ZIMSEC O-Level Mathematics Paper 1 June 2024 Question Paper

About this question paper

This is the ZIMSEC O-Level Mathematics question paper for Paper 1 from June 2024. Use it for exam practice under timed conditions, then check your work against the marking scheme. The paper code is 4004/1. Time allowed: 2 hours 30 minutes. See the marking scheme.

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Extracted text

# NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.

## Question 1
### (a)

Simplify \(0-(-3)\)

Answer (a) \_\_\_\_

### (b)

Express 8 as a recurring decimal.

Answer (b) \_\_\_\_

### (c)

Find \(\sqrt{1 \frac{11}{25}}\).

Answer (c) \_\_\_\_

## Question 2
### (a)

Simplify \(2 \frac{2}{3} \div 2\).

Answer (a) \_\_\_\_

### (b)

Find the value of \(9+6 \div 3\).

Answer (b) \_\_\_\_

### (c)

Evaluate \(0,032 \div 0,4\).

Answer (c) \_\_\_\_

## Question 3
Three learners A, B and C contributed \($ 20, $ 30\) and \($ 50\) respectively. They bought a packet of sweets with 150 sweets worth \($ 100\).

### (a)

Write down the ratio of the money they contributed in an ascending order in its simplest form.

Answer (a) \_\_\_\_

### (b)

If the three learners shared the sweets in the ratio of the money they contributed.

Calculate the number of sweets C got.

Answer (b) \_\_\_\_

![](https://ocr.unopasa.com/p/ocr_assets/217059912a9fa9df1725fa036ce0b647abdd78c49d12b5e9f6a9b579c4cb7b4e.jpg)

## Question 4
Two hills A and B are 3 km apart.
Hill A is 150 metres above sea level.
The person on top of the hill A sees the peak of hill B at an angle of elevation of \(15^{\circ}\).
Use as much information given below as is necessary:
\([ \operatorname{Sin} 15 = 0.2588; \operatorname{Cos} 15^{\circ} = 0.9659; \operatorname{Tan} 15^{\circ} = 0.0875 ]\)
Find the height of hill B above sea level.

Answer \_\_\_\_
[3]

## Question 5
![](https://ocr.unopasa.com/p/ocr_assets/5df3ed1704a4331e24dd9139e12a0e5631f343d0264844633f57751af8d2abb4.jpg)

In the diagram points P, Q and R are on the circumference of a circle, centre O.
\(P \hat{O} R = 300^{\circ}, Q \hat{P} O = Q \hat{R} O = x^{\circ}\),

### (a)

\(P \hat{Q} R\)

Answer (a) \_\_\_\_

### (b)

\(x\).

Answer (b) \_\_\_\_

## Question 6
Solve the simultaneous equations:

$$
\begin{aligned}  |  x = 3 - 3y   |  2y = x - 8
\end{aligned}
$$

Answer \_\_\_\_

|  | Candidate Name | Candidate Number |
| :--- | :--- | :--- |
|  |  |  |

## Question 7
A rectangular wall measuring 6 m by 5 m has a window measuring 1.5 m by \(1.2 \mathrm{~m}\). The wall needs to be painted.
Calculate the area of the wall to be painted.

Answer \_\_\_\_

## Question 8
The Universal set \(\xi\) has subsets A and B, such that, \(\xi = \{x: 1 \leq x \leq 20, x \text{ is an integer}\}\),
\(\mathrm{A} = \{x: x < 10\}\),
\(\mathrm{B} = \{x: x \text{ is a perfect cube}\}\).

### (a)

List all elements of,

#### (i)

B,

Answer (a)(i) \_\_\_\_

#### (ii)

\(\mathrm{A} \cap \mathrm{B}\),

Answer (a)(ii) \_\_\_\_

### (b)

Hence or otherwise state the relationship between sets A and B.

Answer (b) \_\_\_\_

## Question 9
### (a)

Express \(732 \times 10^{-1}\) in standard form.

Answer (a) \_\_\_\_

|  | Candidate Name | Candidate Number |
| :--- | :--- | :--- |
|  |  |  |

### (b)

Three towns A, B and C are situated along a straight road, such that town C is \(\left(4 \times 10^{2}\right) \mathrm{km}\) from town A and town B is \(\left(1.88 \times 10^{2}\right) \mathrm{km}\) from town A.
Find the distance of town B from town C.
Give the answer in standard form.

Answer (b) \_\_\_\_

## Question 10
### (a)

Round off,

#### (i)

\($ 9995.85\) correct to the nearest \($ 10\).

Answer (a)(i) \_\_\_\_

#### (ii)

\(3 \frac{1}{5} \mathrm{~cm}\) correct to the nearest centimetre.

Answer (a)(ii) \_\_\_\_

### (b)

#### (i)

Express 432 as a product of its prime factors.

Answer (b)(i) \_\_\_\_

#### (ii)

Hence find the smallest number by which 432 must be multiplied to get a result which is a perfect square.

Answer (b)(ii) \_\_\_\_

## Question 11
### (a)

A greengrocer bought 80 oranges for \($ 640\) and sold them at \($ 15\) each.
Find the percentage profit made.

Answer (a) \_\_\_\_

### (b)

A woman invested \($ 4000\) in a bank at \(3\%\) simple interest.
The money earned an interest of \($ 240\).
Find the time her money was in the bank.

Answer (b) \_\_\_\_

## Question 12
Learner P walks to school every day which is 5 km from the learner's home. In order for the learner to reach the school at 0715, the time at which the lessons commence, the learner leaves home at 0545.

### (a)

Write 0545 as a time in 12-hour notation.

Answer (a) \_\_\_\_

### (b)

On one of the days, learner P arrived at school at 0725.

#### (i)

Find the time by which learner P was late for the lessons.

Answer (b)(i) \_\_\_\_

#### (ii)

Calculate the average speed, in \(\mathrm{km/h}\), at which learner P was walking on the day that the learner was late.

Answer (b)(ii) \_\_\_\_

![](https://ocr.unopasa.com/p/ocr_assets/b882168dba1bcbd1d29201de81c08feaa25ab831f6e8fdd9fc7c24632992bc86.jpg)

## Question 13
![](https://ocr.unopasa.com/p/ocr_assets/9d33a0b36b6b0202173a7357ae067544401a6cfd4f636d90b35c24db0daa28fa.jpg)

In the diagram triangle PSR is such that
QT is parallel to RS, \(\hat{Q R S} = 50^{\circ}, \hat{Q S R} = 30^{\circ}\) and \(\mathrm{PQ} = \mathrm{QS}\).
Find

### (a)

\(S \hat{Q} T\),

Answer (a) \_\_\_\_

### (b)

\(T \hat{Q} P\),

Answer (b) \_\_\_\_

![](https://ocr.unopasa.com/p/ocr_assets/d02aa41518ae71886f78e020c0c796f368ebc5a04e37f760d43755da428a127f.jpg)

### (c)

\(P \hat{T} Q\)

Answer (c) \_\_\_\_

## Question 14
Two learners P and Q write a Mathematics test.
The probability that P passes the test is \(\frac{3}{5}\).
The probability that Q passes the test is \(\frac{2}{3}\).

### (a)

Complete the tree diagram below by inserting the probabilities not given.

![](https://ocr.unopasa.com/p/ocr_assets/51d1f79c58b9e3d8535b03cd546a2c8385ac574a441bb9f47e379b8395b3b2e1.jpg)

Answer (a) on the diagram \_\_\_\_

### (b)

Find the probability that only one of the learners passes the test.

Answer (b) \_\_\_\_

## Question 15
### (a)

Factorise completely,

#### (i)

\(4x - 2y\),

Answer (a)(i) \_\_\_\_
[1]

#### (ii)

\(4x^{2} - y^{2}\).

Answer (a)(ii) \_\_\_\_
[2]

### (b)

Hence or otherwise, find L.C.M of \(4x - 2y\) and \(4x^{2} - y^{2}\).

Answer (b) …