ZIMSEC O-Level Mathematics Paper 2 November 2010 Question Paper

About this question paper

This is the ZIMSEC O-Level Mathematics question paper for Paper 2 from November 2010. Use it for exam practice under timed conditions, then check your work against the marking scheme. The paper code is 4028/2. Time allowed: 2 hours 30 minutes. See the marking scheme.

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Extracted text

# ZIMBABWE SCHOOL EXAMINATIONS COUNCIL
General Certificate of Education Ordinary Level
**MATHEMATICS**
4028/2

**PAPER 2**
**NOVEMBER 2010 SESSION**

Additional materials:
Answer paper
Geometrical instruments
Graph paper (3 sheets)
Mathematical tables
Plain paper (1 sheet)

TIME 2 hours 30 minutes

### INSTRUCTIONS TO CANDIDATES

Write your name, Centre number and candidate number in the spaces provided on the answer paper/answer booklet.

Answer all questions in Section A and any three questions from Section B.
Write your answers on the separate answer paper provided.
If you use more than one sheet of paper, fasten the sheets together.

All working must be clearly shown. It should be done on the same sheet as the rest of the answer.
Omission of essential working will result in loss of marks.
If the degree of accuracy is not specified in the question and if the answer is not exact, the answer should be given to three significant figures. Answers in degrees should be given to one decimal place.

### INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the end of each question or part question. Mathematical tables or calculator may be used to evaluate explicit numerical expressions.

This question paper consists of 12 printed pages.
Copyright: Zimbabwe School Examinations Council, N2010.
©ZIMSEC N2010

**Section A [64 marks]**

Answer all questions in this section.

## Question 1
### (a)

Find the value of \(\frac{1}{3}+1 \frac{7}{9} \div 2 \frac{2}{3}\).

### (b)

During a sale, the price of a camera was reduced from \($ 160\) to \($ 148,80\).

Calculate the percentage decrease in price.

### (c)

Given that \(f(x)=x^{2}-4 x+3\), find all the values of \(x\) for which \(f(x)=0\).

## Question 2
### (a)

Express \(\frac{1}{x-1}+\frac{2}{x+1}\) as a single fraction in its simplest form.

Hence or otherwise, solve the equation

$$
\frac{1}{x-1}+\frac{2}{x+1}=\frac{3}{x}
$$

### (b)

Solve the inequality

\(y-4<3 y+2 \leq 6-y\).

Hence list the integral values of \(y\) that satisfy the inequality.

### (c)

In an Olympiad test, there were 26 questions. Eight points were given for each correct answer and five points were deducted for each wrong answer.

Tamara answered all questions and scored zero. Find the number of questions she had got correct.

## Question 3
### (a)

It is given that \(s=u t-\frac{1}{2} g t^{2}\).

#### (i)

Find the value of \(s\) if \(g=9,8 ; u=20\) and \(t=2\).

#### (ii)

Make \(g\) the subject of the formula.

### (b)

In the diagram, ADE is a triangle, B is a point on AD such that \(AB=2 cm\) and \(BD=8 cm\). C is a point on AE such that \(AC=4 cm\) and \(CE=1 cm\), \(DE=8 cm\).

#### (i)

Name the triangle that is similar to \(\triangle ABC\).

#### (ii)

Calculate the length of BC.

## Question 4
### (a)

It is given that P varies directly as T and inversely as V.

#### (i)

Write down an equation connecting P, V, T and a constant k.

#### (ii)

Given that \(P=2 \times 10^{5}\) when \(V=1 \times 10^{-3}\) and \(T=300\), calculate the value of \(k\).

#### (iii)

Calculate P if \(V=0,0025\) and \(T=300\).

### (b)

Given that \(\mathbf{M}=\left(\begin{array}{rr}3  |  -2  -1  |  4\end{array}\right), \mathbf{N}=\binom{5}{7}\) and \(\mathbf{R}=\left(\begin{array}{ll}3  |  -1\end{array}\right)\), find

#### (i)

MN

#### (ii)

\(\mathrm{M}^{-1}\)

#### (iii)

RN.

## Question 5
### (a)

![](https://ocr.unopasa.com/p/ocr_assets/e8268aa90d197f54f6c3ff2de5b15d55ddec5f9ff6a469b46430c1b7033e6d14.jpg)

In the diagram, A, B, C, D and E are points on the circumference of a circle centre O. BT is a tangent to the circle and TCD and AEF are straight lines. \(\angle CAE=68^\circ\), \(\angle CAB=36^\circ\) and BD is parallel to AE.

Find the size of

#### (i)

\(\angle CBO\),

#### (ii)

\(\angle BTC\),

#### (iii)

\(\angle DEF\),

#### (iv)

\(\angle ACB\).

### (b)

In a recipe for an apple pie, 500 g of apples and 200 g of flour are needed in making an apple pie for 4 people.

#### (i)

If an apple pie was to be made for 6 people, calculate the quantity of apples needed.

#### (ii)

If the apple pie was to be made for 3 people, calculate the quantity of flour needed.

## Question 6
Answer the whole of this question on a sheet of plain paper.

Use ruler and compasses only and show all construction lines and arcs.
All constructions must be done on a single diagram.

A farmer has a plot in the shape of a quadrilateral \(ABCD\), in which \(AB=110 m\), \(BC=100 m\), \(CD=60 m\), \(AD=70 m\) and \(\angle ABC=60^\circ\).

### (a)

Using a scale of \(1 cm : 10 m\), construct the quadrilateral \(ABCD\).

### (b)

Draw the locus of points

#### (i)

30 m from AB,

#### (ii)

equidistant from A and B,

#### (iii)

inside the quadrilateral which are 60 m from B.

### (c)

The farmer wishes to dig a well inside the plot such that it is at least 30 m from AB, at least 60 m from B and nearer to A than to B.

Shade the region in which the well must be.

**Section B [36 marks]**

Answer three questions in this section.

## Question 7
### (a)

![](https://ocr.unopasa.com/p/ocr_assets/5e35a009c9f61ee15c92860d20455ab2ca1ff31a817ab6fdd8416480d75a873c.jpg)

The diagram shows a wine glass in the shape of a cone mounted on a stand. The depth of the cone is equal to its diameter at the top.

#### (i)

Write down an expression for the volume of the cone in terms of its radius \(r\) and \(\pi\).

#### (ii)

If the wine glass can hold 20 ml of wine when full, calculate the radius of the wine glass at the top.

#### (iii)

Wine is bought in bottles of volume 750 ml. Calculate the number of wine glasses that can be filled from one bottle.

[Volume of cone \(=\frac{1}{3}\) base area × height. \(\pi=\frac{22}{7}\)]

### (b)

The base of a triangle is \(x cm\) and its height is \((x-7) cm\).

#### (i)

Write down an expression for the area of the triangle.

#### (ii)

If the area of the triangle is \(6 cm^2\), form an equation in \(x\) and show that it reduces to \(x^{2}-7x-12=0\). …