Common Entrance Mathematics
Past Questions

AI Explanation

**The reasoning** Addition means combining quantities together. When you have 5 items and add 3 more items, you're finding the total. Think of it practically: If you have ₦5 and someone gives you ₦3, count forward from 5: "6, 7, 8." You now have ₦8 total. Mathematically: 5 + 3 = 8 This is straightforward arithmetic — no tricks, just careful counting or recalling your addition facts. **Why the wrong options tempt you** - **A) 5** — You might pick this if you forgot to add anything at all, just reading the first number. - **B) 7** — This happens if you miscounted by one (maybe you started counting from 5 itself: "5, 6, 7" instead of counting *3 more* after 5). - **D) 10** — You might get this if you multiplied instead of added (5 + 5 = 10), or added an extra number by mistake. **Quick takeaway** Addition means "how many altogether?" — always count forward from your starting number, and double-check you're adding, not multiplying or skipping steps.

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**The reasoning** This is straightforward subtraction: **10 − 4 = 6** Think of it visually: if you have 10 naira and spend 4 naira, you're left with 6 naira. Or count backward from 10: "9, 8, 7, 6" — that's four steps back, landing on 6. The principle here is **basic subtraction** — taking away a smaller number from a larger one to find the difference. **Why the wrong options tempt you** - **Option A (4)**: You might confuse this with "What number did we subtract?" The 4 is what we *removed*, not what remains. - **Option B (5)**: Careless counting or rushing can make you miscount by one. - **Option D (7)**: A common error is subtracting 3 instead of 4, especially under exam pressure when you misread the question. **Quick takeaway** When subtracting, the answer is always *what's left over*, not what you took away — always double-check you've subtracted the exact number shown.

AI Explanation

**The reasoning** Multiplication means adding a number to itself repeatedly. So 2 × 6 means "add 2 to itself 6 times" or "add 6 to itself 2 times." Let's count it out: 2 + 2 + 2 + 2 + 2 + 2 = 12 Or think of it as: 6 + 6 = 12 The multiplication sign (×) is asking "what's the total when you combine these groups?" Two groups of 6 gives you **12**. **Why the wrong options tempt you** - **8** catches you if you mistakenly added instead of multiplying (2 + 6 = 8). Adding and multiplying are different operations! - **10** might come from a careless skip-count error (2, 4, 6, 8, 10 — stopping too early). - **14** could happen if you added after multiplying (2 × 6 = 12, then accidentally +2 = 14). **Quick takeaway** Multiplication builds groups; addition just combines two numbers — so 2 × 6 means "six twos" or "two sixes," which always equals 12, not 2 + 6.

AI Explanation

**The reasoning** Division asks: "How many groups of 4 can I make from 20?" Think of it practically: If you have ₦20 and want to share it equally among 4 friends, how much does each person get? 20 ÷ 4 = 20/4 = 5 You can verify: 5 × 4 = 20 ✓ Another way: Keep subtracting 4 from 20 until you reach zero: 20 - 4 = 16 16 - 4 = 12 12 - 4 = 8 8 - 4 = 4 4 - 4 = 0 You subtracted 4 exactly **5 times**. **Why the wrong options tempt you** - **Option A (3):** You might subtract wrongly or confuse this with a harder problem - **Option B (4):** This is the divisor itself—don't mix up what you're dividing *by* with the answer - **Option D (6):** Careless addition (4 + 2) or rushing without proper calculation **Quick takeaway** Division is asking "how many groups?" or "how much per person?"—always verify by multiplying your answer back with the divisor.

AI Explanation

**The reasoning** A square is a special type of rectangle where **all sides are equal in length**. If you picture a square — like a window frame, a chessboard, or the face of a dice — you can count the edges: top, bottom, left, and right. That's **4 sides**. This is the definition that distinguishes a square from other shapes. It's a quadrilateral (quad = four), meaning it has four sides and four equal angles (90° each). **Why the wrong options tempt you** - **A) 2** — You might think of opposite sides (like top-bottom or left-right), but that's only counting pairs, not all sides. - **B) 3** — This is a triangle's territory. Don't mix up your shapes. - **D) 5** — That's a pentagon. Adding an extra side changes the shape entirely. **Quick takeaway** Every square has exactly **4 equal sides** — it's in the name "quad" (four). Picture it, count it, own it! 🟦

AI Explanation

**The reasoning** "Half of 8" means we're dividing 8 into two equal parts. Mathematically, that's: 8 ÷ 2 = 4 Or you can think of it as: ½ × 8 = 4 The word "half" always means "divide by 2" or "multiply by ½" — they give the same result. So half of any number is that number divided by 2. **Why the wrong options tempt you** - **Option A (2):** You might have divided backward (2 ÷ 8) or confused "half of 8" with "8 halves" (which would be 8 × ½ written differently). - **Option B (3):** This doesn't follow any logical operation — possibly just a rushed guess. - **Option D (5):** You might have subtracted 3 instead of dividing, mixing up different operations. **Quick takeaway** When you see "half of [number]," immediately think **"÷ 2"** — half of 8 is 8 ÷ 2 = 4, always!

AI Explanation

**The reasoning** "Double" means **multiply by 2** or **add the number to itself**. It's asking: what is 7 × 2? 7 × 2 = **14** Or think of it as: 7 + 7 = **14** This is a basic arithmetic concept called **multiplication as repeated addition**. When you double any number, you're simply taking two of that number. **Why the wrong options tempt you** - **A) 10** — You might mistakenly add 3 to 7 instead of doubling. This catches students who rush. - **B) 13** — This is 7 + 6, perhaps from mental confusion or adding the wrong number. - **D) 16** — This is 7 + 9 or could come from doubling 8 instead of 7. Easy mix-up under exam pressure! These distractors are designed to catch careless errors or confusion about what "double" means. **Quick takeaway** **Double always means "times 2"** — so double of any number *n* is simply *n* × 2, nothing more, nothing less!

AI Explanation

## **The reasoning** A **week** is a universally recognized period of **7 consecutive days**. This isn't something you calculate—it's a fundamental unit of time measurement used worldwide, including in Nigeria. The 7-day week cycle includes: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday. This has been the standard since ancient civilizations and is used in all calendars, timetables, and schedules you'll encounter in your exams and daily life. ## **Why the wrong options tempt you** **A) 5** — You might think of a typical school or work week (Monday–Friday), but that's the *working week*, not the full week. **B) 6** — Some students confuse this with a 6-day work week in certain cultures or businesses, but the calendar week remains 7 days. **D) 8** — This has no basis; it might just seem "close enough" if you're guessing carelessly. ## **Quick takeaway** A week always has **7 days**—count them on your fingers if you ever doubt: Mon, Tue, Wed, Thu, Fri, Sat, Sun. Lock it in! 🗓️

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12 × 8 = 96.

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Order of operations: 7 × 2 = 14 first, then 15 + 14 = 29.

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Common denominator: 2/4 + 1/4 = 3/4.

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50% × 80 = 40.

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Perimeter of a square = 4 × side = 4 × 6 = 24 cm.

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0.25 × 100 = 25%.

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x = 15 − 7 = 8.

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Area = length × width = 10 × 4 = 40 cm².

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124 ÷ 2 = 62.

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Pattern: each term increases by 3. 11 + 3 = 14.

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100 − 37 = 63.

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7² = 7 × 7 = 49.

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3 ÷ 4 = 0.75.

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₦750 ÷ 5 = ₦150.

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9 + 3 = 12, so 12:00pm (noon).