🎓 Mastering GCSE Maths – Complex Indices Made Simple!In this short session, I helped my student go from confused to confident with one of the trickiest GCSE Maths topics — Indices — in under 20 minutes.My teaching method is built around a 3-phase approach that really works:1️⃣ Understanding the Principles – We start by breaking down the why behind the rules so students truly understand the logic, not just memorise it.2️⃣ Guided Practice – We then work through real exam-style questions together, applying those principles step by step so they can see the methods in action.3️⃣ Independent Practice – Finally, I set targeted questions for the student to solve on their own. This reinforces everything we’ve covered and builds confidence to work independently — even after the lesson ends.💡 By learning the same concept in three different ways, the student absorbs it deeply and retains it longer — no cramming, no guessing, just real understanding.👨🏫 Watch the promo video below to see how this method transforms complex maths into something that clicks — fast.📲 Want your child to finally feel confident in Maths? Message me today to book a 1-to-1 session or group class.
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09/06/2025
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Try out these GCSE Maths Questions
Easy Questions (40)
Number and Algebra:
1. Calculate 8 + 12 .
2. Simplify 4x + 2x .
3. Find the value of 5^2 .
4. What is 12 \div 3 ?
5. Multiply: 7 \times 6 .
6. Simplify \frac{18}{6} .
7. Write 0.75 as a fraction.
8. Round 15.678 to two decimal places.
9. Solve 2x = 10 .
10. What is 25% of 80?
11. Multiply 3 \times 9 .
12. Calculate the square root of 49.
13. What is 10% of 200?
14. Divide 48 by 6.
15. Write \frac{3}{4} as a decimal.
16. Subtract: 15 - 7 .
17. Solve for x : 3x = 18 .
18. Calculate 6^2 .
19. What is the value of 2 \times 4 + 3 ?
20. Simplify: 5a + 3a .
Geometry and Measure:
21. Identify the type of angle that measures 90 degrees.
22. Find the perimeter of a square with side length 4 cm.
23. What is the area of a rectangle with length 5 cm and width 3 cm?
24. How many sides does a hexagon have?
25. Name a shape that has 4 sides and opposite sides are equal.
26. Calculate the perimeter of a triangle with sides 5 cm, 7 cm, and 8 cm.
27. What is the radius of a circle with a diameter of 10 cm?
28. Convert 3.5 cm into mm.
29. Draw and label a right-angled triangle
30. Find the area of a square with side length 6 cm.
31. What is the volume of a cube with side length 2 cm?
32. Calculate the area of a circle with a radius of 3 cm. Use \pi = 3.14 .
33. How many degrees are in a full turn?
34. Draw an equilateral triangle.
35. Convert 50 cm to metres.
36. Find the circumference of a circle with radius 5 cm. Use \pi = 3.14 .
37. Name the type of triangle with all sides equal.
38. What is the sum of angles in a triangle?
39. How many faces does a cube have?
40. Draw a line segment of 6 cm.
Medium Questions (40)
Number and Algebra:
1. Solve 2x + 5 = 15 .
2. Simplify 3(x + 4) .
3. Calculate \frac{56}{8} \times 3 .
4. Solve 3x + 4 = 16 .
5. Factorise x^2 - 9 .
6. Solve for x : 4x - 3 = 13 .
7. Expand and simplify: (x + 3)(x - 2) .
8. Evaluate 3^3 .
9. Write 0.625 as a fraction in its simplest form.
10. Find the LCM of 6 and 8.
11. Solve 4x + 2 = 18 .
12. Write \frac{7}{20} as a decimal.
13. Calculate 2^3 + 4^2 .
14. Factorise x^2 - 4x .
15. Solve 3x + 5 = 2x + 9 .
16. Expand: 2(x - 3) .
17. Find the HCF of 12 and 18.
18. Simplify 5x - 2 + 3x + 1 .
19. Solve: 5x + 3 = 23 .
20. Find the next number in the sequence: 5, 10, 20, 40, ___.
Geometry and Measure:
21. Find the area of a triangle with base 5 cm and height 8 cm.
22. Calculate the volume of a cuboid with dimensions 3 cm, 4 cm, and 5 cm.
23. Find the angle marked x in an isosceles triangle with angles 50°, 50°, and x .
24. What is the length of the hypotenuse in a right-angled triangle with base 6 cm and height 8 cm?
25. Calculate the area of a trapezium with parallel sides of 5 cm and 7 cm, and height 4 cm.
26. Convert 3500 mm to metres.
27. Draw a regular pentagon.
28. Find the circumference of a circle with diameter 12 cm. Use \pi = 3.14 .
29. Calculate the surface area of a cube with side length 5 cm.
30. Name a 3D shape with 6 faces, all squares.
31. Draw a net of a cube.
32. Calculate the area of a parallelogram with base 8 cm and height 6 cm.
33. What is the exterior angle of a regular hexagon?
34. Draw a bar chart showing the following data: [Monday: 5, Tuesday: 7, Wednesday: 8, Thursday: 6].
35. How many edges does a cuboid have?
36. Calculate the area of a sector with radius 4 cm and angle 60°. Use \pi = 3.14 .
37. Find the volume of a sphere with radius 3 cm. Use \pi = 3.14 .
38. Solve for x : \frac{x}{4} = 6 .
39. What is the surface area of a cylinder with radius 3 cm and height 7 cm? Use \pi = 3.14 .
40. Calculate the missing side in a right-angled triangle with sides 9 cm and 12 cm.
Hard Questions (40)
Number and Algebra:
1. Solve 3(x + 5) = 2x + 15 .
2. Simplify \frac{3x^2 - 12x}{3x} .
3. Factorise x^2 + 5x + 6 .
4. Solve 4x^2 - 9 = 0 .
5. Expand and simplify (x + 3)(x - 2)(x + 1) .
6. Find the gradient of the line passing through the points (2, 5) and (4, 9).
7. Solve \frac{3x}{2} = 9 .
8. Simplify \frac{4}{x} + \frac{3}{x} .
9. Find the quadratic equation that has roots x = 2 and x = -3 .
10. Solve 2x^2 + 3x - 5 = 0 using the quadratic formula.
11. Factorise completely: 4x^2 - 25 .
12. Solve the simultaneous equations: 2x + y = 5 and x - y = 1 .
13. Write 64 as a power of 2.
14. Simplify \frac{x^2 - 9}{x^2 - 4x + 4} .
15. Solve for x and y : 3x + 4y = 18 , 2x - y = 7 .
16. Factorise 3x^2 - 6x + 9 .
17. Solve \frac{5}{x + 2} = 3 .
18. Find the equation of the line perpendicular to y = 2x + 3 passing through (1, 2).
19. Simplify: 4x^3 \times 2x^2 .
20. Solve 3x^2 - 5x + 2 = 0 .
Geometry and Measure:
21. Calculate the surface area of a cone with radius 5 cm and height 12 cm. Use \pi = 3.14 .
22. Find the volume of a sphere with radius 6 cm. Use \pi = 3.14 .
23. Solve for the missing angle in a triangle where two angles are 45° and 85°.
24. Prove that the sum of angles in a quadrilateral is 360°.
25. Find the missing side in a triangle using the cosine rule: a = 7 , b = 8 , \theta = 60° .
26. Calculate the area of a sector with radius 7 cm and angle 120°.
27. Draw the graph of y = x^2 - 4x + 3 .
28. Find the equation of a circle with centre (0, 0) and radius 5.
29. Prove that opposite angles of a cyclic quadrilateral sum to 180°.
30. Calculate the area of a triangle using Heron’s formula: sides are 5 cm, 6 cm, and 7 cm.
31. Find the volume of a cone with radius 4 cm and height 10 cm.
32. Solve for x in the diagram showing a right-angled triangle with hypotenuse 13 cm and one side 5 cm.
33. Calculate the area of a parallelogram with adjacent sides of 6 cm and 8 cm, and an included angle of 30°.
34. Calculate the surface area of a pyramid with a square base of 4 cm and slant height 9 cm.
35. What is the area of an ellipse with axes 6 cm and 10 cm? Use \pi = 3.14 .
36. Solve for the missing side of a right triangle using Pythagoras’ theorem.
37. Calculate the total surface area of a cylinder with radius 3 cm and height 10 cm.
38. Prove that the exterior angle of a triangle is equal to the sum of the opposite interior angles.
39. Find the equation of the tangent to the circle x^2 + y^2 = 25 at the point (3, 4).
40. Calculate the volume of a frustum of a cone with radii 4 cm and 2 cm, and height 6 cm.
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20/12/2021
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14/12/2021
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13/12/2021
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13/12/2021
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08/12/2021
Some simple science questions on a Wednesday afternoon.
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07/12/2021
We thought we’d take a break from exam questions and give you a riddle!
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