Secondary 1 Algebraic Expressions Worksheet

All 5 questions

Each question targets one named concept from the sheet. Read them here, or print the PDF — it has working space under each one.

1. Q1Adding Algebraic Expressions

   Simplify each expression by grouping the like terms.

   1. $5x+3+2x+8$
   2. $9a+4b-3a+b$
   3. Add the two expressions $6m+5$ and $2m-9$.
2. Q2Algebra - Algebraic Expressions

   Consider the algebraic expression $9a+4+3ab-a$.

   1. How many terms does it have?
   2. What is the coefficient of the term $3ab$?
   3. Which term is the constant term?
   4. Name two terms that are like terms.
   5. Evaluate the expression when $a=2$ and $b=5$.
3. Q3Multiplying Algebraic Expressions

   Remove the parentheses and simplify.

   1. $4(2x+5)$
   2. $3(a+6)+2(a-1)$
   3. $6(2m+3)-5$
4. Q4Operations on Algebraic Expressions

   For each pair, state whether the two expressions are equivalent. Justify each answer either by naming the property you used or by giving a value of the variable for which the two expressions disagree.

   1. $3(x+4)$ and $3x+4$
   2. $5y+2y$ and $7y$
   3. $8+n$ and $n+8$
   4. $2(k+3)$ and $2k+6$
5. Q5Synthesis — drawing on several sheets in this topic

   A hockey tournament gives every player a kit: one jersey costing $j$ dollars and one pair of socks costing $8. A team has $12$ players, and each team's coach also receives $2$ jerseys (no socks).

   1. Write a simplified expression for the cost of one team's kits.
   2. The organizers order kits for $5$ teams. Write and simplify an expression for the total cost.
   3. Emma writes the total for the $5$ teams as $70j+96$. Which step did she miss? Explain, then check your own answer using $j=40$.

The 4 challenge problems for this topic are a separate, paid sheet and are not reproduced here.

How to do every concept on this sheet

This is the part worksheet sites usually leave out. Below is the actual reasoning behind each group of questions — not a full solution set, the decisions that get you to one. Read it before you start, or after you get stuck.

An expression is a recipe, not a puzzle

A student meeting 9a + 4 + 3ab − a for the first time usually reads it as a question to answer. It is not. It is a set of instructions waiting for a number: choose a value for a, choose one for b, and the expression produces one result. Q2 is built around exactly that reading — it asks you to count the terms, name a coefficient, find the constant, spot the like terms, and only then substitute and evaluate.

That ordering is deliberate. Most of the marks in this topic are for describing an expression correctly, and a student who cannot name the parts cannot follow an instruction that uses them. “Group the like terms” means nothing until you can point at two.

Grouping like terms: only what you could say out loud (Q1)

Adding 5x + 3 + 2x + 8 is two separate additions that happen to be written on one line: the x terms with each other, the plain numbers with each other. The result is 7x + 11, and the fact that it still has two pieces in it is not a sign of unfinished work. An answer in algebra very often has more than one piece.

Q1(c) adds one wrinkle: it hands you two expressions and asks for their sum. Write the brackets in first — (6m + 5) + (2m − 9) — and then drop them, because a plus sign in front of a bracket changes nothing inside it. That habit costs a second here and saves a great deal later, when the sign in front is a minus.

Multiplying a bracket: every term, without exception (Q3)

4(2x + 5) means four of the whole thing, so both pieces are multiplied:

The number outside is not attached to the first term; it is attached to the bracket. Reaching only the first term is the most common slip in this topic, and it is also the easiest to catch, because a quick substitution exposes it immediately.

Q3(b) puts two brackets on the same line, and the order matters less than the tidying: multiply each bracket out, then collect like terms across the whole expression. Q3(c) finishes with a loose number outside the bracket — and only the constants combine there, because 12m has nothing to pair with.

Equivalent, or not — and the two ways to say so (Q4)

Q4 is where the sheet turns from a computation into an argument. It gives four pairs of expressions and asks whether each pair is equivalent, with a justification. Two kinds of justification are accepted, and which one you owe depends on the answer.

Q5: where the sheet stops being an exercise

The last core question builds an expression for the cost of a team's kit — a jersey at an unknown price plus socks at a known one, for twelve players and a coach — and then multiplies the whole thing by five teams. Every idea on the sheet is in there at once: writing the expression, collecting the like terms, and multiplying a bracket by a number.

It closes by showing you someone else's answer, 70j + 96, and asking which step was missed. It is the bracket again: the 5 was distributed over the jersey term and not over the constant. Finding that in another person's work is a different skill from not making the mistake yourself, and it is the more useful of the two.

Getting the most out of it

Check every simplification with a number

Pick a value — 2 or 3, nothing clever — and put it into the expression you started with and the one you finished with. They must agree. It takes about ten seconds, it catches almost every error on this sheet, and it is why the answers here are written with those checks shown.

Say the terms out loud before combining them

“Seven x plus eleven” is a sentence. “Eighteen x” is a different sentence, and hearing the difference is faster than any rule. If two terms cannot be described as more of the same thing, they do not combine.

Write the substitution with brackets

Replace a by (2), not by 2. Then 9a becomes 9(2) rather than the number 92, and −a becomes −(2) rather than a lost minus sign. A small formatting habit that removes a whole family of mistakes.

Common questions