JAMB Mathematics 2003 Past Questions & Answers

To solve this, we evaluate each logarithm term separately by converting them to index form. For $log√2(4)$, the power that $√2$ must be raised to get 4 is 4. For $log1/2(16)$, the power that $1/2$ must be raised to get 16 is -4. For log4(32), the power that 4 must be raised to get 32 is 2.5. Finally, we combine the results as instructed: 4 + (-4) - 2.5 = 0 - 2.5 = -2.5.

Common mistake: Students often make sign errors, for example by incorrectly calculating $log1/2(16)$ as 4 instead of -4, which leads to the wrong answer of 5.5.

To solve this, you can multiply the numbers directly in base 4, similar to long multiplication in base 10. First, multiply 213₄ by 3, which gives 1311₄, remembering to carry over groups of 4. Next, multiply 213₄ by 20, which gives 10320₄. Finally, add these two results (1311₄ + 10320₄) using base 4 addition rules to get the final answer, 12231₄.

Common mistake: A common mistake is to perform the multiplication or addition steps as if the numbers were in base 10, forgetting to convert sums or products of 4 or more back into base 4.

First, find the number of students who offer at least one subject by subtracting those who offer neither from the total: 40 - 4 = 36 students. Let the number who offer both subjects be x. Using the formula for the union of two sets, we have: n(M ∪ P) = n(M) + n(P) - n(M ∩ P), which translates to 36 = 32 + 24 - x. This simplifies to 36 = 56 - x, and solving for x gives x = 56 - 36 = 20.

Common mistake: A common mistake is to forget to first subtract the 4 students who offer neither subject, leading to an incorrect calculation like $(32 + 24)$ - 40 = 16.

First, evaluate the expression inside the bracket: $1/0.06$ ÷ $1/0.042$ is the same as $(1/0.06)$ x $(0.042/1)$, which equals $0.042/0.06$ or 0.7. The problem now is to find (0.7) to the power of -1. A number raised to the power of -1 is its reciprocal, which means 1 divided by the number. So, we calculate 1 ÷ 0.7, which gives 1.42857... Rounding this to two decimal places gives 1.43.

Common mistake: A common mistake is to correctly calculate the value in the bracket as 0.7 but then forget to apply the negative exponent, which requires finding the reciprocal of 0.7.

First, find the total amount the woman made from selling the oranges. Since she sells 5 oranges for N40.00, the price of one orange is N40 / 5 = N8.00. The total selling price for all 270 oranges is 270 x N8.00 = N2,160.00. Profit is calculated as Selling Price minus Cost Price, so her profit is N2,160.00 - N1,800.00 = N360.00.

Common mistake: A common mistake is to calculate the total selling price (N2,160.00) and incorrectly choose it as the profit, forgetting to subtract the initial cost price.

To solve this, we follow the order of operations (BODMAS). First, we solve the multiplication inside the bracket: $7/3$ x $5/4$ equals $35/12$. The problem then becomes 1 - $35/12$ + $3/5$. Next, we find the Lowest Common Multiple (LCM) of the denominators 1, 12, and 5, which is 60. Converting each fraction, we get $(60 - 175 + 36)$ / 60, which simplifies to $-79/60$.

Common mistake: A common mistake is to ignore BODMAS and calculate from left to right, which leads to an incorrect answer because the multiplication must be done before the subtraction and addition.

To solve this problem, you need to simplify each surd by finding the largest perfect square factor. $√98$ simplifies to $√(49 x 2)$ which is $7√2$, $√50$ simplifies to $√(25 x 2)$ which is $5√2$, and $√32$ simplifies to $√(16 x 2)$ which is $4√2$. Substituting these back gives $(7√2 - 5√2)$ / $4√2$, which simplifies to $2√2$ / $4√2$. After cancelling out the common term $√2$, you are left with $2/4$, which equals $1/2$.

Common mistake: A common mistake is to incorrectly subtract the numbers under the square root, for example, calculating $√98$ - $√50$ as $√48$, which is mathematically wrong.

The total percentage of people in the hall is 100%. First, find the percentage of women by subtracting the percentages of men and children from 100%, which gives 100% - (47.5% + 22.5%) = 30%. Since this 30% represents the 84 women, we can find the total number of people (T) by setting up the equation $(30/100)$ * T = 84, which gives a total of 280 people. Finally, calculate the number of men by finding 47.5% of the total, which is $(47.5/100)$ * 280 = 133.

Common mistake: Students might mistakenly calculate the number of children (22.5% of the total) instead of the number of men, leading them to choose option A.

To solve this equation, first express the numbers 9 and 27 in the same base, which is base 3, so the equation becomes $(3^2)^(2x-1)$ / $(3^3)^(x+1)$ = 1. Using the laws of indices, this simplifies to $3^(4x-2)$ / $3^(3x+3)$ = 1, which is the same as $3^((4x-2) - (3x+3))$ = $3^0$. Since the bases are equal, we can equate the powers: (4x-2) - (3x+3) = 0, which simplifies to x - 5 = 0, giving x = 5.

Common mistake: A common mistake is to incorrectly handle the subtraction of the powers, especially the signs, such as calculating (4x-2) - (3x+3) as $4x-2-3x+3$, which leads to an incorrect answer.

To find the average, you divide the sum of the numbers by the count of numbers. First, convert the sum 1214 in base five to base ten: $(1 × 5³)$ + $(2 × 5²)$ + $(1 × 5¹)$ + $(4 × 5⁰)$ = 125 + 50 + 5 + 4 = 184. Next, divide this base ten sum by 4, which gives 184 ÷ 4 = 46. Finally, convert the average 46 from base ten back to base five, which results in 141₅.

Common mistake: A common mistake is to perform the division directly on the number 1214 as if it were in base 10, instead of correctly handling the base five arithmetic.