JAMB Mathematics 2001 Past Questions & Answers

According to the rule of BODMAS, we must perform multiplication before subtraction. First, calculate 1.6324 multiplied by 0.43, which gives 0.701932. Next, subtract this result from 21.05347, so we have 21.05347 - 0.701932 = 20.351538. Finally, to round the answer to 3 decimal places, we look at the fourth decimal digit (5), and since it is 5 or greater, we round up the third digit, giving 20.352.

Common mistake: Students might incorrectly round down the final answer to 20.351 (Option B) by either truncating the number or forgetting the rule of rounding up when the next digit is 5 or greater.

First, simplify the expression inside the bracket by finding the cube root. The cube root of 64 is 4, and the cube root of a³ is a, so the expression inside the bracket simplifies to 4a. Next, apply the negative power of -1, which means you should find the reciprocal of the term; according to the laws of indices, (4a)⁻¹ is equal to 1 divided by 4a, which is $1/4a$.

Common mistake: A common mistake is to correctly simplify the cube root to get 4a but then forget to apply the negative exponent of -1, leading to the incorrect answer A.

To solve this, first simplify the numerator using the difference of two squares: p² - q² = (p - q)(p + q). Find the values of (p - q) which is $(1 + √2)$ - $(1 - √2)$ = $2√2$, and (p + q) which is $(1 + √2)$ + $(1 - √2)$ = 2. Therefore, the numerator is $(2√2)$ * 2 = $4√2$. For the denominator, 2pq = $2(1 + √2)(1 - √2)$ = $2(1² - (√2)²)$ = $2(1 - 2)$ = -2. Finally, divide the simplified numerator by the denominator: $4√2$ / -2 = $-2√2$.

Common mistake: A common mistake is a sign error when calculating the denominator 2pq, getting 2 instead of -2, which leads to the incorrect answer $2√2$ (Option C).

First, calculate the total cost price by adding the purchase price and the refurbishing cost, which is N250,000 + N70,000 = N320,000. Next, find the gain by subtracting the total cost price from the selling price: N400,000 - N320,000 = N80,000. To find the percentage gain, divide the gain by the total cost price and multiply by 100, so (N80,000 / N320,000) x 100 = 25%.

Common mistake: A common mistake is to calculate the percentage gain using only the initial buying price (N250,000), which leads to the incorrect answer of 60%.

First, use the given relation x = y/2 to find the ratio x/y, which is $1/2$. The expression to evaluate is $(x³/y³ + 1/2)$ ÷ $(1/2 - x²/y²)$. We can calculate x²/y² = $(1/2)²$ = $1/4$ and x³/y³ = $(1/2)³$ = $1/8$. Substituting these values gives $(1/8 + 1/2)$ in the numerator and $(1/2 - 1/4)$ in the denominator, which simplifies to $(5/8)$ ÷ $(1/4)$. To divide by a fraction, you multiply by its reciprocal, so we calculate $5/8$ × $4/1$, which equals $20/8$ or $5/2$.

Common mistake: Students may correctly calculate the numerator as $5/8$ but forget to divide it by the value of the denominator, leading them to mistakenly choose option A.

The formula for Amount in simple interest is A = P(1 + RT/100), where A is the amount, P is the principal, R is the rate, and T is the time. We are given A = N5,500, R = 2%, and T = 5 years. Substituting these values gives 5,500 = $P(1 + (2 * 5)/100)$, which simplifies to 5,500 = $P(1 + 10/100)$ or 5,500 = P(1.1). To find the principal P, we divide the amount by 1.1, so P = 5,500 / 1.1 = N5,000.

Common mistake: A common mistake is to calculate the total interest on the final amount (N5,500) instead of on the unknown principal, leading to an incorrect subtraction.

First, evaluate the numerator: 0.14 squared is 0.0196, and multiplying this by 0.275 gives 0.00539. Next, calculate the denominator by multiplying 7 by 0.02, which equals 0.14. Now, divide the numerator by the denominator, so 0.00539 divided by 0.14 gives 0.0385. Finally, to round this to 3 decimal places, we look at the fourth decimal digit (5) and round up the third digit (8) to get 0.039.

Common mistake: A common mistake is misplacing the decimal point during multiplication, for example calculating 0.14² as 0.196 instead of 0.0196, which leads to an incorrect answer that is ten times too large.

To solve this problem, let's substitute a variable, say 'y', for '$a^x$' to simplify the expression. The question then becomes a standard polynomial division: divide $(y^3 - 26y^2 + 156y - 216)$ by $(y^2 - 24y + 108)$. Performing long division, the quotient is found to be (y - 2) with a remainder of zero. Finally, substituting '$a^x$' back in place of 'y' gives the answer as $a^x$ - 2.

Common mistake: A common mistake is a sign error during the long division process, which could lead a student to get a quotient of 'y + 2' instead of 'y - 2', resulting in the incorrect choice of $a^x$ + 2.

When two graphs intersect at a point, their y-values are equal at that point. So, we set the two equations equal: px² + q = 2x² - 1. Since they intersect at x = 2, we substitute 2 for x, which gives p(2)² + q = 2(2)² - 1. This simplifies to 4p + q = 8 - 1, or 4p + q = 7. To find p in terms of q, we rearrange the equation to make p the subject: 4p = 7 - q, and finally p = (7 - q)/4.

Common mistake: A common mistake is incorrectly calculating p(2)² as 2p instead of 4p, which would lead to an incorrect answer like option C.

The question requires finding positive integer pairs (x, y) that satisfy 3y + 5x ≤ 15, where y is 1 or 2. When y = 1, the inequality becomes 3 + 5x ≤ 15, which simplifies to 5x ≤ 12, so x can be 1 or 2, giving the pairs (1,1) and (2,1). When y = 2, the inequality becomes 6 + 5x ≤ 15, which simplifies to 5x ≤ 9, so x can only be 1, giving the pair (1,2). The complete set of valid pairs is therefore (1,1), (1,2), and (2,1).

Common mistake: Students often misinterpret the condition 'y < 3' as 'y ≤ 3', causing them to incorrectly test for y=3 and include the pair (1,3) in their answer.