Mock Test Paper for E-Math

7/29/2019 Mock Test Paper for E-Math

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O-LEVEL E-Math EXAMINATION

Duration 2 hours

Total marks 100

1. Solve the followings(a) Rearrange the number in ascending order: -5, 3, -1, 5, 0.125, 2 [1](b) State which of the following number are irrational numbers, 82 ,

7

23and e. [1]

2. (a) Evaluate,7

52

3

13 , as a single fraction in its simplest form [1]

(b) Find the value of 0081.0 [1]

3. (a) Express, 386.71, correct to two significant figures [1](b) Express the numbers 168 and 324 as the products of their prime factors [1]

4. (a) Given that e=fgf

gfg

43

1

2

++, find the value of e when f=(-2) and g=

2

1[2]

(b) Express)2(3

1

4

21

2 +

x

x

x

xas a single fraction in its simplest form [2]

5. (a) Given that m=4.5x10-6 and n=1.2x10-3, evaluate 2m - n2, giving your answer instandard form [2]

(b) Given thatm

mqp

+=1

2 , express q in terms of p and m. [2]

6. Factorise completely(a) 12a2-75b2 [1](b) 20x2+xy-12y2 [2]

7. (a) Evaluate 343231 5153 [1](b) Simplify 1045325 ba [1]

8. (a) Given that y is inversely proportional to px-3, find the value of p if y=6 , x=3and y=16 , x=7 [2]

(b)If p:q:r=6:1:5 find the value ofrq

qp

65

32

+

+, give your answer as a fraction in its

simplest form [2]


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9. (a) A dinner bill was $59.80. The price included a 10% service charge and 7%government tax

Find the actual cost of the dinner [1]

(b) At a close-down sale, a man bought a $1000 television set at a 10% discount.He later sold it at a second-hand shop for $1200.Calculate the percentage

profit that he made. [2]

10. (a) A shopkeeper bought 3000 greeting cards at $750. He intends to sell at 95

cents per card

(i) Calculate the cost price of each card [1]

(ii) Calculate the percentage profit per card [1]

(iii) If he sold all the cards at 95 cents each, how much money would he earn in

total [1]

(iv)Find the minimum number of cards he needs to sell in order not to make a

loss [2]

(v) He found that 1123 of the cards were damaged. If he intends to keep thesame profit, how much would he price the rest of the cards for? Give your

answer correct to the nearest cent. [1]

11. (a) Amanda bought a handbag in New York for US $200. If she were to buy the

handbag locally, it would have cost her S$500. Calculate the percentage in

saving she made. (Given that US$1=S$1.50) [3]

(b) A factory manufactures aluminium cans. The current machine can produce980 aluminium cans in 3 minutes. This machine needs to operate for 8 hours a

day in order to meet its daily production target. The factory bought a new

machine to speed up its production of aluminium cans. If the new machine starts

to operate after the current one which has been operating for 3 hours, it willonly take 2 hours 20 minutes to complete its daily production target. Find the

rate of the new machine. [4]

12. (a) Solve the equation2

3

2+a

a=

a23

1

[3]

(b) Given that a+ 5 is one of the solutions of equation x2-8x-b2=0 where b>0find the values of a and of b. [3]

(c) Solve the simultaneous equations

2332

223

=

=+

ba

ba [3]

13. (a) If x and y are integers such that 15 x and 27 y , calculate the

maximum value of (x+2y)(x-2y) [1]

(b) Find the largest prime number p which satisfy the inequality 75-4p>1 [2]

14. Given that 35 x and 28 y , find

(a) The smallest possible value of 2x-y [1]

(b) The largest possible value of (x-y) 2 [1]


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15. A hot-air balloon can be filled up by two helium taps A and B in 3 hours. Taps A

can fill up the balloon in x hours while tap B takes up to 2x+3 hours.

(a) What fraction of the balloon is filled up by Tap A in 1 hour? [1]

(b) What fraction of the balloon is filled up by Tap B in 1 hour? [1]

(c) Hence, form an equation with respect to x and show that it can be reducesto 2x2-6x-9=0 [2]

(d) Solve the equation 2x2-6x-9=0, given both answers correct to 2 decimalplaces [3]

16. The diagram below shows a pentagon and a regular hexagon sharing a common

side DE.

AE and CD are produced to meet at M so that triangle DEM is an isosceles triangle. FE

and ID are produced to meet at N. Given that Angle BAE=CBA=DCB=110, Find

(i) AED [2](ii) DME [1](iii) MDN [1]

The diagram above shows two triangles PQR and ABC. Vertices A, B and C are the

midpoints of PR, PQ and QR respectively.

(i) Show that triangle RAC and RPQ are similar [1](ii) Hence, write down 3 pairs of parallel lines [1](iii)Explain clearly the relationship between triangles PAB and BCQ. [2]


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(iv)Given that the area of triangle PQR is 12cm2, find the area of PACB. [1]17. In the diagram, P, Q, R and S are four points on level ground. S is due east of P, the

bearing of P from Q is 151 and the bearing of Q from R is 246 . PQ=90m, PS=210m,

QR=160m and PSR= 50

(a) Calculate:

(i) PQR [1]

(ii) PR [2]

(iv) PRS [2](v) The area of quadrilateral PQRS [3]

(b) A coconut tree is located at R. The angle of elevation of the top of the tree from P

is 8 .

(i) Calculate the height of the coconut tree [1]

(ii) A monkey is spotted at3

1 up the height of the tree. Calculate the angle of

elevation of the monkey from Q. [2]

18. In the diagram, AB is a tangent to the circle at P. The circle passes through the

points P, Q, R, S and T. Given that PS is the diameter of the circle, APT= 72 ,

RTS= 20 and BPQ= 40 , calculate


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(a) SRT [2]

(b) QRT [2]

(c) QSR [2]

19. In the diagram, TA is the tangent to the circle with centre O, and which passes

through the points A, B, C and D. Another smaller circle, which passes through the

points C, D, E and F, is drawn such that BCF, ADE and TEF are straight lines.

Given that ABF=ATE= 66 and CAD= 26 , calculate and show your reasons

clearly

(a)AOC [1](b)OCA [1](c) ACD [2](d)CFE [1](e)OCB [4](f) BAO [1]


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20. The diagram below shows triangle ABC.

(a) Construct a circle that passes through the vertices of the triangle. Mark the

centre of the circle as O. [1]

(b) Draw the locus of the point X which is equidistant from AB and BC. [1]

(c) Draw the locus of the point Y such that area of triangle AYC=area of triangle

ABC, and Y is on the other side of AC as B. [2]

(d) Z is the point such that ABZ=CBZ. Construct and write down the shortest

length of OZ. [2]


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