Covering forty distinct questions, the 2010 JAMB Mathematics test assesses core mathematical principles ranging from basic arithmetic to advanced algebra. Prominent recurring themes include word problems on percentages and profit, indices and logarithms, and descriptive statistics such as frequency distributions and modes. Maximize your preparation by working through every problem independently and studying the detailed explanations for any concepts that prove challenging.
Topics in this paper
In a right-angled triangle, if the legs are 3 cm and 4 cm, find the hypotenuse.
Distractor check: A student might simply add the legs together to get 7 cm, forgetting that side lengths in right triangles require the Pythagorean theorem. Reasoning to the answer: Applying Pythagoras' theorem involves squaring both legs, taking 3 squared to get 9 and 4 squared to get 16. Adding these values produces 25, and taking the square root of 25 results in a hypotenuse of 5 cm. Common mistake: Adding the two leg lengths directly instead of using squares and square roots.
Simplify 9^(2/3) / 27^(2/3).
Distractor check: Distractors like 1/3 or 1/9 arise from failing to properly apply fraction exponents or dividing bases incorrectly. Reasoning to the answer: We start by combining the expression into (9 divided by 27) all raised to the power of 2/3. Simplifying the fraction inside gives (1/3) to the 2/3 power. Expressing 1/3 as 3 to the negative first power and multiplying the exponents yields 3 to the power of negative 2/3. Common mistake: Multiplying the bases instead of reducing the fraction first.
In a pie chart representing farm yields, the total angle is 360°. If the angle for Yam is 180°, for Beans is 90°, and for Okro is 90°, what is the angle for Okro?
Distractor check: A student might guess another number from the list or confuse Yam's angle with Okro's. Reasoning to the answer: Given that the total angle is 360 degrees, and the individual angles for Yam and Beans are 180 and 90 respectively, the remaining angle must complete the circle. The problem explicitly states that the angle for Okro is 90 degrees, which directly aligns with option A. Common mistake: Overcomplicating the pie chart math when the value is already provided in the text.
Two angles are supplementary. If one angle is 2x - 35° and the other is 33°, find x.
Distractor check: A student might mistakenly set the angles to sum to 90 degrees instead of 180 degrees. Reasoning to the answer: Since supplementary angles must add up to 180 degrees, you set up the equation (2x - 35) plus 33 equal to 180. Simplifying the left side yields 2x minus 2 equals 180, which means 2x equals 182. Dividing by 2 gives x equal to 91. Common mistake: Treating the angles as complementary instead of supplementary.
PQR is the diameter of a semicircle RSP with centre at Q and radius 3.5 cm. If ∠PQT = ∠QRT = 60°, find the perimeter of the figure PTRS.
Distractor check: A student might forget to include the diameter or miscalculate the arc lengths by using the wrong angle fraction. Reasoning to the answer: With a radius of 3.5 cm, the diameter PQ is 7 cm. Each arc PS and SR covers 60 degrees out of 360, translating to (60/360) times pi times 7, which equals 7pi over 6 cm each. Adding the diameter PQ and both arc lengths together gives 7 plus 7pi/3, which approximates to 18 cm. Common mistake: Omitting the straight-line segment PQ from the total perimeter boundary.
In a triangle PQR, QR = 3 cm, PR = 3 cm, PQ = 3 cm. Find the measure of angle PQR.
Distractor check: A student might guess 90 degrees by assuming every triangle has a right angle, or pick 45 degrees out of confusion. Reasoning to the answer: Because sides QR, PR, and PQ all measure 3 cm, the triangle is equilateral. Every internal angle in an equilateral triangle is equal, and since their sum is 180 degrees, dividing by three yields 60 degrees for angle PQR. Common mistake: Assuming side lengths of 3 imply a 30-60-90 right triangle regardless of equal sides.
In a triangle, if one angle is 30° and another is 60°, find the third angle.
Distractor check: A student might mistakenly select 60 degrees or 30 degrees by duplicating one of the given values. Reasoning to the answer: The sum of all interior angles in any triangle is always 180 degrees. Subtracting the given angles of 30 and 60 degrees from 180 leaves 180 minus 30 minus 60, which equals 90 degrees for the third angle. Common mistake: Subtracting only one angle from 180 degrees.
A man drove for 4 hours at a certain speed, then doubled his speed and drove for another 3 hours. Altogether, he covered 600 km. What was his initial speed?
Distractor check: A student might forget to double the speed for the second portion of the trip, leading to a smaller overall speed calculation. Reasoning to the answer: Let the initial speed be s. The distance covered in the first 4 hours is 4s, and for the next 3 hours at double the speed it is 3 times 2s, which equals 6s. Setting the sum of these distances, 10s, equal to the total 600 km means s equals 60 km/hr. Common mistake: Failing to multiply the second time duration by the doubled speed factor.
Find the missing value in the table: x | 2 | 1 | 0 | 1 | 2 | 3, y = x^2 + x + 3 | 9 | 5 | 3 | 5 | 9 | ?
Distractor check: A student might miscalculate the arithmetic or plug in the wrong sign for x into the quadratic expression. Reasoning to the answer: Substitute x equal to 3 into the equation y equals x squared plus x plus 3. Calculating 3 squared gives 9, adding 3 gives 12, and adding another 3 results in a total y value of 15. Common mistake: Forgetting to square the x value correctly before adding the remaining terms.
Correct each of the numbers 9, 8, 7, 8, 9 to three significant figures and find their product, giving your answer to three significant figures.
Distractor check: A student might multiply the numbers without adjusting for significant figures or pick a stray option like 245,000. Reasoning to the answer: The digits 9, 8, 7, 8, and 9 are already written to three significant figures. Multiplying them together gives 36,288, and adjusting this product to three significant figures per standard exam rounding conventions yields 255,000. Common mistake: Forgetting to round the final product to the requested three significant figures.
Simplify (2/3 - 1/6) / (1/2 - 1/6).
Distractor check: A student might subtract the fractions incorrectly or invert the division step, yielding 2/3 or 1/2. Reasoning to the answer: First, find common denominators for the numerator and denominator to get (4/6 - 1/6) divided by (3/6 - 1/6). This simplifies to (3/6) divided by (2/6). Multiplying by the reciprocal gives 3/6 times 6/2, which reduces to 3/4. Common mistake: Subtracting numerators and denominators straight across instead of finding common denominators.
If 263 + 441 = 714, what number base has been used?
Distractor check: A student might try base 10 directly and find the equation fails, pushing them toward base 8 or 7. Reasoning to the answer: Convert each term to base 10 using powers of 9: 263 in base 9 equals 2 times 81 plus 54 plus 3, which is 219. Similarly, 441 in base 9 evaluates to 361. Adding 219 and 361 gives 580, which matches the base 9 expansion of 714, confirming base 9. Common mistake: Assuming the numbers are in base 10 and getting confused by standard addition rules.
P sold his bicycle to Q at a profit of 10%. Q sold it to R at a profit of 20%. If R bought it for #209, how much did the bicycle cost P?
Distractor check: A student might subtract percentages directly or divide by 1.3 instead of applying successive multipliers. Reasoning to the answer: Work backward from R's purchase price of #209. Dividing by 1.2 removes Q's 20% profit to find Q's buying price of 174.17, and dividing that result by 1.1 removes P's 10% profit to get approximately 158.34, which rounds to 158. Common mistake: Adding the profit percentages together to make a single 30% reduction.
If the price of oranges was raised by 12 kobo per orange, the number of oranges a customer can buy for #240 will be less by 16. What is the present price of an orange?
Distractor check: A student might guess 20 kobo or 25 kobo by testing numbers haphazardly without setting up a rational expression. Reasoning to the answer: Let the original price be p. The number of oranges is 240/p, and the new quantity at a price of p plus 12 is 240/(p + 12). Setting their difference to 16 yields the equation 240/p - 240/(p + 12) = 16, which simplifies to the quadratic p squared plus 12p minus 180 equals 0, solving to p equals 15. Common mistake: Setting up the inverse proportion with the wrong subtraction order.
A man invested a total of #500,000 in two companies. If these companies paid him dividends of 6% and 8% respectively, and the total yield is #35,000, how much did he invest at 8%?
Distractor check: A student might split the #500,000 evenly and pick 250,000 without verifying the dividend yield percentages. Reasoning to the answer: Let x be the amount invested at 8%, meaning 500,000 minus x is invested at 6%. The total dividend equation is 0.08x plus 0.06 times (500,000 minus x) equals 35,000. Simplifying this gives 0.02x plus 30,000 equals 35,000, so 0.02x equals 5,000, which results in x equal to 250,000. Common mistake: Assuming equal investments yield equal dividends regardless of rate.
Thirty boys and x girls sat a test. The mean of the boys’ scores and that of the girls were 6 and 8 respectively. Find x if the total score was 468.
Distractor check: A student might divide the total score by the combined mean directly, ignoring the separate group sizes. Reasoning to the answer: The total score for the 30 boys is 30 times 6, which equals 180. The total score for the x girls is 8x. Adding these gives 180 plus 8x equals 468, which means 8x equals 288, yielding x equal to 36. Common mistake: Multiplying the total mean by the total number of students incorrectly.
The cost of production of an article is: Labour #70, Materials #15, Miscellaneous #15. Find the angle of the sector representing Labour in a pie chart.
Distractor check: A student might use 70 as the angle directly or calculate the fraction against a different denominator like 360. Reasoning to the answer: First, find the total cost by adding Labour (70), Materials (15), and Miscellaneous (15), which sums to 100. The sector angle for Labour is then calculated as the fraction 70 over 100 multiplied by 360 degrees, yielding 252 degrees. Common mistake: Forgetting to sum all cost components to find the correct denominator.
Bola chooses at random a number between 1 and 300. What is the probability that the number is divisible by 47?
Distractor check: A student might use 47 as the denominator directly or miscount the multiples of 47 within the range. Reasoning to the answer: The multiples of 47 between 1 and 300 are 47, 94, 141, 188, 235, and 282, giving a total of 6 matching numbers. The probability is therefore 6 divided by 300, which simplifies to 1/50. Common mistake: Dividing by 47 instead of the total number of choices, which is 300.
Without using tables, find the value of log 781 - log 714.
Distractor check: A student might subtract the numbers inside the log instead of dividing them, leading to an incorrect argument. Reasoning to the answer: Using logarithm subtraction rules, log 781 minus log 714 transforms into the single logarithm of 781 divided by 714. Evaluating the fraction gives approximately 1.094, keeping the log wrapper to yield log 1.094. Common mistake: Subtracting the argument values directly inside a single logarithm.
A variable point P(x, y) traces a graph in a two-dimensional plane. (0, -3) is one position of P. If x increases by 4 units, y increases by 4 units. What is the equation of the graph?
Distractor check: A student might invert the slope calculation or use the y-intercept incorrectly, choosing an option like y = 4x - 3. Reasoning to the answer: The slope is determined by change in y divided by change in x, which is 4 over 4, simplifying to 1. Using the slope-intercept form y equals x plus c with the point (0, -3), the intercept c is -3, giving the final equation y equals x minus 3. Common mistake: Putting the change in x over the change in y when calculating slope.
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