O-Level E-Math
Specimen Paper 1
📐MATHEMATICAL FORMULAE
Solve 7 − 8x = 25
(a) Find the lowest common multiple (LCM) of 112 and 168. [2]
(b) Find the highest common factor (HCF) of 112 and 168. [1]
(a) Calculate 302.6² ÷ (12.76 − 10.84). Write your answer correct to 4 significant figures. [1]
(b) Write your answer to part (a) in standard form. [1]
Expand and simplify (3x − y)(2x + 3y)
A number of adults took part in a parachute jump. This pie chart shows the age groups (in years) of the adults that took part.
(a) Find the percentage of adults who are 21-30 years old. [1]
(b) Explain why it is not possible to calculate the number of adults over 60 years old. [1]
The expression x² − 12x + 17 can be written in the form (x − 6)² + n.
(a) Find the value of n. [1]
(b) Explain why when x = 6, the expression x² − 12x + 17 has its minimum value. [1]
The diagram shows a triangle ABC.
(a) Construct the perpendicular bisector of BC. [1]
(b) Construct the bisector of angle ACB. [1]
(c) Point P is equidistant from B and C and equidistant from AC and BC. Mark point P and measure CP. [1]
2 − 5/x = x(x + 2) can be written as x³ + ax² + bx + 5 = 0.
Find the value of a and the value of b.
In the diagram, BDE is a straight line and AB = AD.
Angle ABD = 37°, angle CBD = 50° and angle CDE = 124°.
Explain why it is possible to draw a circle that passes through A, B, C and D.
Give reasons for each step of your working.
Min and Ken each have an amount of money.
The ratio Min's amount : Ken's amount = 5 : 3.
Min gives Ken $22.
The new ratio Min's amount : Ken's amount = 3 : 4.
Find how much money Min has now.
In a group of 20 people, 12 are males and 8 are females.
The mean weight of the group is 78 kg.
The mean weight of the males is 84 kg.
(a) Calculate the total weight of the group. [1]
(b) Calculate the mean weight of the females. [2]
Simplify
Solve
Find the equation of the straight line passing through (−2, 11) and (5, −10).
(a) Simplify
(i) 9x³ × x⁹ [1]
(b)
Find an expression for q in terms of p and r. [2]
ABCD is a trapezium with E on DC such that AE is parallel to BC and BE is parallel to AD.
Show that triangle ADE and triangle BEC are congruent.
Give a reason for each statement you make.
Factorise completely
(a) 9wx + y − 3x − 3wy [2]
(b) 5x⁴ − 80y⁴ [3]
An aircraft has three sections, Business Class (B), Premium (P) and Economy (E).
On an outward flight there are 15 Business Class passengers, 80 Premium passengers and 152 Economy passengers.
On the return flight there are 13 Business Class passengers, 75 Premium passengers and x Economy passengers.
(a) Represent this information in a 2 × 3 matrix, S. [1]
(b) The cost of tickets are: Business Class $280, Premium $120, Economy $90.
Find, in terms of x, the matrix
(c) The ticket sales of the return flight was $1360 more than the ticket sales of the outward flight. Find x. [1]
The diagram shows a shape made from a parallelogram and a hexagon.
Find the sum of the angles a, b, c, d, e, f, g and h.
P, Q and R are points on a circle, centre O.
TP is a tangent to the circle and angle TPR = x°.
Find, in terms of x, angle PQR.
Give a reason for each step of your answer.
A glass block is made in the shape of a frustum of a square-based pyramid.
The vertical height of the frustum is 2 cm.
The diagram shows the side view of the glass block.
(a) Using similar triangles, find x. [2]
(b) 1 cm³ of glass has a mass of 2.6 grams. Calculate the mass of the glass block. [3]
The first five terms of a sequence are 10, 14, 18, 22, 26.
(a) Write down an expression for the nth term of the sequence. [2]
(b) Explain why 264 is not a term of this sequence. [1]
(c) The sum of the first n terms of this sequence is given by 2n² + 8n. Using algebra, find the value of n when the sum is 384. [3]
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Reviewed by: KW Phoon
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Syllabus alignment based on the 2020 G2 and G3 Mathematics Syllabuses published by the Ministry of Education, Singapore.
Exam paper format follows SEAB O-Level Elementary Mathematics (4052) specimen paper.