Maths Mate Term 3 Sheet 4 Answers – A Complete Guide
The maths mate term 3 sheet 4 answers are a frequent search query for students who want to verify their work or understand the reasoning behind each solution. This article walks you through the structure of the sheet, breaks down every problem step by step, highlights common pitfalls, and offers practical tips to boost your confidence in future worksheets. By the end, you will have a clear roadmap that not only supplies the correct answers but also explains the underlying concepts, ensuring lasting mastery of the material Not complicated — just consistent..
Understanding the Maths Mate Workbook
Maths Mate is a structured practice workbook used in many secondary schools across Australia and New Zealand. Each term contains ten sheets, and each sheet is divided into four sections:
- Number and Algebra – calculations, factorisation, and equation solving.
- Measurement and Geometry – perimeter, area, volume, and angle properties.
- Statistics and Probability – data interpretation, mean, median, and simple probability.
- Problem Solving – multi‑step word problems that integrate the above skills.
The design encourages regular revision and self‑assessment. Sheet 4 typically focuses on algebraic manipulation and basic probability, making it a important checkpoint for students transitioning from foundational to more abstract concepts.
What Is Sheet 4 About? In maths mate term 3 sheet 4, you will encounter a mixture of short‑answer and extended‑response questions. The sheet usually contains 12–14 items, each targeting a specific skill. Below is a typical breakdown:
- Questions 1‑4: Simplifying algebraic expressions and factorising quadratics.
- Questions 5‑7: Solving linear equations and checking solutions.
- Questions 8‑10: Calculating probabilities of single‑event outcomes.
- Questions 11‑14: Applying probability to real‑world scenarios, such as drawing cards or rolling dice. Understanding this layout helps you allocate time efficiently during practice and exam conditions.
Step‑by‑Step Guide to Solving Sheet 4 ### 1. Simplifying Algebraic Expressions
Example Question: Simplify (3x + 5 - 2x + 8) Easy to understand, harder to ignore..
Answer: (x + 13) The details matter here..
Explanation:
- Combine like terms: (3x - 2x = x).
- Add the constants: (5 + 8 = 13).
- The simplified form is (x + 13).
Key point: Always look for like terms (terms with the same variable and exponent) before moving on to more complex operations That's the part that actually makes a difference..
2. Factorising Quadratics
Example Question: Factorise (x^2 - 5x + 6).
Answer: ((x - 2)(x - 3)).
Explanation:
- Find two numbers that multiply to +6 and add to ‑5.
- Those numbers are ‑2 and ‑3.
- Write the expression as ((x - 2)(x - 3)).
Tip: When the coefficient of (x^2) is 1, the numbers you need are simply the pair of factors of the constant term that sum to the linear coefficient.
3. Solving Linear Equations
Example Question: Solve (4y - 7 = 9) Worth keeping that in mind..
Answer: (y = 4).
Explanation:
- Add 7 to both sides: (4y = 16).
- Divide by 4: (y = 4).
- Always check by substituting back: (4(4) - 7 = 9) ✔️.
Common mistake: Forgetting to perform the same operation on both sides of the equation Small thing, real impact..
4. Calculating Simple Probabilities
Example Question: A bag contains 4 red, 3 blue, and 5 green marbles. What is the probability of drawing a blue marble?
Answer: (\frac{3}{12} = \frac{1}{4}).
Explanation:
- Total marbles = (4 + 3 + 5 = 12).
- Favourable outcomes (blue) = 3.
- Probability = favourable / total = (3/12 = 1/4).
Remember: Probability is always expressed as a fraction, decimal, or percentage that lies between 0 and 1 (or 0%–100%) Not complicated — just consistent. Turns out it matters..
5. Applying Probability to Real‑World Scenarios
Example Question: If two dice are rolled, what is the probability that the sum is 7?
Answer: (\frac{6}{36} = \frac{1}{6}) Simple as that..
Explanation:
- There are 36 possible ordered outcomes when rolling two six‑sided dice.
- The pairs that sum to 7 are: (1,6), (2,5), (3,4), (4,3), (5,2
, (5,2), and (6,1). These 6 favorable outcomes give a probability of (\frac{6}{36} = \frac{1}{6}) Which is the point..
Advanced tip: Use systematic listing or tree diagrams to avoid missing outcomes when dealing with multiple events.
6. Probability with Cards
Example Question: A standard deck of cards has 52 cards. What is the probability of drawing a heart or a king?
Answer: (\frac{16}{52} = \frac{4}{13}) That alone is useful..
Explanation:
- There are 13 hearts in the deck.
- There are 4 kings, but one of them is already a heart (the king of hearts), so total favorable outcomes = (13 + 3 = 16).
- Probability = (\frac{16}{52} = \frac{4}{13}).
Key takeaway: Use the addition rule for non-mutually exclusive events: (P(A \cup B) = P(A) + P(B) - P(A \cap B)).
7. Solving Quadratic Equations
Example Question: Solve (x^2 + 4x + 4 = 0) Worth keeping that in mind..
Answer: (x = -2).
Explanation:
- Factorise: (x^2 + 4x + 4 = (x + 2)^2).
- Set equal to zero: ((x + 2)^2 = 0).
- Solve: (x = -2) (a repeated root).
Alternative method: Use the quadratic formula (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}) for equations that are hard to factor Nothing fancy..
8. Interpreting Data from Tables
Example Question: The table shows the number of students who prefer different subjects. What is the probability a randomly selected student prefers Maths
Explanation:
- Total students = (10 + 15 + 20 = 45).
- Students preferring Maths = 15.
- Probability = (\frac{15}{45} = \frac{1}{3}).
Key takeaway: Use frequency tables to calculate probabilities by dividing the relevant frequency by the total. Always verify totals before computing ratios.
9. Solving Simultaneous Equations
Example Question: Solve (2x + 3y = 12) and (x - y = 1).
Answer: (x = 3), (y = 2).
Explanation:
- Solve the second equation for (x): (x = y + 1).
- Substitute into the first equation: (2(y + 1) + 3y = 12).
- Simplify: (2y + 2 + 3y = 12 \Rightarrow 5y = 10 \Rightarrow y = 2).
- Back-substitute: (x = 2 + 1 = 3).
Common pitfall: Incorrect substitution or sign errors when eliminating variables.
10. Circle Theorems
Example Question: A circle has a radius of 10 cm. What is the circumference?
Answer: (20\pi , \text{cm}) or approximately (62.8 , \text{cm}).
Explanation:
- Circumference formula: (C = 2\pi r).
- Substitute (r = 10): (C = 2\pi(10) = 20\pi).
Advanced application: Use the relationship (C = \pi d) for diameter-based problems.
11. Percentage Change
Example Question: A shirt costs £40. It is discounted by 25%. What is the new price?
Answer: £30.
Explanation:
- Calculate discount: (25% \times 40 = 10).
- Subtract from original: (40 - 10 = 30).
Important note: Percentage change ≠ percentage of a value. Use (\frac{\text{New} - \text{Original}}{\text{Original}} \times 100%) for change.
12. Function Graphs
Example Question: Plot (y = 2x + 1) and identify the y-intercept.
Answer: Y-intercept = 1.
Explanation:
- The equation is in slope-intercept form (y = mx + c), where (c = 1).
- The graph is a straight line crossing the y-axis at ((0, 1)).
Visual tip: Use a table of values to plot additional points and confirm the line’s slope.
Conclusion
Mastering these topics requires practice and attention to detail. Always:
- Verify answers by substituting values back into equations.
- Use diagrams (e.g., grids, Venn diagrams) for probability and geometry.
- Break down complex problems into smaller steps (e.g., simultaneous equations).
- Memorize key formulas (e.g., (a^2 - b^2), quadratic formula).
By systematically applying these strategies, students can tackle even the most challenging questions with confidence. Remember, clarity in explanations and logical reasoning often outweighs rote memorization in exams.
