SAT Math
Past Questions

AI Explanation

**The reasoning** This is a simple linear equation. Your goal: isolate x on one side. Start with: 3x + 2 = 11 **Step 1:** Get rid of the +2 by subtracting 2 from both sides: 3x + 2 − 2 = 11 − 2 3x = 9 **Step 2:** Divide both sides by 3 to find x: x = 9 ÷ 3 = **3** This is called "inverse operations" — you undo addition with subtraction, and undo multiplication with division. **Why the wrong options tempt you** - **Option A (1):** Maybe you subtracted 2 from 3 instead of solving properly - **Option B (2):** Perhaps you confused the constant term (2) with the answer - **Option D (5):** You might have added instead of subtracted, getting 3x = 13, then made another error These mistakes happen when you rush or skip the step-by-step working. **Quick takeaway** Whatever you do to one side of an equation, do to the other — then work backwards through the operations to free your variable.

AI Explanation

**The reasoning** This is **function evaluation** — you're simply substituting the given value into the function. Given: f(x) = x² − 4, and you need f(3). Replace every "x" with "3": f(3) = (3)² − 4 f(3) = 9 − 4 f(3) = **5** Think of f(x) as a machine: you feed in x = 3, and it squares it, then subtracts 4. --- **Why the wrong options tempt you** **A) 1** — You might have done 3 − 4 + something confused. Wrong order of operations. **C) 9** — You stopped after squaring! You forgot to subtract the 4. This is the most common trap. **D) 13** — You probably added instead: 9 + 4. Sign error — the function says *minus* 4. --- **Quick takeaway** When you see f(3), **substitute 3 everywhere you see x**, then follow BODMAS carefully — square first, subtract last. Function evaluation is just careful substitution!

AI Explanation

**The reasoning** The formula for the area of a circle is **A = πr²** (pi times radius squared). Here, radius r = 5, so: - A = π × (5)² - A = π × 25 - A = **25π** The key word is "squared" — you must multiply the radius by itself first, *then* multiply by π. **Why the wrong options tempt you** - **A) 5π** — You forgot to square! You just wrote πr instead of πr². This is the most common mistake. - **B) 10π** — You multiplied the radius by 2 first (thinking of diameter or circumference formula C = 2πr), then added π. Wrong formula entirely. - **D) 50π** — You multiplied 5 × 10 somehow, maybe confusing diameter (10) with radius. **Quick takeaway** **Area needs squaring: A = πr².** Circumference is the one with "2" in front (C = 2πr). Never mix them up — area grows with the *square* of the radius, so small changes in radius mean BIG changes in area!

AI Explanation

**The reasoning** The slope measures how steep a line is — how much it rises for every step you take horizontally. The formula is: **slope = (change in y) ÷ (change in x)** For points (1,2) and (3,6): - Change in y = 6 − 2 = 4 - Change in x = 3 − 1 = 2 - Slope = 4 ÷ 2 = **2** This means for every 1 unit you move right, the line rises 2 units up. **Why the wrong options tempt you** **A) 1** — You might subtract wrong: maybe 3−1 = 2, then forget to divide properly. **C) 3** — Common trap! You used only the x-values (3−1) without finding the y-change correctly. **D) 4** — You calculated the change in y (which is 4) but forgot to divide by the change in x. **Quick takeaway** Slope is **rise over run** — always divide the *vertical* change by the *horizontal* change, and subtract coordinates in the same order: (y₂−y₁)/(x₂−x₁).

AI Explanation

**The reasoning** The **median** is simply the *middle value* when numbers are arranged in order. Think of it like lining up five students by height — the one in the middle is your median. Your data: 3, 5, 8, 11, 14 (already arranged from smallest to largest — nice!) Count them: 5 numbers total. The middle position = (5 + 1) ÷ 2 = 3rd position. The 3rd number is **8**. That's your median! **Why the wrong options tempt you** - **A) 5** — You might pick the second number by mistake, not counting carefully to the true middle. - **C) 11 and D) 14** — Common if you confuse median with *mode* (most frequent) or *mean* (average). The mean here is (3+5+8+11+14) ÷ 5 = 8.2, but that's a different measure! **Quick takeaway** For an odd number of values, the median is always the number sitting exactly in the middle when arranged in order — count your way to the center, don't calculate!

AI Explanation

**The reasoning** This is a **linear equation** — we need to isolate x by doing the same thing to both sides. Starting with: 2x + 6 = 20 **Step 1:** Subtract 6 from both sides to remove it from the left 2x + 6 − 6 = 20 − 6 2x = 14 **Step 2:** Divide both sides by 2 to get x alone 2x ÷ 2 = 14 ÷ 2 **x = 7** **Why the wrong options tempt you** - **Option A (5):** You might subtract 6 then forget to divide, or make an arithmetic slip with 20 − 6. - **Option C (8):** Classic error — subtracting 6 from 20 gives 14, and you might accidentally think "14 − 6 = 8" or confuse your steps. - **Option D (14):** You stopped halfway! You found 2x = 14 but forgot the final division step. **Quick takeaway** Always **undo operations in reverse order**: remove addition/subtraction first, *then* handle multiplication/division — and check your answer by plugging it back in (2 × 7 + 6 = 20 ✓).

AI Explanation

**The reasoning** The slope of a line tells you how steep it is — specifically, how much the line rises (goes up or down) for every unit it runs (goes left or right). The formula is: **slope = (change in y) / (change in x) = (y₂ − y₁) / (x₂ − x₁)** From (0,0) to (2,4): - Change in y = 4 − 0 = 4 - Change in x = 2 − 0 = 2 So slope = 4/2 = **2** This means for every 1 unit you move right, the line goes up by 2 units. **Why the wrong options tempt you** - **Option A (1):** You might think "the points look balanced" or confuse slope with some other property. - **Option C (0.5):** This is the flip! You divided 2/4 instead of 4/2. Remember: rise comes first (vertical change), then run (horizontal change). - **Option D (4):** You only looked at the y-value and ignored the x-value completely. **Quick takeaway** Slope is always **"rise over run"** — vertical change divided by horizontal change. Don't flip it!

AI Explanation

**The reasoning** This is a simple linear equation. Your goal: isolate x on one side. Starting with: 4x − 8 = 0 **Step 1:** Add 8 to both sides to move the constant across: 4x − 8 + 8 = 0 + 8 4x = 8 **Step 2:** Divide both sides by 4 to get x alone: x = 8/4 = **2** This principle is called **solving by inverse operations** — you "undo" what's being done to x. **Why the wrong options tempt you** - **Option A (1):** You might subtract 4 from 8 instead of dividing. That's mixing up operations. - **Option C (4):** You see the coefficient 4 and think it's the answer. Nope — that's what we *divide by*, not the solution. - **Option D (8):** You stopped at 4x = 8 and forgot the final division step. **Quick takeaway** Whatever is *done* to x, do the *opposite* to free it: subtraction undoes addition, division undoes multiplication — always work backwards to isolate your variable!

AI Explanation

**The reasoning** This is a **linear equation** — we need to isolate x by doing the same thing to both sides. Starting with: 3x + 5 = 20 **Step 1:** Subtract 5 from both sides to remove it from the left 3x + 5 − 5 = 20 − 5 3x = 15 **Step 2:** Divide both sides by 3 to get x alone 3x ÷ 3 = 15 ÷ 3 **x = 5** Always remember: whatever you do to one side, do to the other! **Why the wrong options tempt you** - **A) 3** — You might pick this because 3 appears in "3x", but that's the *coefficient*, not the answer - **C) 7** — Careless students sometimes do 20 ÷ 3 directly, ignoring the "+5" completely - **D) 15** — This is what 3x equals, but the question asks for x itself, not 3x **Quick takeaway** Linear equations are like unwrapping a gift: peel off layers one at a time (subtract first, then divide) until x stands alone — and always check by substituting back: 3(5) + 5 = 20 ✓

AI Explanation

**The reasoning** To find the average (or mean), you add all the numbers together, then divide by how many numbers there are. Here: 12 + 15 + 18 = 45 We have 3 numbers, so: 45 ÷ 3 = **15** The principle is simple: **Average = Sum of all values ÷ Number of values** Notice something beautiful here — 15 is actually the middle number! When numbers are evenly spaced (12, 15, 18 — each 3 apart), the average is always the middle value. **Why the wrong options tempt you** - **14** might come from adding wrong or dividing by 4 instead of 3 - **16** could happen if you miscalculated 45 ÷ 3, or added an extra number by mistake - **17** appears if you rushed and estimated badly, thinking "somewhere between 15 and 18" **Quick takeaway** Always write it out: *add everything up, count how many numbers, divide* — and when numbers are equally spaced, the average sits right in the middle!

AI Explanation

**The reasoning** This is a **linear equation** problem. Let's solve step by step: 5(x − 2) = 15 First, divide both sides by 5 to isolate the bracket: (x − 2) = 15/5 x − 2 = 3 Now add 2 to both sides: x = 3 + 2 x = **5** You can verify: 5(5 − 2) = 5(3) = 15 ✓ **Why the wrong options tempt you** **Option A (3):** This is what you get if you stop too early — it's the value of (x − 2), not x itself. Don't confuse the intermediate step with your final answer! **Option C (7):** You might get this if you mistakenly *add* 2 to 15 before dividing: (15 + 2)/5. Wrong order of operations. **Option D (1):** Possibly from errors like subtracting instead of adding in the final step, or other calculation mix-ups. **Quick takeaway** Always complete every step: expand or simplify brackets first, isolate your variable, then solve — and never mistake an intermediate value for your final answer.

AI Explanation

## The reasoning This is **direct substitution** — one of the most fundamental operations in algebra. You're given two pieces of information: - y = 3x (y equals 3 times x) - x = 4 Simply replace x with 4 in the first equation: y = 3x y = 3(4) y = **12** That's it! When you see "substitute," think "swap in the value." ## Why the wrong options tempt you **Option A (7):** This catches students who *add* instead of multiply — doing 3 + 4 = 7. Always check the operation sign carefully! **Option C (1):** Maybe from confusing division? Or misreading the question entirely. **Option D (34):** This tricks students who just mash the numbers together as "34" instead of calculating 3 × 4. Don't concatenate — calculate! ## Quick takeaway **When you see y = 3x and are given x's value, multiply immediately — substitution means "plug it in and solve."** These questions test if you can follow simple instructions carefully, which JAMB loves to do!