Secondary 4 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.
When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It
reads the working, identifies the step that went wrong, and asks a question that points at the
correction. The worked solution is there once a genuine attempt has been made.
Venn Diagrams, Universal Set, Complement and Subsets
Worked examples
Example 1
Given that C={x:x is a perfect square such that 0<x≤67}, find n(C).
Show the worked solution
A perfect square is the square of a positive integer.
List the perfect squares in order and stop when they exceed the limit:
C={1,4,9,16,25,36,49,64}
Count the elements: there are 8 elements.
n(C)=8
Answer: 8
Example 2
The universal set is ξ={x:x is a positive integer,x≤39} and A={x:x is a multiple of 12,x∈ξ}. Find n(A′).
Show the worked solution
n(ξ)=39 (there are 39 positive integers from 1 to 39)
The multiples of 12 in ξ are: 12,24,36
n(A)=3
Using n(A′)=n(ξ)−n(A)complement formula
n(A′)=39−3
n(A′)=36
Answer: 36
Example 3
A is the set of prime numbers less than 15, and B is the set of odd numbers less than 15. Find n(A∩B).
Show the worked solution
A={2,3,5,7,11,13}primes less than 15
B={1,3,5,7,9,11,13}odd numbers less than 15
A∩B contains elements that are both prime and odd.
Note: 2 is the only even prime; all other primes are odd.
A∩B={3,5,7,11,13}
n(A∩B)=5
Answer: 5
Questions parents ask
Is it really free?
The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.
Which syllabus does this follow?
O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.
Will it just show my child the answer?
No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.