MATHEMATICS
4008/1, 4028/1
2 hours 30 minutes
NOVEMBER 2007 SESSION
Candidates answer on the question paper. Additional materials: Geometrical instruments
TIME 2 hours 30 minutes
INSTRUCTIONS TO CANDIDATES
Write your name, Centre number and candidate number in the space at the top of this page.
Answer all questions. Write your answers in the spaces provided on the question paper. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. Decimal answers which are not exact should be given correct to three significant figures unless stated otherwise.
Mathematical tables, slide rules and calculators should not be brought into the examination room.
INFORMATION FOR CANDIDATES
The number of marks is given in brackets [ ] at the end of each question or part question.
| FOR EXAMINER'S USE | | :--- | | |
This question paper consists of 27 printed pages and 1 blank page.
**NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER**
Question 1
Express
(a)
1548 correct to
#### (i)
one significant figure.
#### (ii)
the nearest ten.
(b)
\(0,00349\) correct to 3 decimal places.
Answer
\_\_\_\_
(a)
#### (i)
\_\_\_\_ ..... [1]
#### (ii)
\_\_\_\_ ..... [1]
(b)
\_\_\_\_
Question 2
(a)
Write down
#### (i)
\(\frac{13}{40}\) as decimal fraction.
#### (ii)
\(4850 \times 10^{-1}\) in standard form.
(b)
John works \(46 \frac{1}{2}\) hours per week and is paid \(\$ 5000\) per hour. Find John's weekly wage.
Answer
(a)
#### (i)
\_\_\_\_
#### (ii)
\_\_\_\_ ..... [1]
(b)
\$ \_\_\_\_
Question 3
Solve the simultaneous equations
$$ \begin{aligned} & x=\frac{1}{2} y \\ & 3 x-y=7 \end{aligned} $$
Answer
$$ \begin{aligned} & x= \\ & y= \end{aligned} $$
Question 4
Peter, John and Sekai share some money in the ratio 2:3:5 respectively.
(a)
Express Peter's share as a fraction of John's share.
(b)
If Sekai received \(\$ 24000\), calculate the total amount shared.
Answer
(a)
\_\_\_\_ [1]
(b)
\$ \_\_\_\_ [2]
Question 5
In the diagram ABCD is a kite in which \(\mathrm{AB}=5 \mathrm{~cm}, \mathrm{BC}=12 \mathrm{~cm}\) and \(\mathrm{A} \hat{\mathrm{B} C}=90^{\circ}\). Given that triangle ABC is the image of triangle ADC under a single transformation,
(a)
describe fully the single transformation,
(b)
calculate the area of the kite.
Answer
(a)
\_\_\_\_
\_\_\_\_
\_\_\_\_ [2]
(b)
\_\_\_\_ \(\mathrm{cm}^{2}\) [1]
Question 6
(a)
Giving your answer as a common fraction in its lowest terms, find the value of \(\frac{3}{16} \times 3.2\).
(b)
Find the value of \(x\) given that \(\frac{1}{x}=\frac{5}{12}+\frac{3}{4}\).
\_\_\_\_
\_\_\_\_
Question 7
Simplify \(\frac{1 \frac{3}{4}+2 \times 7}{10 \div 2-2}\).
Answer \_\_\_\_
Question 8
(a)
Evaluate
$$ 25^{-1} \times 5^{2} \times 125^{\frac{1}{3}} $$
(b)
Solve the equation
$$ 6 x^{-3}=48 $$
Answer
(a)
\_\_\_\_ [1]
(b)
\_\_\_\_
Question 9
In the diagram, BCD is a straight line. \(\mathrm{A} \hat{\mathrm{B} C}=65^{\circ}\) and \(\mathrm{B} \hat{\mathrm{A} C}=75^{\circ}\).
Calculate
(a)
\(\quad A \hat{C} D\),
(b)
\(\quad \mathrm{A} \hat{\mathrm{C}} \mathrm{B}\),
(c)
reflex \(B \hat{A} C\).
Answer
(a)
\(\hat{A} \hat{C} \mathrm{D}=\) \_\_\_\_ [1]
(b)
\(\mathrm{A} \hat{\mathrm{C}} \mathrm{B}=\) \_\_\_\_ [1]
(c)
reflex \(\mathrm{B} \hat{\mathrm{A}} \mathrm{C}=\) \_\_\_\_ [1]
Question 10
In the diagram EC is parallel to AB and AE is parallel to BD. Given that the perpendicular distance between AB and EC is 6 cm and that the area of parallelogram ABDE is \(45 \mathrm{~cm}^{2}\), find
(a)
the length of \(ED\),
(b)
the area of triangle \(ABC\).
Answer
(a)
\_\_\_\_ cm [1]
(b)
\_\_\_\_ \(\mathrm{cm}^{2}\) [2]
Question 11
Express
(a)
\(17 \frac{1}{2} \%\) as a common fraction in its lowest terms.
(b)
\(\quad \frac{x}{2}-\frac{x-1}{2}\) as a single fraction.
Answer
(a)
\_\_\_\_
(b)
\_\_\_\_
Question 12
\(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and P are four points on level ground. The bearing of C from B is \(160^{\circ}\). P is due north of A and \(\mathrm{ABC}=90^{\circ}\).
(a)
Calculate \(\mathrm{P} \hat{\mathrm{A}} \mathrm{B}\),
(b)
Find the three-figure bearing of B from C.
Answer
(a)
\(\mathrm{PA} \mathrm{A} \mathrm{B}=\) \_\_\_\_ [1]
(b)
\_\_\_\_ [2]
Question 13
Write down the 3 inequalities which define the unshaded region marked \(\mathbf{R}\).
Answer
\_\_\_\_ [1]
\_\_\_\_ [1]
\_\_\_\_ [1]
Question 14
(a)
Use the diagram above to write down Pythagoras Theorem in terms of \(x, y\) and \(z\).
(b)
An equilateral triangle is of side 18 cm. Calculate the length of its altitude leaving your answer in surd form.
Answer
(a)
\_\_\_\_ [1]
(b)
\_\_\_\_ cm [2]
Question 15
The pie chart above shows professionals in town \(\Lambda\).
(a)
Calculate the value of \(x\).
(b)
Given that there are 900 teachers in the town, find the number of doctors.