Topic 1: Relations
a). Relations
i. Find relations between two sets
ii. Find relations between members in a set
iii. Demonstrate relations pictorially
b). Graph of a Relation
1. Draw a graph of a relation represented by a linear inequality
c). Domain and Range of a Relation
i. State the domain of relation
ii. State the range of a relation
d). Inverse of a Relation
i. Explain the Inverse of a relation pictorially
ii. Find inverse of a relation
iii. Draw a graph of the inverse of a relation
Topic 2: Functions
a). Representation of a Function
i. Explain the concept of a functions pictorially
ii. Identify functions
b). Domain and Range of a Function
i. State the domain of a function
ii. State the range of function
c). Graphic Function
i. Draw graphs of functions
d). Inverse of a Function
i. Explain the inverse of a function
ii. Show the inverse of a function pictorially
iii. Find the inverse of a function
iv. Draw a graph of the inverse of a function
v. State the domain and range of inverse of functions
Topic 3: Statistics
a). Mean
i. Calculate the mean from a set of data, frequency distribution tables and histogram
ii. Interpret the mean obtained from a set data, frequency distribution tables and histogram
b). Median
i. Explain the concept of median
ii. Calculate the medium from a set of data
iii. Find the median using frequency distribution tables and cumulative curve
iv. Interpret the median obtained from the data
c). Mode
i. Explain the concept of mode
ii. Calculate the mode
iii. Find the mode using frequency distribution and a histogram
iv. Interpret the mode obtained from the data
Topic 4: Rates And Variations
a). Rates
i. Relate rates of quantities of different kinds
ii. Relate quantities of the same kind
iii. Convert Tanzanian currency into other currencies
b). Variations
i. Explain the concept of direct variation
ii. Solve problems on direct variations
iii. Draw graphs of direct variation
iv. Explain the concept of inverse variation
v. Solve problems on inverse variations
vi. Draw graphs relating inverse variations
vii. Use joint variation in solving problems
Topic 5: Sequence And Series
a). Sequences
i. Explain the concept of sequence
ii. Identify an arithmetic progression (AP) and geometric progression (GP)
iii. Find the general term of an AP
iv. Find the general term of GP
b). Series
i. Derive the formula for a sum of an arithmetic progression
ii. Calculate the arithmetic mean
iii. Derive the formula for the sum of a geometric progression
iv. Calculate the geometric mean
c). Compound Interest
i. Calculate compound interest using formula
Topic 6: Circles
a). Definition of Terms
i. Define circle, chord, radius, diameter, circumference, arc, sector, centre and segment of a circle
b). Central Angle
i. Derive the formula for the length of an arc
ii. Calculate the central angle
iii. Explain the concept of radian measure
iv. Convert radians to degree and vice versa
c). Angles Properties
i. Prove circle theorems of inscribed angles
ii. Apply the circle theorems in solving related problems
d). Chord Properties of a Circle
i. Identify chord properties of a circle
ii. Prove the theorem on the perpendicular bisector to a chord.
iii. Prove the theorem on parallel chords
iv. Apply the theorems on chords in solving related problems
e). Tangent Properties
i. Describe a tangent to a circle
ii. Identify tangent properties of a circle
iii. Prove tangent theorems
iv. Apply theorems relating to tangent to a circle in solving problems
Topic 7: The Earth As A Sphere
a). Features and Location of Places
i. Describe the equator, great circle, small circles, meridian, latitudes and longitudes
ii. Locate a place on the Earth’s surface
b). Distances along Great Circles
i. Calculate distances along great circles
ii. Solve navigation related problems
c). Distances along Small Circles
i. Calculate distance along small circles
Topic 8: Accounts
a). Double Entry
i. Explain the meaning of double entry
ii. Explain different types of ledger
iii. Construct a ledger
iv. Post entries in the ledger
v. Close the simple accounts
b). Trial Balance
i. Explain the concept of trial balance
ii. Construct trial balance
iii. Post debit balances and credit balances
iv. Check the balances
c). Trading Profit and Loss
i. Ascertain gross profit/loss using trading account
ii. Ascertain net profit/loss account
d). Balance Sheet
i. Construct a balance sheet
ii. Post entries in balance sheets
iii. Interpret information from the balance sheet
