Danho
ZIMSEC O Level · 4004/1 · J2026

Mathematics Paper 1 June 2026

Questions
48
Total marks
92
Time allowed
150 min
Syllabus code
4004/1

Sit this paper online

Questions
48
Pass mark
29
Sit this paper

Answer every question in the printed order, get marked at the end, then see the answers.

The questions

Question 101

[1 marks]Approximations & Estimations
Express 31,6824 correct to 3 significant figures.

Answer this when you sit the paper.

Question 102

[1 marks]Approximations & Estimations
Express 31,6824 correct to 2 decimal places.

Answer this when you sit the paper.

Question 103

[1 marks]Approximations & Estimations
Express 31,6824 correct to the nearest ten.

Answer this when you sit the paper.

Question 201

[2 marks]Number Bases
Convert 10 011210\,011_2 to a number in base 5.

Answer this when you sit the paper.

Question 202

[1 marks]Number Bases
Simplify 425+13542_5 + 13_5, giving the answer in base 5.

Answer this when you sit the paper.

Question 301

[1 marks]Polygons, Symmetry & Circles
Set S is such that S = {square, rectangle, equilateral triangle, kite, trapezium, parallelogram}. From the set S, write down the name of the shape which has rotational symmetry of order 3.

Answer this when you sit the paper.

Question 302

[1 marks]Polygons, Symmetry & Circles
Set S is such that S = {square, rectangle, equilateral triangle, kite, trapezium, parallelogram}. From the set S, write down the name of the shape which has rotational symmetry of order 2 and exactly 2 lines of symmetry.

Answer this when you sit the paper.

Question 303

[1 marks]Polygons, Symmetry & Circles
Set S is such that S = {square, rectangle, equilateral triangle, kite, trapezium, parallelogram}. From the set S, write down the name of the shape which has one line of symmetry.

Answer this when you sit the paper.

Question 401

[3 marks]Algebraic Fractions
Express 14x−2y−y4x2−y2\dfrac{1}{4x - 2y} - \dfrac{y}{4x^2 - y^2} as a single fraction in its simplest form.

Answer this when you sit the paper.

Question 501

[1 marks]Scales & Simple Map Problems
A model greenhouse is made to a scale of 1200\dfrac{1}{200}. Calculate the length of the model, in centimetres, if the actual length of the greenhouse is 7,8 m.

Answer this when you sit the paper.

Question 502

[2 marks]Scales & Simple Map Problems
A model greenhouse is made to a scale of 1200\dfrac{1}{200}. On the model the base area is 70 cm270\ \text{cm}^2. Calculate the actual base area of the greenhouse, in square metres.

Answer this when you sit the paper.

Question 601

[2 marks]Probability
A rugby team plays 40% of its matches at home. They win 75% of their home matches and only 55% of their away matches. Write down the probability that the team plays away and the probability that it loses a home match.

Answer this when you sit the paper.

Question 801

[3 marks]Inequalities
Solve the inequality −5<2x+3<1-5 < 2x + 3 < 1. Give the solution in the form a<x<ba < x < b, where aa and bb are integers.

Answer this when you sit the paper.

Question 802

[1 marks]Inequalities
Write down the largest integer xx which satisfies −5<2x+3<1-5 < 2x + 3 < 1.

Answer this when you sit the paper.

Question 901

[2 marks]Ordinary & Standard Form
Given that m=6×103m = 6 \times 10^3 and n=8×10−6n = 8 \times 10^{-6}, evaluate mn\dfrac{m}{n}, giving the answer in standard form.

Answer this when you sit the paper.

Question 902

[2 marks]Ordinary & Standard Form
Given that n=8×10−6n = 8 \times 10^{-6}, evaluate n\sqrt{n}.

Answer this when you sit the paper.

Question 1001

[3 marks]Consumer Arithmetic
By selling a drink for $78,00 a shopkeeper makes a profit of 30%. Find the price, in dollars, at which the shopkeeper should sell it to make a profit of 25%.

Answer this when you sit the paper.

Question 1002

[2 marks]Consumer Arithmetic
Value Added Tax (VAT) at the rate of 15% is added to the marked prices of all articles in a shop. An article is marked $60. Find the price of the article, in dollars, including VAT.

Answer this when you sit the paper.

Question 1101

[2 marks]Fractions, Decimals & Percentages
Simplify 214−1232\frac{1}{4} - 1\frac{2}{3}.

Answer this when you sit the paper.

Question 1102

[2 marks]Fractions, Decimals & Percentages
Simplify 13÷45\dfrac{1}{3} \div \dfrac{4}{5}.

Answer this when you sit the paper.

Question 1103

[1 marks]Fractions, Decimals & Percentages
Express 2540\dfrac{25}{40} as a percentage.

Answer this when you sit the paper.

Question 1201

[3 marks]Change of Units
A full water tank had 575 litres of water left when a farmer used 3,865 kilolitres of water on irrigation. Find the capacity, in litres, of the tank when full.

Answer this when you sit the paper.

Question 1202

[2 marks]Ratios, Rates & Proportions
A borehole pump pumps 7 200 litres of water in 1 hour. Find the time taken, in minutes, to fill up a 4 440 litre tank when empty.

Answer this when you sit the paper.

Question 1301

[1 marks]Variation
State the type of variation represented by y=100x2y = \dfrac{100}{x^2}.

Answer this when you sit the paper.

Question 1302

[2 marks]Variation
Given that y=100x2y = \dfrac{100}{x^2}, calculate yy when x=5x = 5.

Answer this when you sit the paper.

Question 1303

[2 marks]Variation
Given that y=100x2y = \dfrac{100}{x^2}, calculate xx when y=4y = 4.

Answer this when you sit the paper.

Question 1401

[2 marks]Travel Graphs
The diagram is the velocity-time graph of a train which travels a distance of 880 metres in 70 seconds. The train accelerates uniformly from rest to V m/s in the first 20 seconds, travels at V m/s until 60 seconds, then retards uniformly to rest at 70 seconds. Calculate the value of V.

Answer this when you sit the paper.

Question 1402

[2 marks]Travel Graphs
A train accelerates uniformly from rest to 16 m/s in the first 20 seconds of its journey. Calculate the acceleration, in m/s2\text{m/s}^2, during the first 20 seconds.

Answer this when you sit the paper.

Question 1403

[1 marks]Travel Graphs
A train travelling at 16 m/s retards uniformly to rest in the last 10 seconds of its journey. Calculate the retardation, in m/s2\text{m/s}^2, during the last 10 seconds.

Answer this when you sit the paper.

Question 1501

[2 marks]Functional Notation
If f(x)=6−xf(x) = 6 - x, find f(2)f(2).

Answer this when you sit the paper.

Question 1502

[3 marks]Functional Notation
If f(x)=6−xf(x) = 6 - x, find the value of xx for which f(x)=xf(x) = x.

Answer this when you sit the paper.

Question 1601

[2 marks]Similarity & Congruency
Two cylindrical buckets are similar. The larger bucket has a height of 30 cm and base diameter 16 cm. The smaller bucket has a base diameter of 8 cm. Calculate the height, in centimetres, of the smaller bucket.

Answer this when you sit the paper.

Question 1602

[3 marks]Similarity & Congruency
Two cylindrical buckets are similar, with base diameters 8 cm and 16 cm. The volume of the smaller bucket is 754 cm3754\ \text{cm}^3. Calculate the volume of the larger bucket, in cm3\text{cm}^3.

Answer this when you sit the paper.

Question 1701

[2 marks]Statistics & Probability
In a survey, some A level learners were asked which of the three categories of subjects, Commercials, Sciences and Arts, they were studying. The results are represented in the pie chart, in which the Sciences sector is 216° and the Commercials sector is 96°. Calculate the percentage of learners who study Arts.

Answer this when you sit the paper.

Question 1702

[1 marks]Statistics & Probability
In a pie chart, the Sciences sector is 216° and the Commercials sector is 96°. Find, in its simplest form m:nm : n where mm and nn are integers, the ratio of the number of learners who study Sciences to those who study Commercials.

Answer this when you sit the paper.

Question 1703

[2 marks]Statistics & Probability
In a pie chart of a survey, the Commercials sector is 96° and 44 learners study Commercials. Calculate the number of learners who took part in the survey.

Answer this when you sit the paper.

Question 1801

[2 marks]Trigonometry, Bearing & Distances
A triangle has sides of length 6 cm and 5 cm, and the angle between these two sides is 120°. Calculate the area of the triangle, in square centimetres. [Cos 60° = 0,5; Sin 60° = 0,866; Tan 60° = 1,73]

Answer this when you sit the paper.

Question 1802

[3 marks]Trigonometry, Bearing & Distances
A triangle has sides of length 6 cm and 5 cm, and the angle between these two sides is 120°. Calculate the length of the third side, leaving the answer in surd form. [Cos 60° = 0,5; Sin 60° = 0,866; Tan 60° = 1,73]

Answer this when you sit the paper.

Question 1901

[2 marks]Vector Geometry
Given that A(2;2)A(2; 2) is a point on a plane relative to the origin O, find ∣OA⃗∣|\vec{OA}|, giving the answer in surd form.

Answer this when you sit the paper.

Question 1902

[1 marks]Vector Geometry
Given that B(0;k)B(0; k) and C(3;2)C(3; 2) are points on a plane, express BC⃗\vec{BC} in terms of kk.

Answer this when you sit the paper.

Question 1903

[3 marks]Vector Geometry
Given that A(2;2)A(2; 2), B(0;k)B(0; k) and C(3;2)C(3; 2) are points on a plane relative to the origin O, find kk given that OA⃗\vec{OA} is parallel to BC⃗\vec{BC}.

Answer this when you sit the paper.

Question 2001

[3 marks]Laws of Indices
Solve the equation 8x+1=328^{x+1} = 32.

Answer this when you sit the paper.

Question 2002

[3 marks]Logarithms
Simplify log⁡36log⁡16\dfrac{\log 36}{\log \frac{1}{6}}.

Answer this when you sit the paper.

Question 2101

[2 marks]Points, Lines & Angles
The diagram shows triangle ABC in which AC = BC. Point D is on AC produced, DE is parallel to CB and BC^D=108°B\hat{C}D = 108°. Calculate the angle marked xx, in degrees.

Answer this when you sit the paper.

Question 2102

[2 marks]Points, Lines & Angles
The diagram shows triangle ABC in which AC = BC. Point D is on AC produced, DE is parallel to CB and BC^D=108°B\hat{C}D = 108°. Calculate the angle marked yy, in degrees.

Answer this when you sit the paper.

Question 2103

[2 marks]Probability
A bag contains 12 red balls and 8 green balls. If two balls are picked at random one after another without replacement, find the probability that they are of the same colour.

Answer this when you sit the paper.

Question 2201

[1 marks]Probability
A bag contains xx red balls and 8 green balls. The probability of picking a red ball is 35\dfrac{3}{5}. Find the probability of picking a green ball.

Answer this when you sit the paper.

Question 2202

[3 marks]Probability
A bag contains xx red balls and 8 green balls. The probability of picking a red ball is 35\dfrac{3}{5}. Calculate the number of red balls in the bag.

Answer this when you sit the paper.

More sittings of this paper

The answers, and why they are the answers

Sit the paper here to see which ones you got right. Danho explains every question, keeps your score, and works without a connection.

Get it on Google PlayDownload on the App Store