Gcse Maths Questions By Topic

GCSE Maths Questions by Topic: A Comprehensive Guide

This article provides a detailed breakdown of GCSE maths questions by topic, designed to help students prepare effectively for their exams. We'll cover key areas, offering example questions and explanations to solidify your understanding. Remember, consistent practice is crucial for success in GCSE maths. This guide will act as a valuable resource for revising and identifying areas needing extra attention. Mastering each topic will build your confidence and improve your overall exam performance. Let's dive in!

1. Number

This fundamental area covers a wide range of concepts, including:

1.1 Number Properties:

• Integers, decimals, and fractions: Understanding their relationships and performing operations (addition, subtraction, multiplication, division) fluently. Example: Calculate (2/3) + 0.75 - 5.

• Order of operations (BIDMAS/BODMAS): Applying the correct sequence of operations: Brackets, Indices, Division and Multiplication (from left to right), Addition and Subtraction (from left to right). Example: Evaluate 3 + 2 x (4 - 1)²

• Prime numbers and factors: Identifying prime numbers and finding the prime factorization of a number. Example: Find the prime factorization of 72.

• Highest common factor (HCF) and lowest common multiple (LCM): Determining the HCF and LCM of two or more numbers. Example: Find the HCF and LCM of 18 and 24.

• Indices (powers and roots): Understanding and applying rules of indices, including positive, negative, and fractional indices. Example: Simplify (x³)² and find the value of √64.

• Standard form: Expressing very large or very small numbers in standard form (scientific notation). Example: Write 3,400,000 in standard form and convert 2.5 x 10⁻³ to an ordinary number.

1.2 Calculations and Estimation:

• Percentages: Calculating percentages, percentage increase/decrease, and finding original values. Example: Calculate 15% of 200 and find the original price if a 10% discount reduces the price to £81.

• Ratio and proportion: Solving problems involving ratios and proportions. Example: Share £60 in the ratio 2:3:5.

• Estimation and approximation: Rounding numbers and using estimation to check answers. Example: Estimate the value of (3.14 x 5.9) / 1.98.

1.3 Number Patterns and Sequences:

• Arithmetic sequences: Identifying and generating arithmetic sequences and finding the nth term. Example: Find the nth term of the sequence 2, 5, 8, 11...

• Geometric sequences: Identifying and generating geometric sequences and finding the nth term. Example: Find the nth term of the sequence 3, 6, 12, 24...

2. Algebra

Algebra forms a significant part of the GCSE maths syllabus, encompassing:

2.1 Expressions, Equations, and Inequalities:

• Simplifying algebraic expressions: Combining like terms and expanding brackets. Example: Simplify 3x + 2y - x + 5y. Expand 2(x + 3) - (x - 1).

• Solving linear equations: Finding the value of the unknown variable in linear equations. Example: Solve 3x + 5 = 14.

• Solving simultaneous equations: Finding the values of two unknowns in a system of equations. Example: Solve the simultaneous equations: x + y = 7 and x - y = 1.

• Solving inequalities: Finding the range of values satisfying an inequality. Example: Solve 2x - 3 > 7. Represent the solution on a number line.

2.2 Quadratic Equations and Graphs:

• Solving quadratic equations by factorization: Factoring quadratic expressions to solve equations. Example: Solve x² + 5x + 6 = 0.

• Solving quadratic equations using the quadratic formula: Applying the quadratic formula to solve equations. Example: Solve 2x² - 3x - 2 = 0 using the quadratic formula.

• Sketching quadratic graphs: Understanding the shape of quadratic graphs and their key features (vertex, intercepts). Example: Sketch the graph of y = x² - 4x + 3, identifying its vertex and intercepts.

2.3 Algebraic Manipulation:

• Factorization: Factoring algebraic expressions, including quadratic expressions and expressions with common factors. Example: Factorize x² - 9 and 3x² + 6x.

• Expanding brackets: Expanding brackets in algebraic expressions. Example: Expand (x + 2)(x - 3).

• Forming and solving equations: Forming equations from word problems and solving them. Example: A rectangle has a length of (x+3) cm and a width of (x-1) cm. If its area is 20cm², form an equation and solve to find the value of x.

3. Geometry and Measures

This section focuses on shapes, space, and measurement:

3.1 Shapes and their Properties:

• Angles and lines: Understanding different types of angles (acute, obtuse, right angle, reflex) and lines (parallel, perpendicular). Example: Find the missing angle in a triangle where two angles are 40° and 70°.

• Triangles: Properties of different types of triangles (isosceles, equilateral, scalene, right-angled) and their angle relationships. Example: Calculate the length of the hypotenuse in a right-angled triangle with sides of length 3cm and 4cm.

• Quadrilaterals: Properties of different types of quadrilaterals (square, rectangle, parallelogram, rhombus, trapezium, kite). Example: Find the area of a parallelogram with base 8cm and height 5cm.

• Circles: Properties of circles (radius, diameter, circumference, area). Example: Find the area and circumference of a circle with radius 7cm.

• Polygons: Properties of polygons (interior and exterior angles, regular and irregular polygons). Example: Find the sum of the interior angles of a pentagon.

3.2 Mensuration:

• Area and perimeter: Calculating the area and perimeter of various shapes. Example: Find the area and perimeter of a rectangle with length 10cm and width 6cm. Find the area of a triangle with base 12cm and height 8cm.

• Volume and surface area: Calculating the volume and surface area of 3D shapes (cuboids, prisms, cylinders, cones, spheres). Example: Find the volume of a cuboid with length 5cm, width 3cm, and height 4cm.

3.3 Transformations:

• Translation, reflection, rotation: Understanding and applying these transformations to shapes. Example: Reflect a triangle in the line y=x.

3.4 Constructions:

• Using compasses and ruler: Constructing geometric shapes and lines accurately. Example: Construct an equilateral triangle with sides of length 5cm.

4. Statistics and Probability

This area covers data handling and chance:

4.1 Data Handling:

• Collecting and representing data: Using various methods to collect and represent data (bar charts, pie charts, histograms, scatter graphs). Example: Create a bar chart to represent the number of students who prefer different subjects.

• Averages and measures of spread: Calculating the mean, median, mode, and range of a data set. Example: Find the mean, median, mode, and range of the data set: 2, 5, 7, 2, 9, 11, 2.

• Interpreting data: Analyzing data from charts and graphs. Example: Interpret a line graph showing the temperature over a period of time.

4.2 Probability:

• Probability calculations: Calculating the probability of simple events and combined events. Example: What is the probability of rolling a 6 on a fair six-sided die? What is the probability of rolling a 6 and then a 3?

• Relative frequency: Understanding relative frequency and its relationship to probability. Example: If a coin is tossed 100 times and lands on heads 55 times, what is the relative frequency of getting heads?

• Tree diagrams and Venn diagrams: Using these diagrams to represent and solve probability problems. Example: Use a tree diagram to find the probability of getting two heads when tossing a coin twice.

5. Ratio, Proportion, and Rates of Change

This section covers proportional reasoning and changes over time:

5.1 Ratio and Proportion:

• Simplifying ratios: Expressing ratios in their simplest form. Example: Simplify the ratio 12:18.

• Direct and inverse proportion: Understanding direct and inverse proportions and solving problems involving them. Example: If y is directly proportional to x, and y=6 when x=2, find the value of y when x=5.

• Scale diagrams and maps: Working with scale diagrams and maps. Example: A map has a scale of 1:50,000. If the distance between two points on the map is 4cm, what is the actual distance?

5.2 Rates of Change:

• Speed, distance, time: Calculating speed, distance, and time using the formula speed = distance/time. Example: A car travels 120km in 2 hours. What is its average speed?

• Density, mass, volume: Calculating density, mass, and volume using the formula density = mass/volume. Example: A cube with a volume of 8cm³ has a mass of 24g. What is its density?

Conclusion

This comprehensive guide provides a structured overview of GCSE maths topics and includes example questions to aid your understanding. Remember to practice regularly, focusing on areas where you feel less confident. Consistent effort and targeted revision will significantly improve your GCSE maths performance. Good luck with your studies! Remember to consult your textbooks and teachers for further support and clarification. Through diligent work and a clear understanding of each topic, you can achieve your desired outcome in your GCSE maths examination. Don't hesitate to revisit challenging topics and seek additional practice questions to reinforce your learning. Success in GCSE Maths is within your reach!