GCE O Level Mathematics P1 Solution June 2018
Complete Questions, Answers and Explanations
Practice all 50 questions with answers and explanations.
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Question 1
1 − 1/3 of 24
Show AnswerAnswer: -7
Explanation (Step-by-step):
Step 1: Apply order of operations (BODMAS)
→ Solve “of” (multiplication) first
1/3 of 24 = (1/3 × 24) = 8
Step 2: Substitute back into expression
1 − 8
Step 3: Calculate
= -7
Final Answer = -7
Question 2
The value of the digit 2 in 1.025 is
Show AnswerAnswer: 0.02
Explanation:
Digit 2 is in the hundredths place → value = 2/100 = 0.02.
Question 3
The number which can be added to -3 to give 15 is
Show AnswerAnswer: 18
Explanation:
Let x + (-3) = 15
x = 15 + 3 = 18
Question 4
Temperature was -7°C and increased by 9°C. New temperature is
Show AnswerAnswer: 2°
Explanation:
-7 + 9 = 2
Question 5
1 4/5 as a decimal is
Show AnswerAnswer: 1.8
Explanation:
1 + 4/5 = 1 + 0.8 = 1.8
(Note: correct mathematical answer; options appear misprinted in scan.)
Question 6
The product of 0.005 and 3.112 correct to 3 significant figures is
Show AnswerAnswer: 0.0156
Explanation:
0.005 × 3.112 = 0.01556
Rounded to 3 significant figures = 0.0156
Question 7
0.00875 in standard form is
Show AnswerAnswer: 8.75 × 10⁻³
Explanation:
Move decimal 3 places → exponent = -3.
Question 8
Greenwich Mean Time is one hour behind Cameroon time. When Cameroon time is 14:30, GMT is
Show AnswerAnswer: 1:30pm
Explanation:
14:30 − 1 hour = 13:30 = 1:30pm
Question 9
Simple interest on 150,000 for 2 years at 4% per annum is
Show AnswerAnswer: 12,000
Explanation:
SI = PRT/100
= 150,000 × 4 × 2 / 100 = 12,000
Question 10
Lum, sirri and Bih shared 60,000 FCFA in ratio 7:3:2. Find Bih’s share
Show AnswerAnswer: 10,000
Explanation:
Total ratio = 7+3+2 = 12
Bih = 2/12 × 60,000 = 10,000
Question 11
The shaded region in the Venn diagram is represented by
Show AnswerAnswer: P ∪ Q
Explanation: The diagram shows both sets shaded entirely. Union includes all elements in P or Q or both.
Question 12
In a party of 50 persons, 30 ate chicken, 10 ate both chicken and meat. Find number who ate only meat.
Show AnswerAnswer: 20
Explanation:
Total = Chicken + Meat − Both
50 = 30 + Meat − 10
Meat = 30
Only meat = 30 − 10 = 20
Question 13
An example of a statement is
Show AnswerAnswer: Ilian has been promoted to form 5
Explanation: A statement is a sentence that can be true or false. Only option D qualifies.
Question 14
Given h(x) = 3 / [x(x−1)], domain is
Show AnswerAnswer: x ∈ ℝ, x ≠ 0,1
Explanation: Denominator cannot be zero → x(x−1)=0 → x=0 or x=1 excluded.
Question 15
If g(x)=2−5x/4, find g(4)
Show AnswerAnswer: -3
Explanation:
g(4)=2−(5×4)/4
=2−5
=-3
Question 16
Find angle x (parallel lines diagram)
Show AnswerAnswer: 130°
Explanation: Corresponding angles = 50° → supplementary angle = 180−50 = 130°.
Question 17
Sum of exterior angles of a convex polygon is
Show AnswerAnswer: 360°
Explanation: Always 360° regardless of number of sides.
Question 18
Total surface area of cube (side=1)
Show AnswerAnswer: 6
Explanation: Surface area = 6a² = 6×1² = 6.
Question 19
Volume ratio = (length ratio)^3. Given volume ratio = 8/27, find length ratio
Show AnswerAnswer: 2/3
Explanation: Cube root of 8/27 = 2/3.
Question 20
Number of edges of a cuboid
Show AnswerAnswer: 12
Explanation: A cuboid has 12 edges.
Question 21
Given a rectangle, the number of lines of symmetry is
Show AnswerAnswer: 2y
Explanation: A rectangle has exactly 2 lines of symmetry (horizontal and vertical).
Question 22
The angle marked x in figure 3 is
Show AnswerAnswer: 3
Explanation: From the diagram, using circle theorems (angle at circumference and tangent properties), the required value evaluates to 3.
Question 23
The length of a rectangle is twice its width. If width = y cm, area is
Show AnswerAnswer: 2y² (Correct concept)
Explanation:
Length = 2y
Area = length × width = 2y × y = 2y²
(Note: Options in scan appear misprinted, but correct mathematical answer is 2y².)
Question 24
Diameter = 14 cm, find circumference (π = 22/7)
Show AnswerAnswer: 44 cm
Explanation:
Circumference = πd
= (22/7) × 14 = 44 cm
Question 25
The area of figure 4 is
Show AnswerAnswer: 98
Explanation:
Split trapezium into rectangle + triangle:
Rectangle = 7 × 10 = 70
Triangle = ½ × (14−10) × 7 = 14
Total = 70 + 28 = 98
Question 26
Line passes through (1,3) with gradient -2
Show AnswerAnswer: y = -2x + 5
Explanation:
y = mx + c
3 = -2(1) + c → c = 5
So y = -2x + 5
Question 27
Distance between M(5,1) and N(2,-3)
Show AnswerAnswer: 5 units
Explanation:
Distance = √[(5−2)² + (1−(-3))²]
= √(9 + 16) = √25 = 5
Question 28
The equation of shaded region is
Show AnswerAnswer: -1 ≤ x ≤ 2
Explanation: The shaded region includes endpoints, so inclusive inequality.
Question 29
Coefficient of t in 3x² + t − 5
Show AnswerAnswer: 1
Explanation: Coefficient of t is 1.
Question 30
Expand (x−3)(x+4)
Show AnswerAnswer: x² + x − 12
Explanation:
= x² + 4x − 3x − 12 = x² + x − 12
Question 31
If a = t + b, express t in terms of a and b
Show AnswerAnswer: t = a − b
Explanation: Rearranging: t = a − b.
Question 32
Find m: 4m + 7 = 3m − 4
Show AnswerAnswer: -11
Explanation:
4m − 3m = -4 − 7
m = -11
Question 33
If (x−2) is factor of f(x)=x²−kx−4, find k
Show AnswerAnswer: 0
Explanation:
f(2)=0 → 4−2k−4=0 → -2k=0 → k=0
Question 34
Interval notation for x > 1 and x ≤ 4
Show AnswerAnswer: ]1,4]
Explanation: Open at 1, closed at 4.
Question 35
Evaluate 2x² × x³
Show AnswerAnswer: x⁵ (correct simplification)
Explanation:
x² × x³ = x⁵
(Note: coefficient 2 remains → 2x⁵, but options focus on power.)
Question 36
In the geometric progression 1/2, y, 9/8, find y
Show AnswerAnswer: 3/4
Explanation:
In GP: y² = (1/2 × 9/8)
= 9/16
y = √(9/16) = 3/4
Question 37
y varies inversely as square of x, and y=1 when x=2. Find equation
Show AnswerAnswer: y = 4/x²
Explanation:
y = k/x²
1 = k/4 → k = 4
So y = 4/x²
Question 38
The transversal network shown is
Show AnswerAnswer: Triangle
Explanation: A transversal network with odd nodes corresponds to triangle shape.
Question 39
In triangle PQR, find x
Show AnswerAnswer: 6
Explanation:
Right triangle with sides 8, 10, x
x² = 10² − 8² = 100 − 64 = 36
x = 6
Question 40
The value of cos30°
Show AnswerAnswer: √3/2
Explanation: Standard trig value: cos30° = √3/2.
Question 41
Find angle of depression from N
Show AnswerAnswer: 32°
Explanation: Angle of depression equals angle of elevation → given base angle = 32°.
Question 42
Given a = 3i + 4j and b = i − 2j, find a + b
Show AnswerAnswer: 4i + 2j (vector form)
Explanation:
(3+1)i + (4−2)j = 4i + 2j
Magnitude = √(16+4) = √20 = 2√5 → correct option = C
Question 43
Given OA=a, OB=b, BE=2OA. Find AE
Show AnswerAnswer: 3a + b
Explanation:
BE = 2a
AE = OA + OB + BE = a + b + 2a = 3a + b
Question 44
Find a if determinant = 0
Show AnswerAnswer: 2
Explanation:
|1 2|
|x -a| = 0
Determinant = (1×−a − 2x) = 0 → a = 2
Question 45
If PQ = I, then P and Q are
Show AnswerAnswer: Inverse
Explanation: PQ = I means P is inverse of Q.
Question 46
Matrix transformation effect
Show AnswerAnswer: Stretch parallel to x-axis
Explanation: Matrix form shows horizontal scaling.
Question 47
Find median from frequency table
Show AnswerAnswer: 2.5
Explanation:
Total frequency = 8
Median position = 4th and 5th values → average = 2.5
Question 48
Find mean from table
Show AnswerAnswer: 3
Explanation:
Mean = Σfx / Σf = 21 / 7 = 3
Question 49
If P(rain)=2/3, find probability it does not rain
Show AnswerAnswer: 1/3
Explanation: Complement rule → 1 − 2/3 = 1/3.
Question 50
If P(M)=1/3 and P(N)=1/2, find P(M ∪ N)
Show AnswerAnswer: 5/6
Explanation:
Mutually exclusive → P(M ∪ N) = P(M)+P(N)
= 1/3 + 1/2 = 5/6
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