Gr 10 Maths Worksheets (Ages 15-16) | Level M26: Real Numbers, Polynomials & Pairs of Equations

🎓 Launch offer: 80% OFF every MathSmith workbook with code LAUNCH80 (first 1000 orders). Click Add to Cart, then enter LAUNCH80 in the discount box before you pay.

Not sure which level your child needs? Take the free 40-question placement test: https://ebooks.thecodecrafters.net/placement

See free sample pages first: https://ebooks.thecodecrafters.net/

Help your child build absolute confidence and mastery in mathematics. This comprehensive workbook from MathSmith takes a highly structured, "one-rung-at-a-time" approach to Real Numbers, Polynomials and Pairs of Equations, ensuring students fully understand concepts before moving forward.

Instead of overwhelming learners with random equations, this workbook uses a carefully scaffolded, predictable learning ladder. It is perfect for homework, structured independent study, or mastery practice.

📊 What Is Included?

1 Complete Level (Level M26)

24 Structured Sub-levels for gradual progression

96 Printable Worksheets

800 Total Problems for thorough practice

Full Answer Key online, unlocked by the order ID on your Payhip receipt, for quick, stress-free marking

🗺️ Curriculum Breakdown

This collection focuses deeply on mastering Real Numbers, Polynomials and Pairs of Equations through a carefully curated system:

The division line, and what it says about a number (6 Sub-levels): Six rungs on one line: dividend = divisor x quotient + remainder, with the remainder smaller than the divisor. Euclid's lemma says it can always be written, in one way only; Euclid's algorithm writes it again one place to the LEFT until nothing is left over, and the last divisor is the HCF - which is the ladder, and the first half of the level's notation. Then the fundamental theorem of arithmetic, which says a number's primes are its own and nobody else's, and what that buys: the HCF and LCM read off the prime powers, a proof that the root of a prime is not a fraction, and the rule that says in advance whether a fraction's decimal will stop - read off its denominator in lowest terms, which is the half that gets skipped.

A polynomial's zeroes, and what its numbers already say (5 Sub-levels): Five rungs. A zero is where a graph meets the x-axis, which a child can count before they can find one. Then the claim that the zeroes are hiding in the coefficients all along - they add to minus b over a and multiply to c over a, and the minus is where it goes wrong - with the cubic's three relations and the question run backwards, where the zeroes are given and the polynomial is wanted. The strand ends with the division line again, with polynomials in it: divided the long way, every power in a column of its own, until the remainder is smaller than the divisor.

Two equations at once, and what their coefficients say (4 Sub-levels): Four rungs before any solving. A pair of equations and its picture - two lines, which cross once or never; the three ratios that say which, before anything is drawn, and the third case the drawing cannot show, where the two equations are one line written twice; the unknown coefficient chosen to make a pair parallel or the same line; and the pair solved by drawing, including the answer 'there is none'.

Solving the pair: every column, every time (6 Sub-levels): Six rungs of the three methods. Substitution, written across the page. Elimination, in the level's own notation - the pair braced, numbered and set in columns, x over x and y over y - first where a column already matches and then where an equation has to be multiplied through first: every term of it, the number included. Cross-multiplication with its diagram, whose order is the one thing nobody can rebuild under time pressure. Choosing between them, and a pair that is linear only once one over x has been given a name of its own.

The pair at work (3 Sub-levels): Three rungs of stories with two unknowns in them - numbers and ages, speeds, and work, money and fractions. The letters are named before they are used, every statement becomes one equation, and the answer is put back into the story rather than into the equations, because a pair can be solved perfectly and still be the wrong pair.

🎯 Who Is This For?

Parents looking to provide structured math support at home.

Homeschoolers searching for a sequential curriculum to guarantee zero gaps in math skills.

Teachers & Tutors looking for bite-sized, scaffolded printables for classroom morning work or targeted intervention.

📖 How To Use This Workbook

Print the workbook, read each rung's method page, and let your child work inside the printed frame. Then check the answers your way: in the printable answer-key PDF included in this download, or online, one page at a time, with the order ID on your Payhip receipt (valid for six months). Please keep the answer key for the adult marking the work and do not share it with your child: the workbook only works if they have worked each answer out for themselves.

Step-by-step manual and video guide: https://ebooks.thecodecrafters.net/manual/

Check the answers: https://ebooks.thecodecrafters.net/answers

⚙️ Digital Delivery Details

Format: four instant-download PDFs (free sample, sample answers, workbook, full answer key). The answer key is also available online.

Print Ready: Easily printable on home or school printers.

Usage: Licensed for individual family or single-classroom use.