Mastering Key Maths Skills: GCSE Essentials
Mastering Key Maths Skills
Lesduur is: 60 minOnderdelen in deze les
Mastering Key Maths Skills
What do you already know about core GCSE maths topics?
Learning Objective
At the end of the lesson you will understand Pythagoras' theorem, trigonometry, percentage change, bar graphs, and division and multiplication of fractions. You will also be able to solve key questions for each topic.
Pythagoras' Theorem: Introduction
Pythagoras' theorem helps find the length of a side in a right-angled triangle. The formula is a² + b² = c².
Example of Pythagoras' Theorem
If a = 3 and b = 4, then c² = 3² + 4² = 9 + 16 = 25. So, c = 5.
Pythagoras' Theorem: Practice Questions
1. a = 5, b = 12: Find c. 2. a = 8, b = 15: Find c. 3. a = 7, c = 25: Find b. 4. b = 9, c = 15: Find a. 5. a = 6, b = 10: Find c.
Answers: Pythagoras' Questions
1. c = 13 2. c = 17 3. b = 24 4. a = 12 5. c = 11.66
Trigonometry Basics
Trigonometry uses ratios to find angles and sides in right-angled triangles. Key terms: Sine, Cosine, Tangent.
Sine, Cosine and Tangent
SOHCAHTOA: Sine = Opposite/Hypotenuse Cosine = Adjacent/Hypotenuse Tangent = Opposite/Adjacent
Trigonometry: Practice Questions
1. sin(30°) = ? 2. cos(60°) = ? 3. tan(45°) = ? 4. In a triangle, opposite = 4, hypotenuse = 5: Find angle A. 5. Adjacent = 3, hypotenuse = 5: Find cos(A).
Answers: Trigonometry
1. 0.5 2. 0.5 3. 1 4. angle A ≈ 53.1° 5. cos(A) = 0.6
Understanding Percentage Change
Percentage change shows increase or decrease. Formula: (difference/original) × 100%.
Example: Percentage Change
If a price rises from £40 to £50: Change = £10. Percentage change = (10/40)×100 = 25% increase.
Percentage Change: Practice Questions
1. £60 to £90 2. £100 to £80 3. 200g to 250g 4. 500ml to 400ml 5. £150 to £180
Answers: Percentage Change
1. 50% increase 2. 20% decrease 3. 25% increase 4. 20% decrease 5. 20% increase
Bar Graphs: What Are They?
Bar graphs display data using rectangular bars. Bars show quantity or frequency for categories.
Interpreting a Bar Graph
Look at axes labels, bar heights and what each bar represents.
Bar Graphs: Practice Questions
1. Which bar is tallest? 2. What is the value for 'B'? 3. What category has the lowest value? 4. Find the total of all bars. 5. How many more does A have than C?
Answers: Bar Graphs
Sample answers: 1. 'D' is tallest. 2. 8. 3. 'F'. 4. 34. 5. 4 more.
Fractions: Multiply & Divide
Flip the second fraction, then multiply. 1/2 ÷ 2/3 = 1/2 × 3/2 = 3/4.
Multiplying:
Multiply tops together, bottoms together. 1/2 × 2/3 = 2/6 = 1/3.
Dividing:
Fractions: Practice Questions
1. 1/3 × 1/4 2. 2/5 × 3/7 3. 2/3 ÷ 4/5 4. 3/8 ÷ 1/2 5. 3/10 × 5/6
Answers: Fractions
1. 1/12 2. 6/35 3. 5/6 4. 3/4 5. 1/4
Well Done!
You have completed practice on Pythagoras' theorem, trigonometry, percentage change, bar graphs, and fractions. Keep practising to master these topics!
Write down 3 things you learned in this lesson.
Write down 2 things you want to know more about.
Ask 1 question about something you haven't quite understood yet.
