CIE Mathematics Paper-1: Specimen Questions 57 - 58 of 175

Question number: 57

Short Answer Question▾

Write in Short

Factorize completely 6xy8xz.

Explanation

Here,

  • Factoring is the decomposition of an object into a product of other objects or factors, which gives the original equation when multiplied together.

So, 6xy8xzwillbe2x(3y4z).

Question number: 58

Essay Question▾

Describe in Detail

In the diagram, the lines AB and CD are parallel. The lines AD and BC intersect at X. Angle XDC = 35° and angle CXD = 120°.

Two parallel lines and two intersecting lines

Two parallel lines and two intersecting lines

Find the below given calculations by using appropriate formulas and methods

(a) (i) Write down the size of angle BAX.

(ii) Write down the size of angle ABX

(b) Complete the statement: Triangle AXB is ________ to triangle DXC.

(c) AB = 8.3 cm, BX = 5.5 cm and CD = 16.6 cm. Calculate the length of CX.

Explanation

(a) (i) Here, in AXBandCXD angles BAX and CDX are alternate interior angles which will be similar.

So, BAX=350 .

(ii) For ABX :

Here, CXD=1200 is given, so AXB=1200(CXDandAXBareverticalangles) .

Now, in any triangle addition of all angles will be 1800.

So, in AXB, ABX+AXB+BAX=1800

ABX+1200+350=1800

ABX+1550=1800

ABX=18001550

ABX=250

So, in CXD , XCD will also be 250 , as XCD and ABX are alternate interior angles

(b) Here, Triangle AXB is similar to triangle DXC because there all three angles are same in both.

  • Two triangles are called as congruent triangles when both have all equal sides and equal angles.
  • Two triangles are called as similar triangles:

o If all angles are same in both.

o If all pairs of sides are in same proportion.

o If two pairs of sides are in same proportion and one angle is also same in both.

(c) Here, AB = 8.3 cm, BX = 5.5 cm and CD = 16.6 cm are given,

So, formula for similar triangles for side: ABCD=BXCX8.316.6=5.5CXCX=5.5×16.68.3CX=11cm.

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