Algebraic Expressions
Match Words to Expressions
Draw a line from each phrase to its algebraic expression.
Write the Expression
Circle the correct algebraic expression.
The cost of 3 apples at p cents each
10 more than twice a number n
A number x divided by 4, then add 1
Three less than five times y
Substitute Values
Substitute the given value and circle the correct answer.
If x = 3, find 4x + 2
If n = 5, find 2n − 3
If y = 4, find y² + 1
If m = 6, find 3m ÷ 2
Like Terms or Unlike Terms?
Sort each pair into the correct column.
Simplify by Collecting Like Terms
Match each expression to its simplified form.
Evaluate Formulas
Use the formula to find the answer.
A = lw. Find A when l = 7, w = 4.
P = 4s. Find P when s = 6.
d = st. Find d when s = 60, t = 3.
A = ½bh. Find A when b = 10, h = 6.
Create and Evaluate Your Own Expression
Write and solve your own algebra problems.
Write an algebraic expression for: 'I start with x books, buy 4 more, then give away 2.' Evaluate when x = 10.
A mobile plan costs $20 per month plus $0.10 per text. Write a formula for monthly cost C when you send t texts. Find C when t = 50.
Expanding Single Brackets
Expand by multiplying each term inside the brackets.
3(x + 4)
2(5 − y)
4(2a + 3)
5(3 − 2m)
Collecting Like Terms — Multi-Variable
Match each expression to its simplified form.
Substituting Negative Values
Substitute the given negative value and simplify.
Find 2x + 7 when x = −3
Find 4 − 3y when y = −2
Find a² + a when a = −4
Find 5n − n² when n = −1
Formulas for Perimeter and Area
Write an algebraic formula and evaluate it.
Write a formula for perimeter P of a rectangle with length (x + 3) cm and width x cm. Find P when x = 5.
A square has side length (2n) cm. Write a formula for its area A. Find A when n = 4.
A triangle has base 2k cm and height (k + 1) cm. Write an expression for its area. Find area when k = 3.
Expression Type Sort
Sort each algebraic item into the correct category.
Perimeter Expressions
Write and simplify an algebraic expression for the perimeter of each shape.
A pentagon has sides: x, x+2, 2x, 3x−1, x+5. Write and simplify the perimeter expression.
A rectangle has length (3n + 4) and width (n − 2). Write and simplify the perimeter formula.
Expanding Brackets with Negatives
Expand each expression, being careful with negative signs.
−2(x + 3)
−(4a − 5)
3 − 2(y − 1)
Algebraic Word Problems
Write an algebraic expression and solve.
Tickets to a concert cost $x each for adults and $y for children. Write expressions for: (a) cost of 3 adults (b) cost of 2 adults and 4 children (c) change from $100 for 1 adult and 3 children
A square garden has side length s metres. It is to be fenced, but one side is against a wall. Write a formula for the length of fencing needed. If s = 8, how much fencing?
Expressions — Sort by Number of Terms
Sort each expression by the number of terms it contains after simplification.
Writing and Evaluating Formulas
Write a formula then evaluate it.
A pizza delivery service charges a $5 delivery fee plus $12 per pizza. Write a formula for total cost C of n pizzas. Evaluate for n = 3.
A car hire company charges $35 per day plus $0.15 per kilometre. Write a formula for total cost C. Find the cost for 5 days and 200 km.
Exploring Algebraic Patterns
Investigate and generalise each pattern.
The sum of the first n odd numbers: 1, 1+3=4, 1+3+5=9. What is the pattern? Write a formula for the sum of the first n odd numbers.
Investigate what happens when you multiply (n+1)(n−1) for several values of n. Write the pattern as an algebraic identity.
Algebraic Proof
Use algebra to prove each result for all values.
Prove that the sum of any two consecutive even numbers is divisible by 4. (Hint: let the even numbers be 2n and 2n+2.)
Prove that the square of an odd number is always odd. (Hint: any odd number can be written as 2n+1.)
Equivalent Expressions
Show that each pair of expressions is equivalent by expanding and simplifying.
Show that 2(3x + 4) − (x + 3) = 5x + 5.
Show that (x + 3)² − 9 = x² + 6x. (Expand both sides.)
Patterns and nth Term
Find the nth term rule for each pattern.
Pattern: 5, 8, 11, 14, 17… Find the rule for the nth term and predict the 20th term.
Pattern: 3, 7, 11, 15, 19… Find the nth term formula. Is 99 in this sequence?
Design a Tile Pattern
Investigate and write an algebraic rule for a growing tile pattern.
Pattern 1: 1 tile. Pattern 2: 5 tiles. Pattern 3: 9 tiles. Pattern 4: 13 tiles. Draw patterns 1–4 and find the nth term rule.
Using your rule, find how many tiles are in Pattern 10 and Pattern 50.
Investigation: Always, Sometimes, Never
For each statement, decide if it is always true, sometimes true, or never true. Justify with algebra or examples.
2(a + b) = 2a + b
n² > n
The sum of two consecutive integers is odd.
Algebraic Reasoning — Number Tricks
Use algebra to explain a number trick.
Think of a number. Double it. Add 10. Halve the result. Subtract the original number. What do you always get? Use algebra to prove it.
Think of a two-digit number. Reverse the digits. Add the two numbers. Divide by 11. The result is always the sum of the two digits. Prove this algebraically. (Let the tens digit be a and units digit be b.)
Create Your Own Algebraic Investigation
Design an algebraic investigation.
Create a number pattern and write its nth term formula. Check by substituting n = 1, 2, 3, 4.
Write a word problem that requires algebra to solve. Include the solution.
Write an algebraic identity (always-true statement) and verify it for three different values.
Reflection: My Algebra Journey
Summarise your learning.
Explain in your own words what 'collecting like terms' means. Give an example.
What is the difference between an expression and an equation? Give one example of each.
What was the most challenging idea in this worksheet? What helped you understand it?
Algebra at Home
Look for algebra in everyday life.
- 1Find a real phone, electricity, or streaming plan and write its cost as an algebraic formula.
- 2Pick a number and create a 'magic number trick' using algebra. Test it on family members.
- 3Research how spreadsheet formulas (like SUM, IF) connect to algebraic expressions.
- 4Find a pattern at home (tiles, fence posts, windows) and write an algebraic rule for it.
- 5Look up 'nth term' or 'arithmetic sequence' on Khan Academy and do 3 practice problems.
Extending — Patterns in Pascal's Triangle
Investigate the connection between Pascal's Triangle and expanding brackets.
Write the first 5 rows of Pascal's Triangle. Identify the pattern in each row.
Expand (x + 1)², (x + 1)³. What connection do you notice with Pascal's Triangle? Write your conjecture.
Extending — Forming and Solving Algebraic Equations
Write an equation for each situation, then solve it.
A rectangle has perimeter 56 cm. Its length is 3 times its width. Find the dimensions.
Five consecutive odd integers sum to 75. Write and solve an equation to find them.
The sum of a number and its square is 42. Write a quadratic equation for this situation. (You do not need to solve it — just form it.)
Extending — Match Expression to Its Simplified Form
Draw a line to match each expression to its simplified or expanded equivalent.
Extending — Evaluating Polynomial Expressions
Circle the correct value of each expression.
x² − 3x + 2 when x = 4
2a³ when a = −2
p² − q² when p = 5, q = 3
Extending — Generalising Visual Patterns
Use algebra to describe visual patterns.
A pattern of L-shapes is made with tiles. Term 1 has 3 tiles, Term 2 has 5 tiles, Term 3 has 7 tiles. Write the nth term formula. How many tiles in Term 20?
Draw Term 4 of this pattern and verify your formula gives the correct count.
A square pattern grows: Term 1 has 1 tile, Term 2 has 4, Term 3 has 9. Write the nth term formula. Is this linear or non-linear? Explain.
Extending — Algebra and Geometry
Use algebraic expressions to solve geometry problems.
The angles of a triangle are x°, (2x + 10)°, and (3x − 40)°. Write an equation using the triangle angle sum and solve for x. Then find all three angles.
A rectangle has area (x² + 5x + 6) cm². If its width is (x + 2) cm, write an expression for its length by factorising.
Extending — Sort by Degree
Sort each expression by its degree (highest power of the variable).
Extending — Algebra Mini-Portfolio
Demonstrate your algebraic skills in a structured mini-portfolio.
Write and simplify three expressions of increasing complexity: one linear, one quadratic, one with two variables.
Describe in your own words the difference between factorising and expanding. Give one example of each.
Pose one algebraic problem of your own at 'extending' level, then solve it. Include a real-world context.