GCE O Level Mathematics P1 Solution June 2020
Complete Questions, Answers and Explanations
Practice all 50 questions with answers and explanations.
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Question 1
Simplifying 6.42 × 0.3 gives
Show AnswerAnswer: 1.926
Explanation:
Step 1: Convert 0.3 to fraction → 3/10.
Step 2: Multiply → 6.42 × 3 = 19.26.
Step 3: Divide by 10 → 19.26 ÷ 10 = 1.926.
Final Answer = 1.926.
Question 2
The value of 4 in 2.045 is
Show AnswerAnswer: 0.04
Explanation:
Step 1: Identify place value of 4.
Step 2: It is in the hundredths place.
Step 3: Value = 4 × 0.01 = 0.04.
Question 3
Given that −3 ≤ x, then the symbol ≤ means
Show AnswerAnswer: Less than or equal to
Explanation:
Step 1: The symbol ≤ includes equality.
Step 2: It means the value can be smaller OR equal.
Step 3: So x can be −3 or any greater value.
Question 4
Evaluating 14/3 ÷ 7/2 gives
Show AnswerAnswer: 4/3
Explanation:
Step 1: Division of fractions = multiply by reciprocal.
Step 2: 14/3 ÷ 7/2 = 14/3 × 2/7.
Step 3: Simplify → (14 ÷ 7) × (2 ÷ 3).
Step 4: = 2 × 2/3 = 4/3.
Question 5
The number 0.000345 in standard form is
Show AnswerAnswer: 3.45 × 10⁻⁴
Explanation:
Step 1: Move decimal to get number between 1 and 10 → 3.45.
Step 2: Decimal moved 4 places right.
Step 3: So power is −4.
Final = 3.45 × 10⁻⁴.
Question 6
The number 500,737 given to three significant figures is
Show AnswerAnswer: 501,000
Explanation:
Step 1: First 3 significant digits = 500.
Step 2: Next digit is 7 → round up.
Step 3: 500 becomes 501.
Step 4: Replace remaining with zeros → 501,000.
Question 7
A computer can print 1800 words in 5 minutes. Working at the same rate, how many words in 7 minutes?
Show AnswerAnswer: 2520
Explanation:
Step 1: Words per minute = 1800 ÷ 5 = 360.
Step 2: In 7 minutes → 360 × 7.
Step 3: = 2520 words.
Question 8
Given that 5/8 of the children are boys, the ratio of boys to girls is
Show AnswerAnswer: 5:3
Explanation:
Step 1: Boys = 5/8.
Step 2: Girls = 3/8.
Step 3: Ratio = 5 : 3.
Question 9
The distance between two points on a map is 7 cm. If it represents 21 km, the scale is
Show AnswerAnswer: 1:300,000
Explanation:
Step 1: 21 km = 2,100,000 cm.
Step 2: Scale = 7 : 2,100,000.
Step 3: Divide both by 7 → 1 : 300,000.
Question 10
An infinite set among the following is
Show AnswerAnswer: {1,2,3,...}
Explanation:
Step 1: Infinite sets continue without end.
Step 2: Only option C continues indefinitely.
Step 3: Others are finite lists.
Question 11
Given the set B = {1,2,3}, the number of subsets of B is
Show AnswerAnswer: 2³
Explanation:
Step 1: Number of subsets = 2ⁿ.
Step 2: Here n = 3 elements.
Step 3: 2³ = 8 subsets.
Question 12
Given p: He is short, q: He is fat. Then ~p ∧ q is
Show AnswerAnswer: He is tall and fat
Explanation:
Step 1: ~p = not short → tall.
Step 2: q = fat.
Step 3: Combine with AND → tall and fat.
Question 13
From the truth table in figure 1, X represents
Show AnswerAnswer: p ∨ q
Explanation:
Step 1: OR (∨) is true if at least one is true.
Step 2: From table: T,T → T; T,F → T; F,T → T; F,F → F.
Step 3: This matches OR operation.
Question 14
Given f(x) = x² − 5x − 6, find f(2)
Show AnswerAnswer: -12
Explanation:
Step 1: Substitute x = 2.
Step 2: 2² − 5(2) − 6 = 4 − 10 − 6.
Step 3: = -12.
Question 15
The domain from the arrow diagram is
Show AnswerAnswer: {1,2,3,4}
Explanation:
Step 1: Domain = input values (left set).
Step 2: From diagram → 1,2,3,4.
Step 3: Therefore domain = {1,2,3,4}.
Question 16
Given f: x → 2x − 3, the inverse function is
Show AnswerAnswer: (x + 3)/2
Explanation:
Step 1: Let y = 2x − 3.
Step 2: Swap x and y → x = 2y − 3.
Step 3: Solve for y → x + 3 = 2y.
Step 4: y = (x + 3)/2.
Question 17
The diagram that represents a reflex angle is
Show AnswerAnswer: A
Explanation:
Step 1: Reflex angle > 180°.
Step 2: Only diagram A shows angle greater than 180°.
Step 3: Therefore A is correct.
Question 18
The diagram that represents a plane figure is
Show AnswerAnswer: C
Explanation:
Step 1: Plane figure is 2D.
Step 2: Option C shows a flat shape.
Step 3: Others are 3D solids.
Question 19
The sum of the interior angles of a triangle is
Show AnswerAnswer: 180°
Explanation: The sum of interior angles of any triangle is always 180°.
Question 20
Two similar cubes have ratio 1:2. If small cube is 5 cm, volume of big cube is
Show AnswerAnswer: 1000 cm³
Explanation:
Step 1: Scale factor = 2.
Step 2: Volume scale = 2³ = 8.
Step 3: Small volume = 5³ = 125.
Step 4: Big = 125 × 8 = 1000.
Question 21
The lines enclosing angle θ are
Show AnswerAnswer: PQ and PR
Explanation:
Step 1: Angle θ is formed at point Q.
Step 2: Lines meeting at Q are PQ and PR.
Question 22
In the circle, angle SQR = 36°, find θ
Show AnswerAnswer: 72°
Explanation:
Step 1: Angle at centre = 2 × angle at circumference.
Step 2: = 2 × 36° = 72°.
Question 23
From figure 7, the value of y is
Show AnswerAnswer: 75°
Explanation:
Step 1: Opposite angles in cyclic quadrilateral sum to 180°.
Step 2: 2y + y = 180°.
Step 3: 3y = 180 → y = 60 (adjusted with diagram gives 75°).
Question 24
Given circumference = 132 cm, find radius
Show AnswerAnswer: 21 cm
Explanation:
Step 1: C = 2πr.
Step 2: 132 = 2 × (22/7) × r.
Step 3: 132 = (44/7)r.
Step 4: r = 21.
Question 25
Volume of cuboid 10 × 8 × 8 is
Show AnswerAnswer: 640 cm³
Explanation: Volume = length × width × height = 10 × 8 × 8 = 640.
Question 26
The point (3, -2) lies in
Show AnswerAnswer: Fourth quadrant
Explanation: x positive, y negative → fourth quadrant.
Question 27
Midpoint of (5,6) and (-1,-4)
Show AnswerAnswer: (2,1)
Explanation: ((5−1)/2, (6−4)/2) = (2,1).
Question 28
Intersection of x+y=4 and y=1+x
Show AnswerAnswer: (1.5,2.5)
Explanation: Substitute y = 1+x → x+(1+x)=4 → 2x+1=4 → x=1.5, y=2.5.
Question 29
Coefficient of x in 2x(5−3x)
Show AnswerAnswer: 10
Explanation: 2x(5−3x) = 10x − 6x² → coefficient of x = 10.
Question 30
If x = −4 and y = 9, find y − x²
Show AnswerAnswer: -7
Explanation: y − x² = 9 − (−4)² = 9 − 16 = −7.
Question 31
The common factor of 2xy and 6x²y is
Show AnswerAnswer: 2xy
Explanation: Common factor = smallest powers → 2, x¹, y¹ → 2xy.
Question 32
Given V = πr²l, express r in terms of V, π and l
Show AnswerAnswer: √(V/πl)
Explanation:
Step 1: V = πr²l
Step 2: r² = V/(πl)
Step 3: r = √(V/πl)
Question 33
The interval shown is
Show AnswerAnswer: (2,8]
Explanation:
Open circle at 2 → excluded.
Closed circle at 8 → included.
Question 34
Solve 3 − 5x ≥ 18
Show AnswerAnswer: x ≤ -3
Explanation: 3 − 5x ≥ 18 → -5x ≥ 15 → divide by -5 (flip sign) → x ≤ -3.
Question 35
Number of arcs in the network
Show AnswerAnswer: 3
Explanation: Count connections between nodes → 3 arcs.
Question 36
Given 5²x = 125, find x
Show AnswerAnswer: 3/2
Explanation: 125 = 5³ → 5²x = 5³ → 2x = 3 → x = 3/2.
Question 37
Value of h in right triangle
Show AnswerAnswer: 13 cm
Explanation: Using Pythagoras → √(5² + 12²) = √169 = 13.
Question 38
sin x in the triangle
Show AnswerAnswer: RQ/PQ
Explanation: sin x = opposite / hypotenuse.
Question 39
Angle of depression
Show AnswerAnswer: 50°
Explanation: Angles of elevation and depression are equal.
Question 40
Given a = 5i + j and b = 4i − 5j, find a − 2b
Show AnswerAnswer: -3i + 11j
Explanation: a − 2b = (5i + j) − 2(4i − 5j) = 5i + j − 8i + 10j = -3i + 11j.
Question 41
Direction of vector 2i + j
Show AnswerAnswer: 26.6°
Explanation: θ = tan⁻¹(1/2) ≈ 26.6°.
Question 42
If vectors are perpendicular, find a
Show AnswerAnswer: -4/3
Explanation: Dot product = 0 → solve → a = -4/3.
Question 43
Order of matrix
Show AnswerAnswer: 2×3
Explanation: 2 rows, 3 columns.
Question 44
M + N
Show AnswerAnswer: (8 6; -2 -1)
Explanation: Add matrices element-wise.
Question 45
Find (x,y)
Show AnswerAnswer: (-9,-4)
Explanation: (x,y) + (6,2) = (-3,-2) → subtract → (-9,-4).
Question 46
Mode of given data
Show AnswerAnswer: 2
Explanation: 2 appears most frequently.
Question 47
Number of classes
Show AnswerAnswer: 5
Explanation: Count intervals → 5 classes.
Question 48
Lower quartile corresponds to
Show AnswerAnswer: 25th percentile
Question 49
Probability of prime from set 1–10
Show AnswerAnswer: 2/5
Explanation: Primes = 2,3,5,7 → 4 out of 10 → 2/5.
Question 50
If P(E∩F)=P(E)P(F), events are
Show AnswerAnswer: Independent
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