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1Final-Year Examination Specimen Paper 1
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
PART I (50 marks)D�rati�n: 1 ���r
1 Ex�ress 592 704 as a �r�d�ct ��� �rime ��act�rs. Hence, find t�e va��e ��� 3√_______
592 704 . [2]
2 Simplify3(2x − 4) + 2__3 (3 − 6y) − (1 − x) − 2(y − x). [2]
3 Eva��ate 3 2__5 − √________
25 × 49_______144 ÷ 1 3__4 . [2]
4 Estimate t�e va��e ��� 3.981 ÷ √_______
101.112 _______________(−1.99)2 , �ivin� y��r answer c�rrect t� 1 si�nificant fi��re. [2]
Final-Year Examination Specimen Paper 1
Marks Obtained
100
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2Final-Year Examination Specimen Paper 1
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
5 (a) Ex�ress 234 915 cm c�rrect t� t�e nearest km. [1] (b) C�nvert 0.019501 km2 t� �a, �ivin� y��r answer c�rrect t� tw� si�nificant fi��res. [2]
6 Giventhata = −3, b = 4 and c = −1, find t�e va��e ���
(a) b − a − c3, [1]
(b) b ___2c − a, [1]
(c) √____
b ____3ac . [2]
7 I�� 4x + 12 > 4 and 7__2y − 14 < 0 s�c� t�at x andy are inte�ers, find
(a) t�e �reatest va��e ��� (y − x), [2]
(b) t�e �east va��e ��� x2__y . [2]
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3Final-Year Examination Specimen Paper 1
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
8 Deb�ra� b����t a dress at $59.40 a��ter a va��e-added tax ��� 8% was im��sed �n it. H�w m�c� m�re w���d s�e need t� �ay i�� t�e va��e-added tax were t� increase t� 10%? [3]
9 A c�ntract�r em���ys 5 men t� �aint 20 r��ms. ��ey take 4 days t� c�m��ete t�e �r�ject by w�rkin� 8 ���rs dai�y. He receives a �r�ject t� �aint 10 simi�ar ���ses �avin� 6 r��ms eac�. H�w many m�re men m�st �e em���y s� t�at �e c���d c�m��ete t�e �r�ject in 5 days by w�rkin� 12 ���rs dai�y? [4]
10 ��ere are 12 ��ami�ies attendin� a ��ami�y ���ncti�n. ��e rati� ��� t�e n�mber ��� ad��ts t� t�e n�mber ofchildrenis2:3.Ifboththeparentsofthefamiliesarepresent,howmanymorechildrenthant�e ad��ts are t�ere in t�e ���ncti�n? [4]
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4Final-Year Examination Specimen Paper 1
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
11 In t�e �inear ���ncti�n y = 2 − 4__5x, ca�c��ate
(a) t�e va��e ��� ywhen (i) x = −2, [1] (ii) x = 3, [1]
(b) t�e va��e ��� xwheny = 10. [1]
12 ��e fi��re be��w s��ws a rectan��e and a sq�are. ��e �en�t� ��� t�e rectan��e is 4 cm ��n�er t�an its widt�. ��e �erimeter ��� t�e sq�are is 3__7oftheperimeteroftherectangle.
xcm
Find (a) an ex�ressi�n ���r t�e �erimeter ��� t�e s�aded re�i�n, [3] (b) t�e va��e ��� x i�� t�e �erimeter ��� t�e s�aded re�i�n is 40 cm, [2] (c) t�e area ��� t�e s�aded re�i�n. [2]
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5Final-Year Examination Specimen Paper 1
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
13 ��e �r���rti�ns ��� n�trients taken by a ��ami�y are s��wn in t�e �ie c�art be��w. Given t�at t�e ��ami�y c�ns�mes 1.2 k� ��� carb��ydrate m�re t�an t�e �r�tein dai�y.
(a) Find t�e va��e ��� x. [2] (b) ��at �ercenta�e ��� t�e n�trients taken is carb��ydrate? [2] (c) Find t�e t�ta� mass, in ki���rams, ��� t�e intake ��� n�trients by t�e ��ami�y dai�y. [2]
Carbohydrate
Protein
Fat
Othersx
5x
14 Inthediagram,UTRisastraightlineandTQR is an is�sce�es trian��e s�c� t�at QT=QR. GiventhatPQ // RS,∠UTQ = 145° and ∠PQT = 90°, find (a) ∠TQR, [2] (b) ∠TRS. [2]
145°
U T
R
S
Q
P
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6Final-Year Examination Specimen Paper 1
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
PART II (50 marks) D�rati�n: 1 ���r
1 ��e tab�e be��w s��ws t�e disc��nts �iven t� c�st�mers ���r di����erent am��nts ��� ��rc�ases in a directsalecompany.
Am��nt ��rc�ased ($x) 0<x500 500<x 1000 x 1000Disc��nt (%) 5 7 10
(a) I�� Henry ��rc�ases items t�at w�rt� $870, ��w m�c� can �e save ��r�m t�e disc��nts �iven t� �im? [2]
(b) Instead ��� ��rc�asin� $870 in �ne s��rt, �e s��its it int� tw� ��rc�ases, $450 and $420. H�w m�c� m�re wi�� �e need t� �ay? [2]
(c) Je����rey �aid $994 ���r s�me items ��rc�ased ��r�m t�e c�m�any. ��at was t�e va��e ��� t�e items ��rc�ased be���re disc��nt? [3]
2 (a) If5y − 2
______y − 6 = 0, find t�e va��e ��� y2 + 4. [3]
(b) S��ve t�e eq�ati�n 3+z _____2 − 4z − 1______3 +1__6 = 0. [3]
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7Final-Year Examination Specimen Paper 1
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
3 �ater fl�ws ��r�m a ta� int� an em�ty cy�indrica� tank ��� radi�s 28 cm at an avera�e rate ��� 400 ml �er sec�nd. ��e ta� is t�rned ����� a��ter 7 min�tes and t�e tank is 5___11 ����� wit� water.
28cm
Find (a) t�e �ei��t ��� t�e tank, [3] (b) t�e s�r��ace area ��� t�e tank t�at is in c�ntact wit� water. [3]
��e water ��r�m a c�bic tank t�at is ����� ��� water is ���red int� t�e cy�indrica� tank. ��e water is j�st en���� t� fi�� t�e cy�indrica� tank.
(c) Find t�e �en�t� ��� t�e c�bic tank, c�rrect t� 2 decima� ��aces. [2]
(�ake � = 22___7)
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8Final-Year Examination Specimen Paper 1
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
4 In Jas�n’s CPF acc��nt, t�e rati� ��� t�e am��nt ��� m�ney �e �as in t�e �rdinary acc��nt t� t�at in t�e medisave acc��nt is 10 : 3. ��e rati� ��� t�e am��nt ��� m�ney in t�e s�ecia� acc��nt t� t�at in t�e medisave acc��nt is 8 : 5. Given t�at �e �as $13 000 m�re in t�e �rdinary acc��nt t�an in t�e s�ecia� acc��nt, ca�c��ate
(a) t�e rati� ��� t�e am��nt ��� m�ney in t�e �rdinary acc��nt t� t�at in t�e medisave acc��nt t� t�at in t�e s�ecia� acc��nt, [2]
(b) t�e am��nt ��� m�ney �e �as in eac� acc��nt. [3]
Given t�at �e �ad wit�drawn 40% ��� t�e m�ney in t�e �rdinary acc��nt s� ��ar, (c) ��w m�c� m�ney did �e �ave in t�e �rdinary acc��nt be���re t�e wit�drawa�? [2]
5 (a) Apentagonisshownasbelow.KLisastraightline.
30° 70°
2x
5x 3x
K L
(i) Find t�e va��e ��� x. [3] (ii) Find its �reatest exteri�r an��e. [2]
(b) Eac� interi�r an��e ��� an n-sided re���ar ���y��n is t�ree times eac� ��� its exteri�r an��e. Name t�e ���y��n. [3]
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9Final-Year Examination Specimen Paper 1
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
6 (a) C�nstr�ct a trian��e PQR s�c� t�at PQ=8.5cm,∠RQP = 75° and ∠RPQ = 60°. [1] (b) C�nstr�ct a circ�e wit� centre R and diameter 9 cm. ��e circ�e c�ts PRandQRatSandT
res�ective�y. Meas�re t�e �en�t� ��� ST. [2] (c) C�nstr�ct t�e �er�endic��ar bisect�r ��� ST. [1]
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10Final-Year Examination Specimen Paper 1
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
7 Answer the whole of this question on a sheet of graph paper.
(a) Usin� a sca�e ��� 1 cm t� re�resent 1 �nit �n b�t� axes, draw t�e �ra�� ��� y = 3 − 2x. [2] (b) Theliney = 3 − 2x �asses t�r���� t�e ��int (a,a). Usin� t�e �ra��, find t�e va��e ��� a. [1] (c) Drawanotherlineargraphofy=3x+8. Find t�e ��int ��� intersecti�n ��� t�e tw� �ines. [2]
8
150°
Sleeping 30°
x + 30°x
H�mew�rk
School
Piano
��e �ie c�art s��ws t�e �r���rti�n ��� time Fi�na s�ends �n 4 activities in a day. Find (a) t�e va��e ��� x, [2] (b) t�e n�mber ��� ���rs Fi�na s�ends �n ��ayin� �ian�, [1] (c) t�e �ercenta�e ��� t�e di����erence in t�e n�mber ��� ���rs Fi�na s�ends in t�e sc���� and
�n d�in� ��mew�rk. Give y��r answer c�rrect t� 2 si�nificant fi��res. [2]
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11Final-Year Examination Specimen Paper 2
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
PART I (50 marks)D�rati�n: 1 ���r
1 (a) Ex�ress 0.04 as a ��racti�n in its ��west terms. [1] (b) Eva��ate 0.281 × 4.13 ÷ 0.074, c�rrect t� (i) 2 si�nificant fi��res, (ii) 3 decima� ��aces. [2]
2 Eva��ate 4 − 5 × [3 − (−1) × 2 ÷ 4 − 8]. [2]
3 Eva��ate 1__2 − 2+3__4
_____1 − 5__2
, �ivin� y��r answer as a ��racti�n in its ��west terms. [2]
4 (a) Ex�ress 2205 as a �r�d�ct ��� �rime ��act�rs. [1] (b) Hence, find t�e �east va��e ��� n s�c� t�at 2205n is divisib�e by 6 and 8. [2]
Final-Year Examination Specimen Paper 2
Marks Obtained
100
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12Final-Year Examination Specimen Paper 2
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
5 (a) Simplify3+m − 1_____6 − 2(m − 2)
________5 . [2]
(b) Factorise1__2ab − 3__2ac − 6c+2b. [2]
6 Giventhat2__5(x − 2) − 1__3 (1 + 2x) = −3, find t�e va��e ��� x2 . [3]
7 In t�e fi��re, KLMNisaparallelogramandKPQ andNMQarestraightlines. Find (a) ∠KNM, [2] (b) ∠PQM. [2]
110°
28°K L
MN
P
Q
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13Final-Year Examination Specimen Paper 2
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
8 Mr. ��n� b����t a re��ri�erat�r at a 15% disc��nt d�rin� a sa�e. He �aid $1273.30 ���r it a��ter a GS� ��� 7% im��sed �n it. H�w m�c� m�ney �ad �e saved? [3]
9 ��ere are 3 sect�rs, A, B and C, in a �ie c�art. I�� t�e rati� ��� t�e sect�rs is 4 : 6 : 5, (a) find t�e s�m ��� t�e an��es re�resentin� sect�rs A and C, [2] (b) w�at �ercenta�e ��� sect�r A is sect�r C? [2]
10 2__7ofthewaterinabottlewastransferredintoapailcontaining0.5l ��� water. ��ere was 190 mlmoreofwaterinthebottlethaninthepail.Find
(a) t�e am��nt ��� water, in l, t�at was trans��erred int� t�e �ai�, [2] (b) t�e rati� ��� t�e am��nt ��� water in t�e b�tt�e t� t�at in t�e �ai� at first. [2]
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14Final-Year Examination Specimen Paper 2
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
11 ��e den�minat�r ��� a ��racti�n is 4 m�re t�an its n�merat�r. A��ter addin� 1 t� a ��racti�n, its n�merat�r is 7 m�re t�an its den�minat�r n�w.
(a) ��at is t�e �ri�ina� ��racti�n? [2] (b) Ex�ress t�e �ri�ina� ��racti�n as a rec�rrin� decima�. [2]
12 A s��id c�nsists ��� a cy�inder j�ined t� a c�be. ��e base radi�s ��� t�e cy�inder is 1__4ofthelength��� t�e c�be. ��e t�ta� �ei��t ��� t�e s��id is 13 cm. I�� t�e �en�t� ��� t�e c�be is 6 cm, find
(a) t�e v���me ��� t�e s��id, [2] (b) t�e t�ta� s�r��ace area ��� t�e s��id. [3] (�ake � = 22___7)
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15Final-Year Examination Specimen Paper 2
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13 ��e tab�e be��w s��ws t�e �rades �btained by 40 ���i�s. 37 1__2 % ��� t�e ���i�s �btained a �rade lessthan3.
Grade 1 2 3 4 5N�mber ��� ���i�s 3 x 13 y 5
Find (a) t�e va��es ��� xandy, [3] (b) t�e an��e re�resentin� �rade 2 i�� t�e in���rmati�n ab�ve is i���strated �sin� a �ie c�art. [1]
14 A b�y j���ed ar��nd a circ��ar fie�d at an avera�e s�eed ��� 1.2 m/s. He c�m��eted j���in� t�ree r��nds a��n� t�e fie�d in 2 min�tes.
(a) Ca�c��ate t�e �erimeter ��� t�e fie�d. [2] (b) H�w m�c� ��aster m�st �e j�� s� t�at �e can c�m��ete j���in� t�e t�ree r��nds in
1 min�te 30 sec�nds? [3]
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16Final-Year Examination Specimen Paper 2
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
PART II (50 marks) D�rati�n: 1 ���r
1 (a) Simplify3__2+3t − 4t − 5_____8t . [3]
(b) S��ve t�e eq�ati�n 1__5(2s − 1) − 2__3 (7 − s) + 6 = 0. [3]
2 (a) ��e s�m ��� Jane’s and Fi�na’s a�es is 35 years ��d. Jane wi�� be twice as ��d as Fi�na int years’ time. �rite an ex�ressi�n, in terms ��� t, ���r t�e di����erence in t�eir a�es. [3]
(b) Given t�at Jane wi�� be 15 years ��der t�an Fi�na in t years’ time, find t�e va��e ��� t. [2]
3 Inthediagram,ABisthediameterofthecircleandAB // DC.Giventhat11___16oftheareaofthefi��re is t�e circ�e and AB = 14 cm, find
(a) thelengthofDC, [4] (b) t�e area ��� t�e fi��re. [2]
(�ake � = 22___7)
A B
CD E
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17Final-Year Examination Specimen Paper 2
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
4 (a) �w� ��� t�e exteri�r an��es ��� an n-sided ���y��n are 46° and 58°. ��e remainin� exteri�r an��es are 32° eac�. Find t�e va��e ��� n. [3]
(b) Inthediagram,KLMNandLPQ are strai��t �ines. Ca�c��ate t�e va��e ��� (i) x, [2] (ii) y. [2]
K L M N
P
Q
R S
x
y
40° 32° 42°
5 (a) Aliney = 2 − 1.5x �asses t�r���� t�e ��int (n,2n). Find t�e exact va��e ��� n. [2]
(b) Giventhatthepoint(1__2 , −4 )liesonaliney = 4x+k, ca�c��ate
(i) t�e va��e ��� k, [2] (ii) t�e va��e ��� ywhenx = −3. [2]
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18Final-Year Examination Specimen Paper 2
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
6 C�nstr�ct t�e ������win� in a sin��e dia�ram:
(a) C�nstr�ct a �ara��e���ram ABCDwithAB=8cm,BD = 12 cm and ∠ABD = 28°. Meas�re thelengthofBC. [3]
(b) C�nstr�ct t�e �er�endic��ar ��r�m CtoAD t� c�t ADatS. Meas�re t�e �en�t� ��� CS. [2] (c) Hence, estimate t�e area ��� t�e �ara��e���ram. [2]
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19Final-Year Examination Specimen Paper 2
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
7 ��e �ine �ra�� in a ��ster s��ws t�e n�mber ��� accidents ca�sed by drivers w�� drink a�c���� w�i�e drivin� in eac� year ��r�m 2008 t� 2013.
2008 2009
50
51
52
53
54
55
No.
of A
ccid
ents
Year
56
492010 2011 2012 2013
(a) Find t�e �ercenta�e increase in accidents ��r�m 2008 t� 2013. [2] (b) In w�ic� year was t�e n�mber ��� accidents t�e �i��est? [1] (c) Whydoesthegraphmisleadthereaders? [2] (d) S���est a ��r��se ���r re�resentin� t�e in���rmati�n t�is way. [1]
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20Final-Year Examination Specimen Paper 2
Be GREA¹T! MATHEMATICS (Secondary 1)© Sin�a��re Asia P�b�is�ers Pte Ltd. A�� ri��ts reserved.Re�r�d�cib�e ���r ��me/c�assr��m �se �n�y.S�RIC�LY NO� FOR SALE.L��k ���r �t�er �se���� res��rces: www.sa��r�.c�m
8 At 14 25, Ke��y dr�ve ��r�m ��me t� �am�ines at a c�nstant s�eed ��� 90 km/�. A��ter st���in� ���r �a��� an ���r, s�e �eaded back ��me wit� a c�nstant s�eed ��� 60 km/�. S�e reac�ed ��me at 17 25.
(a) Find t�e t�ta� time taken ���r trave��in� in t�e car. [2] (b) Find t�e distance between �er ���se and �am�ines. [3] (c) At w�at s�eed m�st s�e drive s� t�at s�e can reac� �am�ines 15 min�tes ear�ier? [2]
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