Drawing and shading Venn diagrams with two or three sets, filling in region counts from the inside out, and solving word problems and number problems with sets.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
“In a class of 40, 25 like cricket, 18 like football and 8 like both…” Once you can draw the diagram, these questions are just careful counting.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Change the numbers in each region and read the set notation.
Copy these into your notebook in your own words — that is how they stick.
The rectangle; every element is inside it.
A ∩ B overlap; A ∪ B both circles; A′ outside A; (A ∪ B)′ outside both.
Fill A ∩ B first, then A only and B only, then the outside = total − (A ∪ B).
Centre first, then pairs (minus the centre), then “only” regions, then outside.
All region counts + outside must equal n(ξ).
Let an unknown region be x; write all regions in terms of x; sum = n(ξ).
Treat the universal set as 100%: both = 100 − (A only) − (B only) when nobody is outside.
Write what each number represents: “x = number who play both”.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (18 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [9 marks]
In a class of 50 students, 28 play basketball (B) and 22 play volleyball (V). Six students play neither sport. x students play both.
(a) Write an equation in x and solve it to show that x = 6. [3]
(b) Draw a Venn diagram showing the number of students in each region. [3]
(c) How many students play exactly one sport? [1]
(d) A student is chosen at random. Find the probability that the student plays volleyball. [2]
Question 2 [9 marks]
ξ = {x : 1 ≤ x ≤ 20, x ∈ ℕ}, A = {even numbers}, B = {multiples of 3} and C = {prime numbers}.
(a) List the elements of A ∩ B. [1]
(b) List the elements of C, and write down A ∩ C. [3]
(c) Determine n(A ∪ B ∪ C). [3]
(d) List the elements of (A ∪ B ∪ C)′. [2]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.