Mathematics Learning Path
High School (9–10) Mathematics
Explore structured mathematics courses, solved problems, simulations and Python activities.
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The Mean of Grouped Data
A teacher cannot read forty journey times aloud, so she groups them. Use the class marks of the groups to find the mean three ways: the direct method, the assumed mean method and the step deviation method. See when each one saves work, and check all three with Python.
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Mode and Median of Grouped Data
The mean can be pulled by one huge value, so shops, schools and councils often report the mode or the median. Find the modal class and the mode, build a cumulative frequency table and find the median, then compare the three averages and see when the rule of thumb that links them works.
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Cumulative Frequency Curves
How many students scored less than 40? How many scored more than 60? A cumulative frequency curve, called an ogive, answers both at a glance. Draw the less than and more than curves, read the median where they cross, find quartiles, and solve the standard problems with a missing frequency.
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Surface Area of Solids Joined Together
The curved and total surface areas of the cube, cuboid, cylinder, cone, sphere and hemisphere. Then solids joined or hollowed out, such as a toy, a capsule and a tent, and the rule for which faces count.
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Volume and Recasting of Solids
The volumes of the basic solids and of solids joined together. Then a solid melted and made into another shape, and water flowing through a pipe into a tank or a well dug and its earth spread out.
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The Frustum of a Cone
A cone with its top sliced off by a plane parallel to the base: a bucket, a glass, a lampshade. Its slant height, curved and total surface area and volume, and the standard word problems. The frustum is not in the current NCERT text, but state boards, IGCSE and GCSE use it.
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Circumference, Area and Rolling Wheels
How far does a wheel roll in one turn, and how much paint covers a round table? The circumference and the area of a circle, the ring between two circles, and wheels, turns and clock hands, with lengths in centimetres and metres in the same problem.
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Arcs, Sectors and Segments
A slice of pizza is a sector, and the cap cut off by a straight knife is a segment. You find the length of an arc, the area of a sector, and the area of a minor and a major segment. The angle is given in degrees or as a fraction of the circle.
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Shaded Regions and Combined Figures
A square with four quarter circles, a circle with a triangle inside it, a flower bed and a running track. You split every design into plain shapes, find each area, and add or subtract, keeping the exact value of pi until the last step.
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Chords, Arcs and the Angles They Make
The parts of a circle, and how chords and the centre are related. Equal chords, the perpendicular from the centre, and the angle that an arc makes at the centre and at the rim.
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Cyclic Quadrilaterals
A four-sided figure with all its corners on a circle. Why its opposite angles add to 180 degrees, how to tell whether a quadrilateral is cyclic, and problems that use these facts.
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Tangents to a Circle
A line that touches a circle at one point. The tangent is perpendicular to the radius, two tangents from a point are equal, and problems about circles inside triangles and quadrilaterals.
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