NECO Mathematics
Past Questions

AI Explanation

**The reasoning** This is a simple linear equation. We need to isolate x by doing the opposite operations in reverse order: 3x + 5 = 20 First, subtract 5 from both sides: 3x + 5 − 5 = 20 − 5 3x = 15 Then divide both sides by 3: 3x ÷ 3 = 15 ÷ 3 x = 5 The principle here is **inverse operations** — whatever was done to x, we undo it step by step. **Why the wrong options tempt you** - **Option A (3)**: You might pick the coefficient of x by mistake, confusing the number multiplying x with the value of x itself. - **Option C (7)**: This trap catches students who subtract 5 from 20 but forget to divide by 3 — they stop halfway. - **Option D (15)**: You got 3x = 15 correctly but forgot the final step of dividing by 3. **Quick takeaway** Always perform inverse operations in reverse order: undo addition/subtraction first, then undo multiplication/division — and never stop until x stands alone!

AI Explanation

## The reasoning The **mean** (or average) is the sum of all values divided by how many values you have. Step 1: Add all the numbers together: 2 + 4 + 6 + 8 + 10 = 30 Step 2: Count how many numbers there are: 5 numbers Step 3: Divide the sum by the count: Mean = 30 ÷ 5 = **6** This is the **arithmetic mean** — you're finding the "middle value" if all the numbers were equal. ## Why the wrong options tempt you **A) 5** — You might pick this thinking "2 to 10, so the middle is 5" but that's just looking at the range, not calculating the actual average. **C) 7** — This could trap you if you miscounted the numbers (thinking there are only 4) or made an addition error. **D) 8** — You might choose this if you just picked the second-to-last number or rushed without calculating. ## Quick takeaway **Mean = Sum of all values ÷ Number of values** — always add everything first, then divide by how many items you counted!

AI Explanation

**The reasoning** This is a **linear equation** — we need to get all the *y* terms on one side and all the numbers on the other. Start: 7y - 4 = 3y + 12 **Step 1:** Subtract 3y from both sides (to collect y's together) 7y - 3y - 4 = 12 4y - 4 = 12 **Step 2:** Add 4 to both sides (to isolate the y term) 4y = 12 + 4 4y = 16 **Step 3:** Divide both sides by 4 y = 16 ÷ 4 = **4** Check: 7(4) - 4 = 28 - 4 = 24, and 3(4) + 12 = 12 + 12 = 24 ✓ --- **Why the wrong options tempt you** - **y = 2** comes from mistakenly doing 12 - 4 = 8, then 8 ÷ 4 = 2 (forgetting to properly collect terms) - **y = 3** appears if you divide 12 by 4 too early, ignoring the -4 - **y = 8** tricks you if you forget to divide by the coefficient: 12 + 4 = 16, but you must still divide by 4 --- **Quick takeaway** Collect like terms first (all y's together, all numbers together), *then* divide by the coefficient — never skip that final division!

AI Explanation

**The reasoning** The area of a triangle uses a simple formula: **Area = ½ × base × height** Think of it this way: a triangle is exactly *half* of a rectangle. If you had a rectangle with length 8 cm and width 6 cm, its area would be 8 × 6 = 48 cm². But a triangle with the same base and height takes up only half that space. So: Area = ½ × 8 × 6 = ½ × 48 = **24 cm²** **Why the wrong options tempt you** - **Option A (14 cm²)**: This trap catches students who *add* base and height (8 + 6 = 14) instead of multiplying. Area is never found by addition! - **Option C (48 cm²)**: You forgot to multiply by ½. You calculated the full rectangle instead of half of it. - **Option D (96 cm²)**: You might have doubled instead of halving — maybe you multiplied 48 × 2 by mistake. **Quick takeaway** Triangle area is *always* half the rectangle with the same base and height: **A = ½bh**. Never add dimensions to find area!

AI Explanation

**The reasoning** This is a simple linear equation. The principle here is **collecting like terms** — get all the y's on one side, all the numbers on the other. Starting with: 7y − 4 = 3y + 12 Subtract 3y from both sides: 7y − 3y − 4 = 12 4y − 4 = 12 Add 4 to both sides: 4y = 12 + 4 4y = 16 Divide both sides by 4: y = 16 ÷ 4 = **4** **Why the wrong options tempt you** **Option A (2):** Maybe you subtracted wrong or divided 12 by 4 instead of 16. **Option B (3):** Perhaps you made an arithmetic slip when collecting terms — forgetting to carry the negative sign properly. **Option D (8):** This likely comes from forgetting to add 4 before dividing, so you divided 12 by something incorrectly, or added instead of subtracting somewhere. **Quick takeaway** Always move variables to one side, numbers to the other, then isolate your unknown — JAMB loves testing if you can handle signs carefully!

AI Explanation

**The reasoning** The area of a triangle uses this formula: **Area = ½ × base × height** You have: - Base = 8 - Height = 6 So: Area = ½ × 8 × 6 = ½ × 48 = **24** That "½" (one-half) is the key! A triangle is literally half of a rectangle. If you drew a rectangle with length 8 and width 6, its area would be 48. A triangle with the same base and height takes up exactly half that space. **Why the wrong options tempt you** - **A) 14** — You might have added 8 + 6 instead of multiplying. Area needs multiplication, not addition! - **C) 48** — You forgot to divide by 2! You calculated base × height but missed that crucial "half." - **D) 96** — Double trouble: you multiplied 8 × 6, then multiplied by 2 instead of dividing by 2. **Quick takeaway** Triangle area is always **half** of base times height — never forget that "½" or you'll pick the rectangle's area instead!

AI Explanation

**The reasoning** This is a simple linear equation. Your goal: isolate x on one side. Starting with: 2x + 3 = 11 First, remove the 3 by subtracting it from both sides: 2x + 3 − 3 = 11 − 3 2x = 8 Now divide both sides by 2 to find x: x = 8 ÷ 2 x = 4 **Why the wrong options tempt you** - **Option A (2):** You might have divided 11 by something incorrectly, or confused the coefficient with the answer. - **Option B (3):** This is the constant we subtracted! Don't mistake a number in the equation for the final answer. - **Option D (5):** Perhaps you subtracted 3 from 8 instead of dividing, getting 8 − 3 = 5. **Quick takeaway** Whatever you do to one side of the equation, do to the other — subtraction first to remove constants, then division to isolate the variable.

AI Explanation

## The reasoning The equation x² = 49 asks: **"What number, when multiplied by itself, gives 49?"** The principle here is **finding square roots**. When you square root both sides: √(x²) = √49 You get x = ±7 Why the **±** (plus-minus)? Because: - 7 × 7 = 49 ✓ - (-7) × (-7) = 49 ✓ (negative × negative = positive!) Both 7 and -7 satisfy the equation. ## Why the wrong options tempt you **Option A (±5):** You might rush and think 5² = 25... wait, that's not 49. This catches students who don't verify their answer. **Option B (±6):** 6² = 36, not 49. Close, but math doesn't reward "almost." **Option D (±8):** 8² = 64, which overshoots. Some students guess upward when uncertain. The real trap across all wrong options? **Forgetting to check your multiplication** or **forgetting the negative solution** (though here, all options include ±, so they're testing if you know 7² = 49). ## Quick takeaway **When x² = a number, x equals BOTH the positive and negative square root** — always consider both solutions unless the context says otherwise!

AI Explanation

**The reasoning** To find 10% of 250, remember that "percent" means "per hundred" or "out of 100." So 10% = 10/100 = 0.1 Now multiply: 10% of 250 = 0.1 × 250 = **25** Alternative method: 10% is the same as dividing by 10 (since 10% = 1/10). So 250 ÷ 10 = **25** **Why the wrong options tempt you** - **Option A (10):** You might confuse the percentage value itself (10) with the answer. Don't just copy the percentage number! - **Option C (50):** This is 20% of 250. Easy to get if you accidentally doubled somewhere. - **Option D (100):** This is 40% of 250. Way too large—happens if you mixed up your calculation steps. **Quick takeaway** For 10%, just divide by 10—it's your quickest friend! 10% of *any* number is that number ÷ 10. Master this shortcut and you'll breeze through percentage questions in seconds.

AI Explanation

**The reasoning** The mean (or average) is found by adding all numbers together, then dividing by how many numbers you have. Here's the working: - Add them up: 3 + 5 + 7 + 9 = 24 - Count how many numbers: 4 numbers - Divide: 24 ÷ 4 = **6** This is the **principle of arithmetic mean** — you're finding the "middle value" that represents all the numbers fairly. **Why the wrong options tempt you** - **Option A (5)** and **Option C (7)** are actual numbers *in* the list, so your eyes might jump to them. But mean isn't about picking from the list — it's calculated. - **Option D (8)** might come from adding incorrectly or dividing by 3 instead of 4. Always count carefully! **Quick takeaway** Mean = Sum of all values ÷ Number of values — it's *always* calculated, never just picked from the list.

AI Explanation

**The reasoning** A cube has all sides equal. The volume formula is: **Volume = side × side × side = side³** Given: side = 4 Volume = 4 × 4 × 4 = **64 cubic units** Think of it like stacking smaller cubes: if you have a 4×4 layer, that's 16 small cubes. Stack 4 such layers high, and you get 16 × 4 = 64 cubes total. **Why the wrong options tempt you** - **A) 16** — This is side × side (4 × 4), which gives you the *area* of one face, not the volume. You forgot the third dimension! - **B) 32** — Maybe you did 4 × 4 × 2 or 4 × 8. There's no logical formula here; it's a calculation slip. - **C) 48** — Possibly confused with surface area thinking (though 6 × 4² = 96 actually). Another miscalculation trap. **Quick takeaway** For any cube: **Volume = side³**. Always multiply the side *three times* because volume fills 3D space—length, width, and height!

AI Explanation

**The reasoning** The formula for circumference is **C = 2πr**, where r is the radius. Given: r = 7 and π = 22/7 Substitute into the formula: C = 2 × (22/7) × 7 Let's work through it: C = 2 × 22 × 7/7 C = 2 × 22 × 1 C = **44** Notice how the 7s cancel out perfectly! This is actually a common exam setup — when they give you π = 22/7 and radius = 7 (or 14, 21, etc.), the calculation becomes super clean. **Why the wrong options tempt you** - **A) 22** — You might forget to multiply by 2, using just πr instead of 2πr - **C) 88** — You might accidentally do 2 × 2 × 22 (multiplying the 2 by itself) - **D) 154** — This is the **area** (πr² = 22/7 × 49), not circumference. Classic trap when you're rushing! **Quick takeaway** Circumference = "going around" = 2πr (always has that 2); Area = "filling inside" = πr² (has the square). Know your formulas cold!

AI Explanation

**The reasoning** This is one of the most fundamental principles in geometry: **The Angle Sum Property of Triangles**. No matter what type of triangle you're dealing with — whether it's equilateral, isosceles, scalene, right-angled, acute, or obtuse — the three interior angles *always* add up to **180°**. You can prove this by drawing any triangle and extending one side. The exterior angle formed equals the sum of the two opposite interior angles. This relationship only works because the three angles total 180°. Example: In a right-angled triangle, one angle is 90°. If another angle is 50°, the third *must* be 40° because 90° + 50° + 40° = 180°. **Why the wrong options tempt you** - **90°** — That's just *one* angle in a right triangle, not the sum of all three - **270°** — You might confuse this with three right angles multiplied, but they don't all fit in one triangle - **360°** — This is the sum of angles in a *quadrilateral* (four-sided shape), not a triangle **Quick takeaway** Triangle = 180°, Quadrilateral = 360° — the angle sum increases by 180° for each extra side!

AI Explanation

**The reasoning** A standard die has 6 faces numbered 1, 2, 3, 4, 5, and 6. Even numbers are those divisible by 2: **2, 4, and 6** — that's 3 even numbers. Probability = (Number of favorable outcomes) / (Total possible outcomes) So: Probability = 3/6 = **1/2** This is the **basic probability principle**: count what you want, divide by what's possible. **Why the wrong options tempt you** **A) 1/6** — You might think there's only ONE even number, or confuse this with the probability of getting a specific number like "only 2" or "only 4". **B) 1/3** — Easy mistake: you count 3 even numbers but forget there are 6 total, not 9. Or you might wrongly simplify. **D) 2/3** — You counted the 4 numbers that aren't what you want (the odd ones plus something), mixing up favorable vs unfavorable. **Quick takeaway** Half the numbers on a die (2, 4, 6) are even, so there's a **50-50 chance** — always count carefully and simplify your fraction!

AI Explanation

**The reasoning** 5³ means "5 to the power of 3" or "5 cubed" — you multiply 5 by itself **three times**: 5³ = 5 × 5 × 5 Let's calculate step by step: - First: 5 × 5 = 25 - Then: 25 × 5 = **125** This is the **Law of Exponents**: the small number (exponent) tells you how many times to use the base number in multiplication. **Why the wrong options tempt you** - **A) 15** tricks you if you mistakenly *add* instead of multiply (5 + 5 + 5 = 15). Wrong operation! - **B) 25** catches you if you stop halfway — that's just 5 × 5, which is 5². You forgot the third multiplication. - **C) 75** tempts you if you multiply the base by the exponent (5 × 15), mixing up the rules completely. **Quick takeaway** The exponent tells you **how many times** to multiply the base by itself, not how many to add or what to multiply it by — 5³ always means 5 × 5 × 5 = 125.

AI Explanation

**The reasoning** "Half of 80" means dividing 80 into two equal parts. Mathematically, we write this as: 80 ÷ 2 = 40 Or you can think of it as: ½ × 80 = 40 Either way, you're splitting 80 into two groups. If you have ₦80 and share it equally between two people, each person gets ₦40. Simple! **Why the wrong options tempt you** - **A) 20** — This is ¼ of 80 (80 ÷ 4). You might pick this if you rushed and divided by 4 instead of 2. - **B) 30** — This doesn't follow any clean division of 80. Pure distraction. - **D) 50** — This looks "round" and close to 80, so your brain might grab it if you're guessing quickly. But 50 × 2 = 100, not 80! **Quick takeaway** "Half" always means "÷ 2" — if doubling your answer doesn't give you back the original number, it's wrong!

AI Explanation

**The reasoning** This is straightforward **multiplication** — one of the basic arithmetic operations you must master cold. 7 × 8 means "7 groups of 8" or "8 added to itself 7 times": 8 + 8 + 8 + 8 + 8 + 8 + 8 = 56 Or you can count by 8s seven times: 8, 16, 24, 32, 40, 48, **56**. The answer is **B) 56**. **Why the wrong options tempt you** - **A) 54** — This is 6 × 9. Easy to confuse when rushing through your times tables. - **C) 63** — This is 7 × 9. You might mix up the 8 and 9 under exam pressure. - **D) 48** — This is 6 × 8. You're one step short — counted only 6 groups instead of 7. All these wrong answers are *nearby* multiplication facts designed to catch students who haven't drilled their tables thoroughly. **Quick takeaway** Memorize your multiplication tables from 1 to 12 until they're automatic — exams punish hesitation, and strong tables unlock speed in fractions, percentages, and algebra.

AI Explanation

## The reasoning This is a **basic algebraic equation** where we need to isolate x. Starting with: **x/3 = 4** To find x, we need to "undo" the division by 3. We do this by multiplying both sides by 3: **x/3 × 3 = 4 × 3** The 3s on the left cancel out: **x = 12** Think of it practically: "What number divided by 3 gives 4?" That's 12, because 12 ÷ 3 = 4. ## Why the wrong options tempt you **A) 7** — You might mistakenly add 3 to 4 instead of multiplying. Wrong operation! **C) 1** — Perhaps you divided 4 by 3 instead of multiplying. You went the wrong direction. **D) 4** — You might have confused x with the answer on the right side. Don't just copy what you see! ## Quick takeaway **To solve x/a = b, multiply both sides by a to get x = a × b.** Division problems need multiplication to solve them — they're inverse operations!

AI Explanation

## The reasoning A **square has 4 equal sides**. The perimeter means the total distance around the shape — you're basically walking around all four sides and adding them up. Given: Each side = 5 cm **Perimeter of a square = 4 × side** So: Perimeter = 4 × 5 = **20 cm** Think of it like fencing a square plot of land. If one side needs 5 meters of wire, you'll need that same amount for all four sides. --- ## Why the wrong options tempt you **A) 10 cm** — This catches you if you only added two sides (5 + 5). Remember, a square has *four* sides, not two! **C) 25 cm** — This is the **area** (5 × 5), not perimeter. Don't confuse "space inside" with "distance around." **D) 15 cm** — You might get this by adding only three sides. Always count all four! --- ## Quick takeaway **Perimeter = distance AROUND = add all sides; for a square, that's 4 × side length.**

AI Explanation

**The reasoning** To convert a fraction to a percentage, you multiply by 100%. Here's why: "percent" literally means "per hundred," so we're finding how many parts out of 100. **1/4 × 100% = 100/4 % = 25%** Think of it this way: If you divide something into 4 equal parts, each part is 1/4. Now imagine dividing that same thing into 100 parts instead — each of your original quarters would contain 25 of those smaller parts. So 1/4 = 25/100 = 25%. **Why the wrong options tempt you** **A) 14%** — You might mistakenly write "1" and "4" side by side without doing the actual division. **C) 40%** — This comes from flipping the fraction (doing 4 ÷ 1 instead of 1 ÷ 4). **D) 4%** — You're just using the denominator and ignoring the numerator entirely. **Quick takeaway** To turn any fraction into a percentage: **multiply by 100%** — or simply divide the top by the bottom and add the % sign (1 ÷ 4 = 0.25 = 25%).

AI Explanation

## The reasoning This is an **arithmetic sequence** (also called arithmetic progression or A.P.). Look at the pattern: - From 5 to 10: we add **5** - From 10 to 15: we add **5** - From 15 to 20: we add **5** The **common difference** is 5. So the next term = 20 + 5 = **25**. The general formula is: **Next term = Last term + Common difference** ## Why the wrong options tempt you **Option A (22):** You might think "20 + 2 = 22" if you rushed and didn't spot the consistent pattern. Don't guess randomly! **Option C (30):** This looks tempting if you accidentally doubled the common difference (5 × 2 = 10), then added 20 + 10 = 30. Classic calculation slip under exam pressure. **Option D (24):** Maybe you thought "just add 4" without checking the actual pattern. Always verify the difference between *all* consecutive terms. ## Quick takeaway **In arithmetic sequences, find what you're CONSISTENTLY adding (or subtracting) between terms—that's your common difference, and it never changes.**