
(c)
Determine the least common multiple (LCM) of the three numbers obtained in part (a).
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Question 3 View Details
A bakery uses two types of flour to make a special bread. Type A flour contains \(\frac{1}{3}\) kg of protein per kilogram of flour, while type B flour contains \(\frac{1}{5}\) kg of protein per kilogram. The baker wants to produce 12 kg of a flour mixture that contains exactly 0.28 kg of protein per kilogram. Determine how many kilograms of each type of flour must be used.
Question Parts
(a)
Set up the linear equation(s) that represent the condition on the protein content of the mixture.
(b)
Solve the equations to find the quantities of type A and type B flour required.
(c)
Verify that the mixture obtained indeed contains 0.28 kg of protein per kilogram of mixture.
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Question 4 View Details
A shopkeeper bought a batch of 250 metres of fabric at a total cost of ₦45,000. He sold part of the fabric at a profit of 20 % on cost and the remaining part at a loss of 10 % on cost. If the total revenue from the whole batch was ₦48,600, determine how many metres were sold at a profit and how many at a loss, and state the overall percentage gain or loss on the whole batch.
Question Parts
(a)
Let \(x\) metres be the amount sold at a profit. Write expressions for the cost and selling price of the profit portion and the loss portion.
(b)
Formulate and solve the equation to find \(x\), the metres sold at a profit.
(c)
State the quantities sold at profit and at loss, and compute the overall percentage gain or loss on the whole batch.
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Question 5 View Details
A school canteen sells a pack of 12 biscuits. The shopkeeper first gives a discount of 15 % on the marked price and then adds a sales tax of 5 % on the discounted price. A student buys the pack and pays ₦540. The shopkeeper’s cost price for the pack is ₦400.
Question Parts
(a)
Determine the marked price of the pack.
(b)
Calculate the profit earned by the shopkeeper on this sale.
(c)
If the shopkeeper wants to achieve a profit margin of 25 % on the cost price after giving the same discount and tax, what should be the new marked price? (Assume the discount and tax rates remain 15 % and 5 % respectively.)
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Question 6 View Details
A recipe for fruit juice requires water and concentrate in the ratio 3 : 2 by volume. To make a large batch, a vendor mixes 45 L of water with the concentrate. However, due to a mistake, only 30 L of water were added while the amount of concentrate remained the same.
Question Parts
(a)
Find the total volume of the intended large batch (i.e., the volume that would have been obtained if the correct ratio had been used).
(b)
Determine the percentage by which the actual mixture (30 L water and 30 L concentrate) is more concentrated than the intended mixture.
(c)
To correct the mixture without discarding any concentrate, how much additional water must be added?
(d)
If the vendor wants to prepare a batch that is 20 % more concentrated than the intended mixture, what should be the new ratio of water to concentrate (expressed in the simplest whole numbers)?
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Question 7 View Details
A solid is formed as follows: a right circular cylinder of radius 6 cm and height 12 cm has a right circular cone of the same base radius and height 8 cm removed from its top, creating a conical cavity. A solid hemisphere of radius 4 cm is fixed on the top of the cylinder, covering the circular opening. All dimensions are shown in the diagram.
Question Parts
(a)
Calculate the total volume of the solid (in cm³).
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Question 8 View Details
A tree casts a shadow that is 12.5 metres long. The angle of elevation of the sun is measured with a clinometer that only gives readings at 30° and 35°. The recorded reading is 33°, which must be estimated by linear interpolation between the two known values. Given: - tan 30° = 0.577 - tan 35° = 0.700 Using linear interpolation, estimate tan 33° and then determine the height of the tree, giving your final answer to the nearest metre.
Question Parts
(a)
Perform a linear interpolation to estimate tan 33° using the given values for tan 30° and tan 35°.
(b)
Using the interpolated value of tan 33°, calculate the height of the tree and round your answer to the nearest metre.
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Question 9 View Details
In a laboratory experiment, the quantity of reagent A is expressed as \(2^{x}\) and the quantity of reagent B as \(5^{x+2}\). The combined amount required is obtained by dividing the product of the two quantities by \(10^{2x-1}\). It is known that the resulting ratio equals 25.
Question Parts
(a)
Determine the integer value of \(x\).
(b)
Using the value of \(x\) obtained, evaluate \(\dfrac{2^{3x}\,5^{2x-1}}{20^{x+1}}\).
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Question 10 View Details
Consider the cubic algebraic expression \(P(x) = ax^{3}+bx^{2}+cx+d\) where \(a, b, c, d\) are integers.
Question Parts
(a)
Given that \(a = 2\), \(P(x)\) is exactly divisible by \((x-1)\) and \((x+2)\), and that \(P(0)=12\), determine the values of \(b, c\) and \(d\).
(b)
Write \(P(x)\) in fully factored form.
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