1
Class / Index Number / Name/ ANG MO KIO SECONDARY SCHOOL
PRELIMINARY EXAMINATION 2012
SECONDARY FOUR NORMAL ACADEMIC
MATHEMATICS SYLLABUS A
Paper 1 / 4042/01
TUESDAY / 21 AUG 2012 / 2 hours
Candidates answer on the Question Paper
INSTRUCTIONS TO CANDIDATES
Write your class, index number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all questions.
The number of marks is given in brackets [ ] at the end of each question or part question.
If working is needed for any question it must be shown with the answer.
Omission of essential working will result in loss of marks.
The total of the marks for this paper is 80.
You are expected to use a scientific calculator to evaluate explicit numerical expressions.
If the degree of accuracy is not specified in the question and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.
For , use either your calculator value or 3.142.
This document consists of 18printed pages
[Turn over
AMKSS Preliminary Exam 2012, 4042/01
1
Mathematical Formulae
Compound Interest
Total amount =
Mensuration
Curved surface area of a cone = πrl
Surface area of a sphere = 4πr2
Volume of a cone =
Volume of a sphere =
Area of triangle ABC =
Arc length = rθ, where θ is in radians
Sector area = , where θ is in radians
Trigonometry
a2 = b2 + c2 − 2bccosA
Statistics
Mean =
Standard deviation =
Answer all the questions.
1 / Evaluate , correct to 4 significant figures.Answer / [1]
2 / (a) / Find the highest common factor of 252 and 120.
Answer (a) / [2]
(b) / (i) / Solve the inequality −3 ≤ 4x + 5 < 21.
(ii) / Hence write down the negative integer values of x which satisfy the inequality.
Answer (b) / (i) / [2]
(ii) / [1]
3 / (a) / The star called Alpha Centauri is 41 305Tera meters from Earth.
Express the distance in metres written in standard form. /
Answer (a) / m / [1]
(b) / A space ship travels at a speed of 2.998 × 107 m/s. How long would it take to reach Alpha Centauri? Give your answer in days expressed in standard form.
Answer (b) / days / [2]
4 / (a) / Express 756 as a product of its prime factors.
Answer / (a) / [2]
(b) / Given that 756k is a perfect cube, state the smallest integer value of k.
Answer / (b) / [1]
5 / (a) / A bus left its depot at 0450 and arrived at the Ang Mo Kio Bus Interchange at 0504. How many minutes did the journey take?
Answer (a) / min / [1]
(b) / The distance from the depot to the interchange is 12 km.
Calculate the average speed of the bus in kilometres per hour.
Answer / km/h / [2]
6 / A map is drawn to a scale of 1 : 350 000.
(a) / Find the actual distance, in km, of a wall which is represented on the map by a line which is 4.8 cm long.
Answer / km / [1]
(b) / A building has an actual area of 200 km2. Find the area, in cm2, of the rectangle which represents the building on the map.
Answer / cm2 / [2]
7 / (a) / Wei Min bought a laptop and sold it a week later at a profit of 5%. If he sold it at a price of $2150, find the original cost of the laptop.
Answer / (a) / $ / [2]
(b) / Collin invested $4500 in a Real Estate Investment Trust which paid 4% per annum interest compounded every 6 months. Calculate the total amount of money that Collin would receive after 8 years.
Answer / (b) / $ / [2]
8 / Solve the simultaneous equations
y − 1.5x = 5,
6y + 5x = −12.
Answer / x = / y = / [3]
9 / Jeffrey and his family went to Canada during the school holidays.
(a) / Before they went on the trip, Jeffrey changed SGD 5000 into Canadian dollars when the exchange rate was CAD 1 = SGD 1.25. Calculate the amount of Canadian dollars he received.
Answer / (a) / CAD / [1]
(b) / When they returned to Singapore 3 weeks later, Jeffrey had CAD 230 left which he changed back into Singapore dollars. The exchange rate at this time was
CAD 1 to SGD 1.23. Calculate the amount of Singapore dollars he received.
Answer / (b) / SGD / [1]
10 / (a) / Evaluate when a = −1 and b = −2.
Answer / (a) / [1]
(b) / Given that x2 + y2 = 13 and xy = 6, find the value of x + y.
Answer / (b) / [2]
11 / In the diagram, ABCD is a parallelogram and CE is perpendicular to AB.
Find
(a) / ∠EBC,
Answer / (a) / ° / [1]
(b) / ∠GDA,
Answer / (b) / ° / [1]
(c) / ∠ECB.
Answer / (c) / ° / [1]
12 / (a) / Evaluate .
Answer / (a) / [2]
(b) / Solve for x in the equation 31−2x = 27x + 2.
Answer / (b) / x = / [2]
13 / (a) / The nth term of a sequence is 3n + 4. Write down the first four terms of this sequence.
Answer / (a) / [1]
(b) / The first five terms of another sequence are
14, 20, 26, 32, 38
Find the nth term of this sequence.
Answer / (b) / [1]
14 / The graph below shows the production cost per day ($) of a certain item for x number of items per day.
(a) / Use the graph to find the production cost per day if 20 items were produced each day.
Answer(a) / $ / [1]
(b) / On a particular day, the cost of production was $11. Find the number of items produced on that day.
Answer (b) / [1]
15 / (a) / Factorise 4p2 − 16 completely.
Answer / (a) / [2]
(b) / Expand and simplify 3(m − 2n) − (4m − 5n).
Answer / (b) / [2]
(c) / Solve 4x − 5 = 7x + 13.
Answer / (c) / x = / [2]
16 / The diagram shows the sector of a circle, centre O. It is given that the radius of the circle is 12 cm and ∠AOB = 120°.
Find
(a) / the perimeter of the sector OAB,
Answer / (a) / cm / [2]
(b) / the area of the sector AOB.
Answer / (b) / cm2 / [2]
17 / The diagram shows a right-angled triangle PQR with PR = 12.5 cm and . The line QR is extended to S.
(a) / Calculate the length of PQ.
Answer / (a) / [2]
(b) / State the values of
(i) / ,
Answer / (b) (i) / = / [2]
(ii) / .
Answer / (b) (ii) / = / [1]
18 / In the diagram,L is the point (−1, 2), M is the point (1, 2) and N is the point (1, −1).
(a) / Write down the equations of the lines LM and MN.
Answer / (a) / LM: / [1]
MN: / [1]
(b) / (i) / Find the gradient of NL.
Answer / (b) (i) / [1]
(ii) / Hence write down the equation of the line NL.
Answer / (b)(ii) / [1]
(c) / Calculate the area of triangle LMN.
Answer / (c) / unit2 / [1]
19 / In the diagram,BA is parallel to ED, BC = 5 cm, AC = 2 cm and EC = 8 cm.
/
(a) / Name a pair of similar triangles.
Answer / (a) / and / [1]
(b) / Find the values of
(i) / ,
Answer / (b)(i) / [1]
(ii) / .
Answer / (b)(ii) / [1]
20 / The graph of y = (x − 2)(x + 5) cuts the x-axis at P and Q. It cuts the y-axis at R.
Write /
(a) / the coordinates of the point R,
Answer / (a) / R / ( / , / ) / [1]
(b) / the coordinates of P and Q,
Answer / (b) / P / ( / , / ) / [1]
Q / ( / , / ) / [1]
(c) / the equation of the line of symmetry,
Answer / (c) / [1]
(d) / the coordinates of the minimum point.
Answer / (d) / ( / , / ) / [1]
21 / The data below shows the number of golf balls collected from a golf course over
20 days.
/
(a) / Complete the following frequency table.
/ [1]
(b) / State the modal number of golf balls collected.
Answer / (b) / [1]
(c) / Find the mean number of golf balls collected.
Answer / (c) / [2]
(d) / Represent the information by drawing a histogram on the given axes provided.
/ [2]
22 / PQR is a triangle. It is given that PQ = 11 cm, PR = 7 cm and ∠QPR = 70°. The line PQ is drawn below. /
Answer (a) (b) (c)
(a) / Construct the triangle PQR. / [2]
(b) / Construct the perpendicular bisector of PQ. / [1]
(c) / Construct the bisector of ∠PQR. / [1]
(d) / Given that the two bisectors meet at S, measure the distance PS.
Answer / (d) / cm / [1]
END OF PAPER
AMKSS Preliminary Exam 2012, 4042/01