Algebra Quest – Learn Algebra through Stories & Games

Welcome to Algebra Quest

Algebra isn’t just about letters and numbers – it’s a way to solve real problems and tell stories about our lives. You will follow Zainab, a young student from Abuja, as she discovers how algebra helps her plan her savings, budget her market purchases and even calculate travel times across Nigeria. Each level contains engaging games, interactive challenges and quizzes to help you understand and master algebra from the basics through more advanced topics.

Use the navigation above to choose your level. Your progress and points are saved automatically, so you can return at any time. Good luck, adventurer!

Level 1: Foundations of Algebra

Meet Zainab. She has a dream of opening her own stall at the Wuse market in Abuja and is at the beginning of her Algebra Quest. To price her goods and keep track of her profits she needs to speak the language of algebra – this is the first step in her journey.

In algebra we use variables (x or y) to represent unknown quantities^ℹ️, and constants (fixed numbers) to represent known values^ℹ️. The numbers that multiply variables are called coefficients^ℹ️, and when we combine variables and constants without an equals sign we call this an expression^ℹ️.

For example, if Zainab sells a bowl of beans for ₦300 and makes ₦100 profit per sale, we could write her daily profit as P = 100x, where x is the number of bowls she sells and the coefficient 100 tells us the profit per bowl. Understanding this helps her set prices and plan how many bowls she needs to sell each day to reach her goals.

Once you are comfortable with these building blocks, you can combine them into equations^ℹ️, which use an equals sign to show that two expressions are the same. Don’t worry if this is new; we will practise together using a game and a quiz.

Help Zainab match each algebra term with its definition. Each correct pair earns you points!

Level 2: Linear Equations & Real‑Life Problems

Zainab’s quest continues. She now wants to plan her time and budget wisely. For example, if she wants to arrive at Jabi Park before the last bus leaves at noon, she must figure out how long it takes to reach the park given different speeds and distances. This leads us to linear equations^ℹ️, equations where variables are not squared or multiplied together.

A typical linear equation looks like ax + b = c, where a, b and c are constants and x is the unknown quantity we are trying to find. When you solve the equation you find the value of x that makes both sides equal. In Nigeria, you might use a linear equation to plan how many yams to buy for a party within a given budget or to calculate travel time when visiting family in Lagos. Zainab uses linear equations to schedule her deliveries and balance her travel time with her business hours.

To form a linear equation you start by identifying the unknown quantity (the variable) and then describe how it relates to known amounts. For instance, if bus fare from Abuja to Kaduna costs ₦150 per passenger and you have ₦700 in your pocket, you can write an equation to find how many passengers you can pay for: 150x = 700. Here x represents the number of passengers. To solve, divide both sides by 150 to find x = 700 ÷ 150 ≈ 4.67, meaning you can pay for four passengers and will need a little more money for a fifth ticket.

Example: Solve 3x + 5 = 14

We want to find the value of x that makes the equation true.

Start with the equation: 3x + 5 = 14.
Subtract 5 from both sides to isolate the term with x: 3x = 14 − 5 = 9.
Divide both sides by 3 to solve for x: x = 9 ÷ 3 = 3.

So the solution is x = 3. We check by substituting back: 3 × 3 + 5 = 9 + 5 = 14, which matches the right side.

Practice Solving a Linear Equation

Use the controls below to explore how linear equations balance. Adjust the constant difference k (this represents how far the left‑hand side is shifted) and the multiplier m (this tells us how many times faster the right‑hand side grows), then move the slider to simulate different times. Watch how the left‑hand side (LHS) and right‑hand side (RHS) of the equation change. When you are ready, try the generated problems and test yourself with the quiz.

Constant difference (k): Multiplier (m):

Minutes before noon (x): 30 min

Current clock time (T): — this is the clock time corresponding to minutes after 10 am.

Left‑hand side (LHS = T − k):

Right‑hand side (RHS = m × x):

Solution: x = (120 − k)/(m + 1) = min, and therefore T = min after 10 am ().

Quick Linear Equation Quiz

Level 3: Quadratics & Beyond

As Zainab’s quest advances, she faces more challenging problems, such as quadratic equations and systems of equations. Quadratic equations involve terms like x² (squared variables) and can describe real situations like the arc of a football kicked across a field or the profit curve for her business.

The general form of a quadratic equation is ax² + bx + c = 0, where a, b and c are constants and a ≠ 0. When Zainab writes her profit as a polynomial in terms of the number of items she produces, she might get a quadratic function. Her quest now is to learn how to solve such equations.

To determine how many solutions a quadratic has, we calculate the discriminant^ℹ️, which is the part under the square root in the quadratic formula. If b² − 4ac is positive, there are two distinct real solutions; if it equals zero there is exactly one real solution (a repeated root); and if it is negative the solutions are complex numbers. We then use the quadratic formula

x = \frac{-b \pm \sqrt{b² - 4ac}}{2a}

to find the roots (solutions). In Nigeria, quadratics can help with everything from calculating the best time to harvest crops to predicting profits from an investment. Zainab uses these tools to model her business’s profit and decide how many products to make.

Example: Solve x² + 5x + 6 = 0

To solve a quadratic equation we can try to factorise^ℹ️ or use the quadratic formula.

Identify the coefficients: a = 1, b = 5, c = 6.
Look for two numbers that multiply to c (6) and add up to b (5). These numbers are 2 and 3.
Rewrite the equation as (x + 2)(x + 3) = 0. If a product is zero then one of the factors must be zero.
Set each factor equal to zero: x + 2 = 0 or x + 3 = 0, giving solutions x = -2 and x = -3.

You can check by substituting each solution back into the original equation and confirming that it equals zero.

Example: Solve 2x² + 3x − 2 = 0 using the quadratic formula

Sometimes factorisation isn’t easy or possible. In those cases we use the quadratic formula:

Identify the coefficients: a = 2, b = 3, c = -2.
Compute the discriminant: Δ = b² − 4ac = 3² − 4×2×(-2) = 9 + 16 = 25. Because the discriminant is positive, there will be two real solutions.
Apply the quadratic formula: x = [−b ± √Δ] / (2a) = [−3 ± 5]/(4).
This gives two solutions: x = (−3 + 5)/4 = 2/4 = 0.5, and x = (−3 − 5)/4 = −8/4 = −2.

We check both solutions by substituting back into 2x² + 3x − 2 and verifying they make the expression zero.

Show your working (optional): First root: Second root:

Congratulations on reaching the final level! Keep practising and exploring algebra. The skills you’ve learned—from understanding variables to solving equations—will help you in everyday life and future studies. Remember, mathematics is a tool to describe and solve problems in the world around you.

Real‑World Applications of Algebra

Algebra isn’t just an academic exercise—it’s the engine behind many of the calculations and predictions we make every day. Below are some ways algebra touches the real world in Nigeria and beyond, with polynomials and other algebraic tools playing central roles:

Polynomials & Profit: Entrepreneurs model profit with quadratic or cubic functions to see how revenue changes with the number of products sold. For example, Zainab might find that her profit follows a curve like P(x) = -2x² + 8x + 10. Solving P(x) = 0 tells her the break‑even points and helps her decide how many items to produce.
Budgeting & Finance: Linear equations and inequalities are used to plan monthly expenses and savings. Compound‑interest formulas (exponential functions) show how money grows over time in a bank account or investment.
Agriculture & Environment: Farmers calculate fertiliser or seed amounts per hectare and model crop growth using quadratic, exponential or logistic functions that depend on rainfall and soil quality. Algebra also helps design irrigation systems and predict harvest yields.
Transportation & Navigation: Systems of equations help plan efficient routes and schedules. Equations of motion allow us to estimate travel time, speed and fuel consumption for vehicles travelling between Abuja and Lagos, for example.
Technology & Engineering: Engineers use algebra to design buildings, smartphones and bridges, solving simultaneous equations to calculate forces, voltages and trajectories. In physics, quadratic and higher‑order equations describe projectile motion, electrical circuits and signals.

These examples show that algebra is a toolkit for solving real problems—from business decisions to scientific discoveries. As you continue your quest, keep looking for algebra in the world around you and imagine how you might use it to make smart choices.

Review & Feedback

Here you can review your answers to previous quizzes and practice problems. See which questions you answered correctly or incorrectly and read the step‑by‑step solutions to understand how to solve them.

Glossary of Algebra Terms

This glossary contains definitions of the key concepts used throughout the course. Click on the information icons ℹ️ in the lessons to see brief explanations, and refer here for more detail.

🔤 Variable – A symbol (usually a letter) that stands for an unknown number. For example, in 3x + 5 = 11, x is the variable.
🔢 Constant – A fixed number that does not change. In the expression 4y − 8, the numbers 4 and −8 are constants.
🎯 Coefficient – The number that multiplies a variable. In 7a, the coefficient of a is 7.
📄 Expression – A combination of variables, constants and operators without an equals sign, such as 5x + 3.
= Equation – A statement that two expressions are equal, like 2x + 3 = 11.
➗ Linear equation – An equation in which the highest power of the variable is 1, typically written in the form ax + b = c.
📈 Quadratic equation – An equation where the variable is squared (power of 2), usually written as ax² + bx + c = 0.
💡 Discriminant – The part of the quadratic formula under the square root (b² − 4ac) that indicates the number and type of solutions.
✂️ Factorisation – Writing an expression as a product of simpler expressions or factors. For example, x² − 5x + 6 can be factorised as (x − 2)(x − 3).
🧮 Solution – The value(s) of the variable that make an equation true.