Eight multiple choice and two written, marked as you go. Free, no account.
Circle Theorems
Answer: B. 296°
Inscribed-angle theorem: the angle at the centre is twice the angle at the circumference subtending the same arc.
∠LNM (at the circumference) = 32°, so the (non-reflex) ∠LOM (at the centre) = 2 × 32° = 64°.
Reflex ∠LOM = 360° − 64° = 296°, option B.
Sets & Venn Diagrams
Answer: A. $\{x: -3 < x ≤ 0\}$
On the number line:
Combining: x is greater than -3 AND ≤ 0.
In set-builder notation: {x: -3 < x ≤ 0}.
Logic
Answer: A. F (False)
Implication table for $p \to q$.
| $p$ | $q$ | $p \to q$ |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
The implication $p \to q$ is false only when $p$ is true and $q$ is false. All other combinations give true. Hence $R = F$, option A.
Quadratic Functions & Graphs
Answer: D. (x + 2)
By the factor theorem: if $f(a) = 0$ then $(x - a)$ is a factor.
From the graph, $f(x)$ crosses the $x$-axis at $x = -2$ and $x = 3$. So $f(-2) = 0$, meaning $(x - (-2)) = (x + 2)$ is a factor.
(Note: $(x - 3)$ is also a factor but is not among the options.)
Mensuration: Circles (Circumference, Arc, Sector)
Answer: D. 29 1/3 cm
A sector is a fraction of a whole circle. The fraction is the sector angle divided by 360°.
Step 1 , find the fraction of the circle:
120/360 = 1/3, so the sector is one third of the circle.
Step 2 , find the full circumference:
C = 2πr = 2 × 22/7 × 14 = 88 cm.
Step 3 , take the same fraction of the circumference:
arc AB = 1/3 × 88 = 88/3 = 29 1/3 cm.
So the answer is D.
Watch out: 44 cm (option A) is half the circumference — that is the arc for a 180° angle, not 120°. 22 cm (option C) is a quarter, i.e. 90°. Always convert the angle to a fraction of 360° first.
Angles of Elevation & Depression
Answer: D. 30√3 m
tan 60° = opposite / adjacent = h / 30.
h = 30 × tan 60° = 30 × √3 = 30√3 m, option D.
(Approximately 51.96 m.)
Coordinate Geometry (Straight Lines & Circles)
Answer: D. 3/5
Gradient = (y₂ - y₁)/(x₂ - x₁) = (4 - 1)/(5 - 0) = 3/5 — option D.
The line rises 3 units for every 5 units across.
Probability
Answer: C. 1/2
Multiply along the top (Pass-Pass) branches of the tree:
P(Pass both) = P(Pass 1) × P(Pass 2 | Pass 1) = 2/3 × 3/4 = 6/12 = 1/2, option C.
Marking guide
This is a conditional (implication) statement in mathematical logic.
Let p = "James is an Art student" Let q = "he is a good Literature student"
The statement is written symbolically as: p => q
This reads: "If James is an Art student, then he is a good Literature student."
The antecedent (hypothesis) is p: "James is an Art student" The consequent (conclusion) is q: "he is a good Literature student"
Truth table for p => q:
| p | q | p => q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
The conditional is only false when p is true and q is false.
Marking guide
Step 1. Total marked price (1 mark).
$3 × 217.00 = \text{GH₵}\,651.00$.
Step 2. Subtract amount paid (1 mark).
Discount $= 651.00 - 594.00 = \text{GH₵}\,57.00$.
Step 3. State the answer (1 mark).
Discount allowed $= \text{GH₵}\,57.00$.
Answer: GH₵ 57.00.
Topics on this page: Circle Theorems; Sets & Venn Diagrams; Logic; Quadratic Functions & Graphs; Mensuration: Circles (Circumference, Arc, Sector); Angles of Elevation & Depression; Coordinate Geometry (Straight Lines & Circles); Probability; Commercial Arithmetic (Interest, Profit/Loss, Percentages).
Notes, practice questions and a mark scheme for topics on the syllabus.
Some are from past papers and show their year. The rest are written in the style of the WASSCE, and every one comes with the correct answer and a worked explanation.
Yes, on this page: type your answer and the coach marks it with AI and shows you where the marks are, a few a day with no account. Inside GLearn, every answer you write.
No. You need one only to save your score and to keep going once the free marking for the day is used.
Nobody can promise that. These test the same topics and the same kind of thinking the WASSCE does, which is what practice is for. There are thousands more across BECE and WASSCE inside GLearn; this page shows a small sample.