Mastering Algebra: O Level Foundations, Practice & Problem Solving

Start your algebra journey with a clear study routine. Prepare your learning materials, set personal targets and learn how to practise, check answers and correct mistakes.

Understand variables, coefficients, terms and constants. Translate words into algebra and substitute positive and negative values through worked examples and short practice activities.

Test your understanding with ten questions on algebraic vocabulary, expressions, substitution and everyday applications. Show your working before checking the separate solutions lesson.

Check your answers to all ten practice questions. Follow the explained methods, identify mistakes and strengthen your understanding of signs, brackets and substitution.

Check your understanding of variables, coefficients, constants, expressions and substitution.

Answer all 10 questions. Each question carries 1 mark; the pass mark is 7 out of 10.

Work without a calculator and use your notebook for calculations. If you score below 7, review the study guide and explained solutions before trying again.

Apply your algebra skills to everyday situations. Allow approximately 30 minutes.

Write your answers in a document or neatly in your notebook. Submit a PDF or clear photographs using the assignment submission options. Show all working, define your variables and include units where needed.

TASK 1 — Identify the Parts (4 marks)

Consider the expression 7x − 4y + 12.

a) Name the two variables. (1 mark)
b) State the coefficient of x. (1 mark)
c) State the coefficient of y. (1 mark)
d) State the constant term. (1 mark)

TASK 2 — Translate into Algebra (4 marks)

Let n represent a number. Write an expression for each statement.

a) Nine more than the number. (1 mark)
b) Four less than twice the number. (1 mark)
c) Three times the sum of the number and two. (1 mark)
d) The sum of the number and five, divided by four. (1 mark)

TASK 3 — Substitute Accurately (6 marks)

Show your substitution and calculation.

a) Evaluate 4p − 3 when p = 6. (2 marks)
b) Evaluate q² − 2q when q = −5. (2 marks)
c) Evaluate 3a + 2b when a = −2 and b = 7. (2 marks)

For each part, 1 mark is awarded for correct substitution and 1 mark for the correct final answer.

TASK 4 — Model a Real Situation (6 marks)

A learning club charges a one-time registration fee of PKR 350 plus PKR 150 for each session attended.

a) Choose and define a variable for the number of sessions. (1 mark)
b) Write a formula for the total cost C in PKR. (2 marks)
c) Use your formula to calculate the total cost for eight sessions. Show your working. (2 marks)
d) Explain why the registration fee is added once rather than multiplied by the number of sessions. (1 mark)

BEFORE SUBMITTING

• Answer every part.
• Keep negative signs with their terms.
• Use brackets when substituting negative values.
• Show your calculations.
• Include PKR with your final cost answer.

Total: 20 marks.
Passing grade: 14 out of 20.

Your instructor will review your submission. If you need to resubmit, use the feedback to correct your work before your next attempt.

Identify like terms and simplify expressions by combining their coefficients. Work accurately with negative signs, constants and powers through examples and short practice activities.

Use the distributive law to expand single brackets. Multiply every term accurately, handle negative signs and simplify the result by collecting like terms.

Expand products of two brackets by multiplying every term in one bracket by every term in the other. Collect like terms and handle negative signs, squared brackets and conjugate pairs.

Review explained solutions to all twelve practice questions. Check your handling of like terms, negative signs and bracket products, then correct mistakes and reattempt difficult questions.

Check your skills in collecting like terms and expanding single and double brackets.

Answer all 10 questions without a calculator. Use your notebook for working. Each question carries 1 mark; the pass mark is 7 out of 10.

If you score below 7, review the relevant lessons and practise again before your next attempt.

Demonstrate your skills in simplifying expressions and expanding brackets. Allow approximately 35 minutes. Work without a calculator.

Write your answers in a document or neatly in your notebook. Submit a PDF or clear photographs using the available submission options. Show your working: marks are awarded for method as well as final answers.

TASK 1 — Collect Like Terms (4 marks)

Simplify:

a) 9a − 4a + 2a. (2 marks)
b) 7x + 5y − 3x − 8y + 6 − 2. (2 marks)

For each part: 1 mark for correctly grouping or combining like terms and 1 mark for the correct final expression.

TASK 2 — Expand Single Brackets (4 marks)

Expand:

a) 5(2x − 3). (2 marks)
b) −4(3y − 2). (2 marks)

For each part: 1 mark for showing multiplication of both bracket terms and 1 mark for the correct final expression.

TASK 3 — Expand and Simplify (4 marks)

a) Simplify 10p − (4p − 7). (2 marks)
b) Expand and simplify 3(2t + 5) − 2(t − 1). (2 marks)

For each part: 1 mark for correctly removing or expanding the brackets and 1 mark for collecting like terms correctly.

TASK 4 — Expand Double Brackets (4 marks)

Expand and simplify:

a) (x + 6)(x − 2). (2 marks)
b) (2m − 1)(m + 4). (2 marks)

For each part: 1 mark for showing all four products correctly and 1 mark for the correct simplified expression.

TASK 5 — Explain and Check (4 marks)

A student writes:

(x + 4)² = x² + 16

a) Explain which products the student has missed. (1 mark)
b) Write the correct expansion of (x + 4)². (1 mark)
c) Substitute x = 2 into both (x + 4)² and x² + 16. Show the two results and explain how they demonstrate the error. (2 marks)

BEFORE SUBMITTING

• Answer every part.
• Keep negative signs with their terms.
• Multiply every term inside each bracket.
• Show four products when expanding double brackets.
• Combine only like terms.
• Check that squared brackets include the middle term.

Total: 20 marks.
Passing grade: 14 out of 20.

Your instructor will review your submission. Use any feedback to improve your working before resubmitting.