Test for Mathematics Low Level

8/8/2019 Test for Mathematics Low Level

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TEST 1 FOR MATHEMATICS 2ND

SEMESTER FINAL EXAMINATION

1. (a) Solve the equation where 0360. [3](b) On the same axes, sketch the graph ofy = andy =

for

0 x 2.

Hence, state the number of solutions in this interval of the equation . [5]

2. A number is selected at random from the set . Find theprobability of selecting a number which is not aperfect square. [2]


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3. There are 33male teachers andx female teachers in a school. Ifa teacher is selected atrandom from the school, the probability of selecting a female teacher is

. Find x. [2]

4. As shown in the diagram, is an isosceles triangle with . Find(a) the length ofAB;

(b)ACB. [4]

5. Abasket contains 40 oranges. 6 of themare rotten.(a) Ifan orange is chosen randomly from the basket, what is the probability that it is rotten?

(b) If the first orange chosen is good and another one is chosen randomly from the basket,

find theprobability that the second orange is also good.

(c)A number of good oranges are taken out from the basket, the probability of choosing a

good orange is

. Find how many good oranges have been taken out. [5]


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6. Diagrambeside shows a right prism with a horizontal rectangularbase PQRS. PQVU is auniform cross-section of the prism. Calculate the angle between the plane TQRand the

plane PQRS. [3]

7. Given that sin A =

and cos B =

, where both Aand Bare obtuse angles. Find the

value of:(a) cos 2A;

(b) tan(AB). [3]

8. The diagram shows apyramid with a triangularbase BCD. M is the midpoint of CD.Given CD = 18 cm, calculate

(a) the anglebetween the line AD and the plane BCD.


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(b) the length of BM.

(c) the anglebetween the line AM and the point BCD. [5]

9. As shown in the diagram:

K lies on the straight line FG whereFK= 5.333 cmand GKC= . KPis the normal to

the planeABCD. Find

(a) the value of tan ;

(b) the anglebetween the line AKand the plane ABCD. [5]


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10.A cube with one of its faces marked PQRS, is rolled on a flat surface. Find the probabilitythat

(a) the face PQRStouches the surface;

(b) the edge PQ touches the surface;

(c) the vertexQ touches the surface. [4]

11.A number is selected at random from each of the sets, {4,5,6}and {7,8,9}. Find theprobability that

(a)both the numbers are even;

(b) the sum of the numbers is 13. [4]

12.B C

The diagramabove shows twopoints B and C on a horizontal ground. The distance

between the two points is 340 m. A helicopter is vertically abovepoint B. Given that the

angle of depression from the helicopter topoint C is 57, state the height of the helicopter

frompoint B. [2]


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13.In the diagram,ACDandBCEare straight lines.Find the length ofBC. [3]


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Test for Mathematics Low Level

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