Maths · AQA Paper 1
Geometry and Measures
The geometry and measures skills tested on AQA Paper 1: angles and polygons, area and circles, volume and surface area, Pythagoras' theorem and trigonometry, all done without a calculator.
Lessons
Ticks are remembered on this device only.
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1
Angles in Parallel Lines and Polygons
Angle facts, angles in parallel lines, and the interior and exterior angles of polygons.
9 terms -
2
Area, Perimeter and Circles
Areas of standard shapes and compound shapes, and the circumference and area of circles, semicircles and sectors.
9 terms -
3
Volume and Surface Area
Volumes and surface areas of cuboids, prisms, cylinders, cones and spheres.
9 terms -
4
Pythagoras' Theorem
Using Pythagoras' theorem to find sides, test for right angles and solve problems.
9 terms -
5
Trigonometry in Right-Angled Triangles
Using sine, cosine and tangent, and the exact trigonometric values, to find sides and angles.
9 terms
Key terms in this chapter
All 45, gathered from every lesson.
- Transversal
- A line that crosses two or more other lines.
- Parallel lines
- Lines that stay the same distance apart and never meet, marked with arrows.
- Alternate angles
- Equal angles on opposite sides of a transversal between two parallel lines, forming a Z shape.
- Corresponding angles
- Equal angles in matching positions at each crossing of a transversal, forming an F shape.
- Co-interior angles
- Angles between parallel lines on the same side of a transversal, which add up to 180 degrees.
- Vertically opposite angles
- The equal angles opposite each other where two straight lines cross.
- Polygon
- A closed shape made from straight sides.
- Regular polygon
- A polygon with all sides equal and all angles equal.
- Exterior angle
- The angle between one side of a shape and the extension of the next side.
- Perimeter
- The total distance around the outside of a shape.
- Area
- The amount of surface inside a shape, measured in square units.
- Compound shape
- A shape made up of simpler shapes joined together.
- Perpendicular height
- The height of a shape measured at a right angle to its base.
- Circumference
- The distance around a circle.
- Radius
- The distance from the centre of a circle to its edge.
- Diameter
- The distance across a circle through its centre, twice the radius.
- Sector
- A slice of a circle between two radii and an arc.
- In terms of pi
- An answer that keeps the symbol \(\pi\) instead of using its decimal value.
- Volume
- The amount of space inside a 3D shape, measured in cubic units.
- Surface area
- The total area of all the faces of a 3D shape.
- Cuboid
- A 3D shape with six rectangular faces.
- Prism
- A 3D shape with the same cross-section along its whole length.
- Cross-section
- The shape you see when you cut through a solid at a right angle to its length.
- Cylinder
- A prism with a circular cross-section.
- Cone
- A 3D shape with a circular base that rises to a point.
- Sphere
- A perfectly round 3D shape, like a ball.
- Net
- A flat pattern that folds to make a 3D shape.
- Right-angled triangle
- A triangle with one angle of 90 degrees.
- Hypotenuse
- The longest side of a right-angled triangle, opposite the right angle.
- Pythagoras' theorem
- In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
- Pythagorean triple
- Three whole numbers that fit Pythagoras' theorem, such as 3, 4, 5.
- Square root
- The number that gives a stated number when multiplied by itself.
- Converse
- The reverse of a statement, used here to test whether a triangle has a right angle.
- Diagonal
- A line joining two opposite corners of a shape.
- Surd
- A root that cannot be written as a whole number or a fraction, such as the square root of 5.
- Isosceles triangle
- A triangle with two equal sides and two equal angles.
- Trigonometry
- The study of the links between the sides and angles of triangles.
- Sine
- The ratio of the opposite side to the hypotenuse in a right-angled triangle.
- Cosine
- The ratio of the adjacent side to the hypotenuse in a right-angled triangle.
- Tangent
- The ratio of the opposite side to the adjacent side in a right-angled triangle.
- Opposite
- The side across from the angle being used.
- Adjacent
- The side next to the angle being used, other than the hypotenuse.
- Inverse function
- A function that undoes another, such as sin\(^{-1}\), which turns a ratio back into an angle.
- Exact value
- A value written as a fraction or surd instead of a rounded decimal.
- SOH CAH TOA
- A memory aid for the three trigonometric ratios.