JAMB Mathematics 2014 Past Questions & Answers

To add these binary numbers, arrange them vertically and add column by column from right to left, remembering that in base 2, 1 + 1 = 10 (so you write 0 and carry 1). Starting from the right: $1+0=1$; $1+0=1$; $1+1=0$ carry 1. Then, $0+0+1(carry)=1$; $1+1=0$ carry 1; $1+1(carry)=0$ carry 1. Finally, bring down the last carried 1 to get the result 1001011₂.

Common mistake: A common mistake is to incorrectly handle the carry-over, for example by writing '1' instead of '0' when a column's sum is 2 (which is 10 in base 2), leading to an incorrect answer like 1001111₂.

The cost price of the grinder is N60,000. A loss of 15% means the selling price is 15% less than the cost price. First, find the loss amount: 15% of N60,000 is $(15/100)$ * 60,000 = N9,000. To find the selling price, subtract the loss from the cost price: N60,000 - N9,000 = N51,000.

Common mistake: A common mistake is to calculate the loss amount (N9,000) and then add it to the cost price as if it were a profit, or to make a simple arithmetic error when calculating the percentage.

To find the product, first express each number in standard form. 0.00043 is 4.3 x 10⁻⁴ and 2000 is 2 x 10³. Next, multiply the numbers $(4.3 x 2 = 8.6)$ and then multiply the powers of ten by adding their exponents (10⁻⁴ x 10³ = 10⁻⁴⁺³ = 10⁻¹). Combining these results gives the final answer, 8.6 x 10⁻¹.

Common mistake: A common mistake is to incorrectly add the exponents, for instance, calculating 4 - 3 = 1 instead of -4 + 3 = -1, which would lead to the wrong answer 8.6 x 10.

Let the man's net monthly income be 'I'. The problem states that 10% of his income is N4,500, which can be written as the equation $(10/100)$ * I = 4,500. To find the total income 'I', we rearrange the equation to I = 4,500 * $(100/10)$. Solving this gives I = 4,500 * 10, which equals N45,000.

Common mistake: Students may mistakenly subtract the donated amount from the correct total income (N45,000 - N4,500 = N40,500), confusing the total income with the amount left after the donation.

To solve this, we use the laws of logarithms. First, express log75 and log750 in terms of the given log7.5. We can write log75 as log(7.5 x 10), which equals log7.5 + log10, giving 0.8751 + 1 = 1.8751. Similarly, log750 is log(7.5 x 100), which equals log7.5 + log100, giving 0.8751 + 2 = 2.8751. Now, substitute these values into the expression 2log75 + log750 to get 2(1.8751) + 2.8751, which simplifies to 3.7502 + 2.8751 = 6.6253.

Common mistake: Students may make a small calculation error during the final addition of 3.7502 and 2.8751, leading them to incorrectly choose option A.

To solve for x, first understand that a negative power means 'one over', so x⁻² is the same as 1/x². The equation becomes 8 * (1/x²) = $2/25$, which simplifies to 8/x² = $2/25$. To find x, you can cross-multiply to get 2 * x² = 8 * 25, which gives 2x² = 200. Dividing both sides by 2 gives x² = 100, and taking the square root of 100 gives x = 10.

Common mistake: The most common mistake is misinterpreting the negative index, for example by incorrectly calculating 8x⁻² as 1/(8x²), which leads to a completely different and incorrect answer.

To simplify the expression, you need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator, which is $(√2 - √3)$. When you multiply the numerators, $(2√2 - √3)(√2 - √3)$, you get 7 - $3√6$. Multiplying the denominators, $(√2 + √3)(√2 - √3)$, gives 2 - 3, which is -1. Dividing the new numerator by the new denominator gives $(7 - 3√6)$ / -1, which simplifies to $3√6$ - 7.

Common mistake: Students often make a sign error when expanding the numerator, for example calculating 4 - 3 instead of 4 + 3, which leads to the incorrect option C.

To solve this, you can use the laws of logarithms where addition becomes multiplication and subtraction becomes division, giving you Log₂((8 x 16) / 4). This simplifies to $Log₂(128 / 4)$, which is Log₂(32). Since 2 raised to the power of 5 equals 32 (2⁵ = 32), the final answer is 5. Alternatively, you can evaluate each term: Log₂8 = 3, Log₂16 = 4, and Log₂4 = 2, so the calculation is 3 + 4 - 2 = 5.

Common mistake: A common mistake is to evaluate each logarithm separately $(Log₂8=3, Log₂16=4, Log₂4=2)$ and then incorrectly multiply and divide these results $(3 x 4 ÷ 2 = 6)$, instead of adding and subtracting them as the question requires.

The union of two sets, P ∪ Q, is the set containing all elements that are in P, or in Q, or in both. We are given P = 1,2,3,4,5 and P ∪ Q = 1,2,3,4,5,6,7. By comparing the elements in P with the elements in the union, we see that the extra elements are 6,7. These extra elements must have come from set Q, so the elements in Q are 6,7.

Common mistake: A common mistake is to choose only one of the missing elements, like 6 or 7, forgetting that all elements in the union that are not in P must be in Q.

To make 'g' the subject of the formula, you need to isolate it on one side of the equation. Start with gt² - k - w = 0. First, move '-k' and '-w' to the other side, which changes their signs to positive, giving you gt² = k + w. To get 'g' by itself, you must divide both sides by t², which results in g = (k + w) / t².

Common mistake: Students often choose option B because they forget to change the sign of '-w' to '+w' when moving it to the right side of the equation.