Post-UTME Mathematics
Past Questions

AI Explanation

**The reasoning** This is a **linear equation** — we need to isolate x on one side. Starting with: 2x + 3 = 11 **Step 1:** Subtract 3 from both sides to remove it from the left 2x + 3 − 3 = 11 − 3 2x = 8 **Step 2:** Divide both sides by 2 to get x alone 2x ÷ 2 = 8 ÷ 2 **x = 4** Verify: 2(4) + 3 = 8 + 3 = 11 ✓ **Why the wrong options tempt you** - **x = 3**: You might get this if you subtract 3 from 11 first (getting 8), then forget to divide by 2. - **x = 5**: This happens if you subtract 3 from 11 (getting 8), then mistakenly think 2x means "x + 2", so 8 − 3 = 5. - **x = 7**: You get this if you only subtract 3 but ignore the coefficient 2 entirely, or mix up operations. **Quick takeaway** Whatever you do to one side of an equation, do to the other — always work systematically to isolate the variable, dealing with addition/subtraction first, then multiplication/division.

AI Explanation

**The reasoning** The square root symbol (√) asks: "What number, when multiplied by itself, gives me this value?" So √16 means: "What number × itself = 16?" Let's check: 4 × 4 = 16 ✓ Therefore, √16 = **4** The principle here is **understanding square roots** — you're finding the number that was squared to produce what's under the root sign. **Why the wrong options tempt you** - **A) 2** — You might confuse this with ∜16 (the fourth root). Yes, 2⁴ = 16, but that's not what the question asks. - **C) 8** — This is half of 16, but that's division (16 ÷ 2), not square root. Don't mix up operations! - **D) 16** — Some students think √16 means "keep it the same," but that's not how roots work. You must find what squared gives 16. **Quick takeaway** Square root asks "what times itself?" — so √16 = 4 because 4 × 4 = 16; always multiply your answer by itself to verify!

AI Explanation

**The reasoning** "20% of 500" means "20 per hundred of 500" — or mathematically, 20/100 × 500. Here's the working: - 20% = 20/100 = 0.2 - 20% of 500 = 0.2 × 500 = **100** **Quick method:** 10% of any number is just that number ÷ 10. So 10% of 500 = 50. Since 20% is double of 10%, then 20% of 500 = 50 × 2 = **100**. **Why the wrong options tempt you** - **Option A (50):** This is 10% of 500, not 20%. You might divide by 10 but forget to double it. - **Option C (150):** This would be 30% of 500. Perhaps you miscalculated 20 + 10 somewhere. - **Option D (200):** This is 40% of 500. Maybe you doubled twice by accident, or confused "20% of 500" with "500 minus 20%." **Quick takeaway** To find any percentage: convert to a decimal (move the decimal point two places left), then multiply — so 20% always means "multiply by 0.2."

AI Explanation

**The reasoning** This is a simple linear equation. To find x, we need to isolate it on one side. We have: 4x = 24 Divide both sides by 4: x = 24 ÷ 4 = 6 **The principle:** When solving equations, perform the inverse operation to isolate the variable. Since x is being multiplied by 4, we divide by 4 to "undo" it. **Why the wrong options tempt you** - **Option A (4):** You might confuse the coefficient with the answer itself. Don't just pick the number you see attached to x! - **Option C (8):** This comes from subtracting instead of dividing (24 − 16 = 8). Wrong operation! - **Option D (10):** Perhaps from faulty mental math or adding instead of dividing. **Quick takeaway** Whatever operation is happening to x, do the opposite to both sides — multiplication becomes division, addition becomes subtraction, and so on. Practice this "inverse thinking" and you'll never miss these again! 💪

AI Explanation

**The reasoning** The formula for the area of a triangle is: **Area = ½ × base × height** Given: base = 10, height = 5 Area = ½ × 10 × 5 Area = ½ × 50 Area = **25** This formula works for ANY triangle. The "½" exists because a triangle is literally half of a rectangle with the same base and height. Picture cutting a rectangle diagonally — you get two equal triangles! **Why the wrong options tempt you** - **A) 15** — You might have added base + height (10 + 5). That's not how area works! - **C) 50** — This is base × height WITHOUT the ½. You forgot that triangles are half rectangles, not full ones. - **D) 75** — Perhaps confused multiplication or added all three numbers somehow. **Quick takeaway** Triangle area is ALWAYS "half base times height" — remember: triangles are half of rectangles, so don't forget that crucial ½!

AI Explanation

**The reasoning** The cube root asks: "What number, when multiplied by itself THREE times, gives 27?" Let's call this mystery number *x*. We're looking for: x × x × x = 27 Try x = 3: 3 × 3 × 3 = 9 × 3 = 27 ✓ So ∛27 = 3 Think of it like unpacking a cube: if you have a cube with volume 27 cm³, each side measures 3 cm. **Why the wrong options tempt you** - **A) 1** — You might confuse this with ∛1 = 1, but 1×1×1 = 1, not 27 - **C) 9** — This is the *square* root trap! √27 is close to 5, but students often see 3×9 = 27 and pick 9. Remember: 9×9×9 = 729, way too big! - **D) 27** — This assumes the cube root of a number is itself, which only works for 1 **Quick takeaway** Cube root means "what number times itself THREE times gives this?" — always multiply your answer three times to verify: 3×3×3 = 27. ✓

AI Explanation

**The reasoning** This question tests **BODMAS/PEMDAS** — the order of operations in mathematics. BODMAS stands for: **B**rackets, **O**rders (powers), **D**ivision, **M**ultiplication, **A**ddition, **S**ubtraction. The key rule: **Multiplication comes before Addition.** So in 8 + 7 × 2, don't just work left to right! First, handle the multiplication: 7 × 2 = 14 Then add: 8 + 14 = **22** **Why the wrong options tempt you** - **Option C (30)**: You added first (8 + 7 = 15), then multiplied by 2. That's working left to right, ignoring BODMAS. - **Options B & D**: These come from other calculation errors, possibly mixing operations or misreading the question. The trap is natural — we read left to right in English, so our brain wants to calculate that way. But maths has its own rules! **Quick takeaway** **"Multiply and divide BEFORE you add or subtract"** — unless brackets say otherwise. BODMAS is your best friend in JAMB Maths!

AI Explanation

**The reasoning** When you see 0.5, read it as "five-tenths" — literally 5/10. Now simplify by dividing both numerator and denominator by their highest common factor (5): 5/10 = (5÷5)/(10÷5) = **1/2** This is **equivalent fractions** — the value stays the same, just expressed in simplest form. You can verify: 1÷2 = 0.5 ✓ **Why the wrong options tempt you** - **1/4** deceives you if you confuse 0.5 with 0.25 (which *is* 1/4) - **1/3** catches you if you're thinking of 0.333... - **2/3** is actually 0.666..., not even close, but it looks "official" enough to trick a rushed student The trap? Not converting the decimal place value correctly, or forgetting to simplify. **Quick takeaway** 0.5 means "5 out of 10" which simplifies to 1/2 — think of it as splitting something into two equal halves; that's literally what "half" means!

AI Explanation

**The reasoning** HCF (Highest Common Factor) means the largest number that divides both numbers perfectly. For two numbers to have HCF = 1, they must be **coprime** — sharing no common factors except 1. Let's check what divides 9: only 1, 3, and 9. - **A) 3**: Factors are 1, 3. Both 3 and 9 share 3 as a factor → HCF = 3 ❌ - **B) 5**: Factors are 1, 5. Only 1 divides both 5 and 9 → HCF = 1 ✓ - **C) 6**: Factors are 1, 2, 3, 6. Both 6 and 9 share 3 → HCF = 3 ❌ - **D) 12**: Factors are 1, 2, 3, 4, 6, 12. Both 12 and 9 share 3 → HCF = 3 ❌ **Why the wrong options tempt you** All the wrong answers (3, 6, 12) are multiples of 3 or contain 3 as a factor — and since 9 = 3², they all share 3 as a common divisor. If you don't carefully check the factors, these look innocent enough to pick. **Quick takeaway** To have HCF = 1 with 9, pick a number that doesn't have 3 as a factor — because 9 is built entirely from 3s!

AI Explanation

**The reasoning** This tests **order of operations** (BODMAS/PEMDAS) and basic squaring. Break it down step by step: - 10² means 10 × 10 = **100** - 5² means 5 × 5 = **25** - Now add them: 100 + 25 = **125** The key principle: Handle each square **separately first**, then add. Don't try to add 10 + 5 before squaring! **Why the wrong options tempt you** **A) 75** — You might have done (10 + 5) × 5 = 75, mixing operations incorrectly. **C) 150** — Perhaps you did 10² + 5 × 10, forgetting to square the 5. **D) 200** — This looks like (10 + 5)² which would be 15² = 225... or you doubled something by mistake. The trap is **rushing and combining numbers before completing the squaring**. **Quick takeaway** **"Square each number separately, THEN add the results"** — never combine numbers inside brackets unless the question shows them there!

AI Explanation

**The reasoning** The **median** is the middle value when numbers are arranged in order. Think of it as the "center position" in a lineup. Your numbers: 3, 5, 7 They're already arranged from smallest to largest. Count them: there are **3 numbers** total. For an odd number of values, the median is simply the one in the middle position. Position 1: **3** Position 2: **5** ← This is the middle! Position 3: **7** So the median = **5** **Why the wrong options tempt you** - **A (3)** and **C (7)** are the endpoints. Students sometimes confuse median with "first" or "last" value. - **D (9)** might trick you if you accidentally added something (like 3+5+7 = 15, then made an error). The median isn't about addition at all—it's purely about *position*. **Quick takeaway** Median = middle value when arranged in order; for odd-numbered sets, it's literally the center number—count to the middle and pick it!

AI Explanation

**The reasoning** This is a **linear equation** — our job is to isolate x on one side. Start with: 2x + 3 = 11 **Step 1:** Remove the 3 by subtracting it from both sides: 2x + 3 − 3 = 11 − 3 2x = 8 **Step 2:** Divide both sides by 2 to find x: x = 8 ÷ 2 = **4** Check: Does 2(4) + 3 = 11? Yes! 8 + 3 = 11 ✓ **Why the wrong options tempt you** - **Option A (3):** You might subtract 3 from 11 first and forget to divide by 2, getting 8, then misread. - **Option C (5):** Common if you subtract 3 from 11 (getting 8) but don't divide — or if you divide 11 by 2 instead of working step-by-step. - **Option D (6):** Happens if you subtract 3 from 11, then subtract 2 instead of dividing. **Quick takeaway** Whatever you do to one side of the equation, do to the other — subtract first to remove constants, then divide to isolate x.