This guide gives you 100 numbered maths questions and answers for Grades 9 to 12, split into 34 fully worked, step-by-step examples (highlighted in boxes) and 66 additional practice questions with answers. Every topic starts with one simple trick, shows it working across 3 to 4 worked examples, then hands you more questions to try using that same trick. The topics (algebra, slope, factoring, trigonometry, exponents, logarithms, derivatives, and statistics) are the same core high school math skills taught in most countries, whether your course is called Grade 9-12, Class 9-12, or Years 9-12. This works best if you actually cover the answer and attempt each question before checking it. The tradeoff is that reading the worked examples alone will not build the skill on its own; you still need to attempt the practice questions yourself.

Key Highlights of Maths Questions and Answers

• 100 questions in total: 34 fully worked, step-by-step examples shown in highlighted boxes, plus 66 further practice questions with answers, all numbered continuously from 1 to 100.
• Every topic section teaches one memorable trick first, like recognizing the 3-4-5 triangle pattern to skip a Pythagorean theorem calculation entirely.
• These topics (linear equations, factoring, trigonometry, functions, logarithms, derivatives, and statistics) are standard across Grade 9-12 math curricula in Canada, the US, the UK, India, and Australia, just under different course names.
• Stanford researcher Jo Boaler’s work on math mindsets shows that students improve fastest when they see the reasoning behind a shortcut, not just the shortcut itself.
• A trick only sticks if you use it on a question you have not seen before, which is why every section ends with unsolved practice questions and answers to check yourself.

100 Maths Questions and Answers, Solved Step by Step With Tricks

If you think you hate math, there is a good chance nobody ever showed you the shortcut that makes a topic click. A flat list of 100 questions with one-word answers does not teach you anything. What actually works is seeing one clear trick, watching it solve a real question step by step, and then trying it yourself while the reasoning is still fresh.

That is exactly how this guide is built. Eight core high school math topics, one trick per topic, 3 to 4 fully worked examples per trick shown in highlighted boxes, and more practice questions with answers so you can test yourself. Every single item, worked example and practice question alike, is numbered continuously from 1 to 100, so nothing is hidden behind a plain answer key.

These topics are not tied to one country’s course codes. Algebra, linear equations, factoring, trigonometry, functions and exponents, logarithms, derivatives, and statistics form the backbone of Grade 9 through Grade 12 math almost everywhere, whether your school calls it Grade 10 Math, Class 10 Maths, or Year 10 Maths. The names change. The skills do not.

How to Actually Use This Guide

Reading a solved example without trying it yourself first feels like progress, but it barely builds any real skill. Cover the answer, attempt the question using the trick, then check your work.

A simple process for each section:

1. Read the trick and make sure you understand why it works, not just what it says.
2. Cover the highlighted box for Question 1 in that section and try to solve it yourself first.
3. Check your steps against the box, not just your final number.
4. Move to the numbered practice questions and attempt all of them before checking any answers.
5. If you get 2 or more wrong, reread the trick and redo the highlighted worked examples once more before trying new questions.

Topic 1: Solving Equations With the “Move and Flip” Trick (Questions 1-12)

Most students learn to solve equations by memorizing steps for every different type of problem. There is a faster way to think about it.

The trick: When a term crosses the equals sign, it flips its operation. A number that was added becomes subtracted. A number that was multiplying becomes dividing. Think of the equals sign as a mirror that flips the sign of anything that crosses it.

Question 1: Solve for x: 2x + 5 = 17

Step 1: The +5 is on the same side as x. Move it across the equals sign, and it flips to -5. 2x = 17 – 5

Step 2: Simplify the right side. 2x = 12

Step 3: The 2 is multiplying x. Move it across, and it flips to dividing. x = 12 / 2

Answer: x = 6

Question 2: Solve for x: 3x – 7 = 2x + 5

Step 1: Move the 2x from the right side to the left. It flips to -2x. 3x – 2x – 7 = 5

Step 2: Simplify the left side. x – 7 = 5

Step 3: Move the -7 across. It flips to +7. x = 5 + 7

Answer: x = 12

Question 3: Solve for x: x/4 + 3 = 9

Step 1: Move the +3 across. It flips to -3. x/4 = 9 – 3

Step 2: Simplify. x/4 = 6

Step 3: The 4 is dividing x. Move it across, and it flips to multiplying. x = 6 × 4

Answer: x = 24

Question 4: Solve for x: 5(x – 2) = 25

Step 1: Expand the brackets first, before moving anything. 5x – 10 = 25

Step 2: Move the -10 across. It flips to +10. 5x = 25 + 10

Step 3: Simplify, then move the 5 across as dividing. 5x = 35 x = 35 / 5

Answer: x = 7

Now Try These Yourself

Topic 2: Slope and Linear Equations With the “Rise Over Run, Begin and Move” Trick (Questions 13-24)

Students often mix up which number in y = mx + b does what. This trick removes the guesswork.

The trick: In y = mx + b, think of “b” as where you Begin on the graph (the y-intercept) and “m” as how much you Move for every step to the right (the slope). To find slope from two points, count the vertical change (rise) over the horizontal change (run).

Question 13: Find the slope between the points (2, 3) and (6, 11)

Step 1: Find the rise (change in y): 11 – 3 = 8

Step 2: Find the run (change in x): 6 – 2 = 4

Step 3: Divide rise by run: 8 / 4

Answer: slope = 2

Question 14: Write the equation of a line with slope 3 that begins at (0, 5)

Step 1: “Begin” tells you b, the y-intercept: b = 5

Step 2: “Move” tells you m, the slope: m = 3

Step 3: Plug both into y = mx + b.

Answer: y = 3x + 5

Question 15: Find the slope of the line 2x + 4y = 8

Step 1: Rearrange into y = mx + b form. Move 2x across (it flips to -2x). 4y = -2x + 8

Step 2: Divide every term by 4. y = -0.5x + 2

Answer: slope = -0.5

Question 16: Do the points (1, 2), (3, 6), and (5, 10) lie on the same straight line?

Step 1: Find the slope between the first two points: (6 – 2) / (3 – 1) = 4 / 2 = 2

Step 2: Find the slope between the second two points: (10 – 6) / (5 – 3) = 4 / 2 = 2

Step 3: Both slopes match, so the points move at the same rate.

Answer: Yes, all three points lie on the same line.

Now Try These Yourself

Topic 3: Factoring Quadratics With the “Multiply and Add” Trick (Questions 25-36)

Factoring feels like guesswork until you have a system. This one works for almost every simple quadratic you will see.

The trick: For x² + bx + c, find two numbers that multiply to give c and add to give b. Those two numbers go straight into your brackets.

Question 25: Factor x² + 7x + 12

Step 1: List factor pairs of 12: (1,12), (2,6), (3,4)

Step 2: Find the pair that adds to 7: 3 and 4

Step 3: Write the brackets using those two numbers.

Answer: (x + 3)(x + 4)

Question 26: Solve x² – 5x + 6 = 0

Step 1: Find two numbers that multiply to 6 and add to -5: -2 and -3

Step 2: Write the factored form. (x – 2)(x – 3) = 0

Step 3: Set each bracket equal to zero and solve.

Answer: x = 2 or x = 3

Question 27: Factor x² – 9

Step 1: Recognize this as a “difference of squares” pattern: a² – b² = (a – b)(a + b)

Step 2: Here, a = x and b = 3, since 3² = 9.

Answer: (x – 3)(x + 3)

Question 28: Solve x² + 2x – 8 = 0 using the quadratic formula

Step 1: Identify a = 1, b = 2, c = -8, then use x = (-b ± √(b² – 4ac)) / 2a

Step 2: Calculate the discriminant: b² – 4ac = 4 – 4(1)(-8) = 4 + 32 = 36

Step 3: Take the square root of 36, which is 6, then plug into the formula. x = (-2 ± 6) / 2

Answer: x = 2 or x = -4

Now Try These Yourself

Topic 4: Right-Angle Trigonometry With the “Spot the Triple” Trick (Questions 37-48)

Trigonometry gets a bad reputation, but a lot of it is pattern recognition once you know what to look for.

The trick: Certain sets of numbers, called Pythagorean triples, always form a right triangle: 3-4-5, 5-12-13, 8-15-17, and their multiples (like 6-8-10). If you spot one, you can skip the Pythagorean theorem calculation entirely.

Question 37: A right triangle has legs of 6 and 8. Find the hypotenuse.

Step 1: Notice that 6 and 8 are double 3 and 4, a multiple of the 3-4-5 triple.

Step 2: The hypotenuse must be double 5.

Answer: hypotenuse = 10

Question 38: Find sin(30°) without a calculator

Step 1: Recall the special 30-60-90 triangle, where the sides are always in the ratio 1 : √3 : 2.

Step 2: Sine is opposite over hypotenuse. For the 30° angle, the opposite side is 1 and the hypotenuse is 2.

Answer: sin(30°) = 1/2

Question 39: A ladder reaches 12 metres up a wall, with its base 5 metres from the wall. Find the length of the ladder.

Step 1: Recognize 5 and 12 as a Pythagorean triple: 5-12-13.

Step 2: The missing side (the ladder, which is the hypotenuse) is 13.

Answer: ladder length = 13 metres

Question 40: Find angle A if tan(A) = 1

Step 1: Recall the special angles: tan(0°) = 0, tan(30°) ≈ 0.577, tan(45°) = 1, tan(60°) ≈ 1.73.

Step 2: Match tan(A) = 1 to the special angle where this is true.

Answer: A = 45°

Now Try These Yourself

Topic 5: Exponent Laws With the “Multiply Adds, Divide Subtracts” Trick (Questions 49-60)

Exponent rules look like a long list to memorize, but they collapse into one idea once you see the pattern.

The trick: When bases match, multiplying means you add the exponents, dividing means you subtract them, and a power raised to another power means you multiply them.

Question 49: Simplify (2³)(2⁴)

Step 1: The bases match (both are 2), and the operation is multiplication, so add the exponents. 2^(3+4) = 2^7

Answer: 128

Question 50: Simplify x⁵ / x²

Step 1: The bases match, and the operation is division, so subtract the exponents. x^(5-2)

Answer: x³

Question 51: Simplify (x³)²

Step 1: This is a power raised to another power, so multiply the exponents. x^(3×2)

Answer: x⁶

Question 52: Solve for x: 3^x = 81

Step 1: Rewrite 81 as a power of 3: 81 = 3 × 3 × 3 × 3 = 3⁴

Step 2: Since the bases now match, the exponents must be equal.

Answer: x = 4

Now Try These Yourself

Topic 6: Logarithms With the “Log Is Just Asking a Question” Trick (Questions 61-72)

Logarithms confuse students mainly because the notation looks intimidating. The idea underneath it is simple.

The trick: log_b(x) is just asking, “What power do I raise b to, to get x?” Rewrite every log question as that plain-English question before doing anything else.

Question 61: Evaluate log₂(8)

Step 1: Ask the question: 2 raised to what power gives 8?

Step 2: 2³ = 8, so the power is 3.

Answer: 3

Question 62: Solve log(x) = 2 (base 10 is assumed when no base is written)

Step 1: Ask the question: 10 raised to what power gives x? The power is 2.

Step 2: So x = 10²

Answer: x = 100

Question 63: Solve log₃(x) = 2

Step 1: Ask the question: 3 raised to what power gives x? The power is 2.

Step 2: So x = 3² = 9

Answer: x = 9

Question 64: Simplify log(100) + log(10)

Step 1: log(100) asks: 10 to what power gives 100? Answer: 2.

Step 2: log(10) asks: 10 to what power gives 10? Answer: 1.

Step 3: Add the two answers together.

Answer: 3

Now Try These Yourself

Topic 7: Derivatives With the “Bring It Down, Then Take One Off” Trick (Questions 73-84)

Calculus looks intimidating on paper, but the very first rule you learn does almost all of the work.

The trick: For f(x) = xⁿ, bring the exponent down in front as a multiplier, then subtract one from the exponent. Any plain number on its own (a constant) simply disappears, since a flat number has no slope.

Question 73: Find the derivative of f(x) = x³

Step 1: Bring the 3 down in front, then subtract one from the exponent. 3x^(3-1)

Answer: f'(x) = 3x²

Question 74: Find the derivative of f(x) = 5x² + 3x

Step 1: Apply the trick to each term separately. For 5x², bring the 2 down and multiply it by the 5: 10x^(2-1)

Step 2: For 3x (which is really 3x¹), bring the 1 down: 3x^(1-1) = 3x⁰ = 3

Answer: f'(x) = 10x + 3

Question 75: Find the derivative of f(x) = x⁴ – 2x² + 7

Step 1: Apply the trick to x⁴: 4x³

Step 2: Apply the trick to -2x²: -4x

Step 3: The constant 7 disappears entirely, since constants have no slope.

Answer: f'(x) = 4x³ – 4x

Question 76: Find the derivative of f(x) = 1/x

Step 1: Rewrite 1/x as x⁻¹, so the trick still applies.

Step 2: Bring the -1 down and subtract one from the exponent: -1x^(-1-1) = -1x⁻²

Answer: f'(x) = -1/x²

Now Try These Yourself

Topic 8: Mean, Median, Mode, and Probability With the “Share, Line Up, Most Popular” Trick (Questions 85-96)

Statistics questions look different from algebra, but each measure has one plain-English job.

The trick: Mean means share equally among everyone. Median means line everyone up and find the middle. Mode means the most popular value. Probability always means favorable outcomes divided by total outcomes.

Question 85: Find the mean of 4, 8, 6, 10, 12

Step 1: Add all the values: 4 + 8 + 6 + 10 + 12 = 40

Step 2: Divide by how many values there are: 40 / 5

Answer: mean = 8

Question 86: Find the median of 3, 7, 9, 12, 15

Step 1: The values are already in order, and there are 5 of them (an odd number).

Step 2: The middle value, the 3rd one, is the median.

Answer: median = 9

Question 87: Find the median of 8, 3, 10, 6

Step 1: Arrange in order: 3, 6, 8, 10. There are 4 values (an even number).

Step 2: Average the two middle values: (6 + 8) / 2

Answer: median = 7

Question 88: Find the probability of rolling a 4 on a standard six-sided die

Step 1: Count the favorable outcomes: only one side shows a 4.

Step 2: Count the total outcomes: 6 sides in total.

Answer: probability = 1/6

Now Try These Yourself

Bonus Round: Mixing Tricks Together (Questions 97-100)

Real tests rarely stick to one topic per question. These last few combine two tricks at once, which is exactly the skill that separates a strong test score from an average one.

Question 97: Solve 2(x + 3)² = 32 for x

Step 1: Move the 2 across using “move and flip.” It becomes dividing. (x + 3)² = 16

Step 2: Take the square root of both sides. Remember both the positive and negative root. x + 3 = ±4

Step 3: Solve both cases separately: x + 3 = 4 gives x = 1, and x + 3 = -4 gives x = -7.

Answer: x = 1 or x = -7

Question 98: Factor and solve x² – 2x – 15 = 0

Step 1: Find two numbers that multiply to -15 and add to -2: -5 and 3.

Step 2: Write the factored form and solve each bracket. (x – 5)(x + 3) = 0

Answer: x = 5 or x = -3

Now Try These Yourself

Why Tricks Work Better Than Memorizing Steps

A trick works because it gives you one idea to hold onto instead of ten disconnected steps. Stanford education researcher Jo Boaler’s work on math mindsets found that students who understand the reasoning behind a shortcut retain it far longer than students who memorize a procedure without knowing why it works.

A mistake to avoid: using a trick without understanding why it works. If you only memorize “multiply adds the exponents” without knowing it comes from repeated multiplication, you will forget it the moment the question looks slightly different.

Common Mistakes Students Make Even When They Know the Trick

• Forgetting the negative root when solving an equation involving a square, like x + 3 = ±4 instead of just +4.
• Applying a trick to a question it was never meant for, like using the difference-of-squares pattern on a trinomial that does not fit it.
• Rushing past the “why” of a trick and only memorizing the “what,” which falls apart on an unfamiliar question.
• Mixing up mean and median when a question specifically asks for the “middle” value.
• Forgetting that a constant disappears when finding a derivative, and accidentally leaving it in the answer.

Conclusion

The fastest way to stop hating math is to stop treating every question as brand new. Underneath 100 different-looking problems are just 8 core ideas, and once a trick clicks, entire categories of questions get easier at the same time. Revisit any section here where you got more than 2 practice questions wrong, and rework the highlighted examples again before moving on.

If your child needs one-on-one support turning these tricks into consistent test results, USCA Academy’s credit courses in Mississauga cover every one of these topics across Grade 9 through Grade 12, with small classes built around exactly this kind of trick-first teaching. Apply for Admissions to get matched with the right course level.

Frequently Asked Questions