GCSE Maths Revision Higher Tier (Geometry)

Explore cylinder volume and surface area using V = π r^2 h and SA = 2π r^2 + 2π r h, with cross-sections and curved surface drawn as a rectangle.

Explore volume and surface area of spheres and hemispheres, using radius-based formulas 4/3 pi r^3 and 4 pi r^2, including curved surface area and total surface area.

Explore volume and surface area of pyramids, from pentagonal and square bases, using base area, height, and slant height; apply formulas and Pythagoras to calculate volumes and surface areas.

Explore how to calculate cone volume and surface area using 1/3 pi r^2 h and pi r l, with l from Pythagoras, and examine frustum volumes and their cm^3 units.

Work backwards to find a cylinder's radius from its volume and height using pi r^2 h, with V=100 and h=10, then take square root to get r ≈ 1.8 m.

Solve problems on volume and surface area, deriving radius from a hemisphere's surface area and volume, then equating volumes of a cone-hemisphere shape to a cylinder to find the height.

Finish this topic with exam questions to deepen practice and master the concept, using carefully selected recent questions with answers on the final page.

Explore upper and lower bounds for rounded measurements on a number line, using giraffe height rounded to the nearest foot and donkey weight rounded to the nearest five kilograms.

Learn how to use lower and upper bounds to find the smallest or largest possible area, with rules for multiplication, division, addition, and subtraction in GCSE geometry.

Explore an exam question on a rectangle's perimeter, deriving lower and upper bounds from rounding to the nearest centimeter. Use the formula 2(width + height) to compute the height's bounds.

Finish this topic with exam questions that offer even more practice, challenging your understanding to master the concept and noting that answers are on the document's final page.

Explore similarity in geometry, distinguishing it from congruence, and learn to use length ratios to scale shapes, including real-world examples with triangles and proportional reasoning.

Learn how to use similarity to compute area and volume ratios from a length ratio, by squaring for areas and cubing for volumes, with cone and height examples.

Explore exam-style questions on similarity and similar triangles. Derive scale factors from base ratios, convert area ratios to lengths, and apply cube scaling for volumes.

Practice exam questions to challenge your understanding and master the topic, with answers included on the final page of the document for self-checking and continued revision.

Apply Pythagoras' theorem to find the hypotenuse: use c^2 = a^2 + b^2 with a = 2 and b = 4, giving x = sqrt(20) ≈ 4.47.

Apply Pythagoras to find the shorter side with hypotenuse 7 and the other side 3, rewrite as a^2+b^2=c^2, and solve for x: x = sqrt(40) ≈ 6.32.

Apply Pythagoras to harder problems by building heights in equilateral triangles and using base–height relations to find area and missing sides, with exact surd forms.

Apply the trapezium area formula with perpendicular height, then use Pythagoras to find missing lengths; compute AD in a right triangle via midpoint, producing 67 cm² and 13.2 cm.

Practice recent GCSE geometry exam questions with included answers to master the concepts and reinforce your revision, finishing the topic with confidence.

Explore trigonometry for right-angled triangles, labeling hypotenuse, opposite and adjacent sides in relation to theta, and applying sine, cosine and tangent via sohcahtoa to find a missing length.

Explore finding a missing angle in a right-angled triangle using sine, cosine, and tangent, with opposite, adjacent, and hypotenuse labels, and applying inverse functions to theta.

Explore harder trigonometry problems by drawing the height of an isosceles triangle to form right triangles, then apply cosine and sine to find base and hypotenuse lengths.

Apply trig concepts to exam questions by using tan and cos in right-angle triangles, then decompose a regular pentagon to find area of a central triangle.

Master exam questions for geometry with targeted practice, as this unit provides a set of recent GCSE questions with answers on the final page.

Use the sine rule to find missing lengths in non right angled triangles. Relate side lengths to the sine of opposite angles and follow the A, B, C labeling.

Learn how to apply the sine rule to find a missing angle by flipping fractions, solving for sine theta, and using inverse sine with a worked example.

Learn to find a missing angle using the cosine rule by rearranging to isolate cos alpha and applying cos^-1. Use labeled triangles and numerical examples to calculate theta.

Learn to calculate the area of a non-right angled triangle using half a b sine c, with proper angle labeling and unit awareness, and relate to sector and segment areas.

Four advanced trigonometry problems use the cosine rule and sine rule to find angles and sides, then compute arc length, sector perimeter, and segment perimeter.

Analyze an exam-style problem that uses the cosine rule on a 120-degree triangle to relate the rectangle's height and width, then express the area as a quadratic.

Master geometry exam-style questions with a curated set of recent GCSE questions to sharpen understanding and exam technique. Check the final page for answers to verify solutions and track progress.

Analyze 3d Pythagoras and trigonometry through exam-style questions, applying gradient concepts, Pythagoras, Pythagorean triples, and tan-based methods to find angles between lines and planes.

Review recent GCSE geometry exam questions to challenge your understanding and sharpen exam ready skills. Answers are on the final page to support practice and mastery in higher tier geometry.

Recap circle parts: radius, diameter, tangent, and center, with points on the circumference. Define a chord, and distinguish minor and major arcs.

Explore the first three circle theorems: angle in a semicircle is a right angle; the center angle is twice the circumference angle; and angles in the same segment are equal.

Explain circle theorems four to six, including opposite angles of a cyclic quadrilateral sum to 180 degrees, radius-tangent right angles, and equal tangents, with practice questions to apply these concepts.

Circle theorems seven and eight show that a radius to a chord at right angles bisects it, and that a chord–tangent angle equals the angle in the alternate segment.

Solve harder circle theorem problems using diameter properties, semicircles, radii, and isosceles and equilateral reasoning to find angles such as 30° and 24°.

Apply circle theorems to find angles in a circle with tangents and radii, using central and circumference angle relationships to solve exam questions.

Engage with a curated set of recent GCSE maths exam questions to gain extra practice, with answers on the final page for self-checking and mastery of geometry concepts.

Define vectors as movement from a starting point to an ending point, expressed as letters, coordinates A to B, or a column. Learn scalar multiplication, direction, and parallelism.

Learn to add and subtract vectors by adding components, practice sums like a plus b and a minus b, and use scalar multiples such as 2a.

Learn how to determine the magnitude of vectors with Pythagoras, calculating A, B, and C lengths as sqrt(10), sqrt(26), and sqrt(32) = 4√2, noting signs vanish when squared.

Master geometric vector problems in a trapezium using vectors a and b, express A to C as a+b, C to D as -2a, and A to D as b-a.

Explore geometric vector problems in an isosceles triangle and a parallelogram, using midpoints and ratios to express AX, AY, and XY involving AB, BC and KD.

Discover vector proof concepts in geometry: determine parallelism via scaling and factoring, analyze collinearity with shared points, and use ratios and midpoints to compare vectors.

Explore vector methods in GCSE maths: compute D to A and E coordinates using position and translation vectors, and analyze a parallelogram with 2:3 ratio to find X and Y.