CIE Mathematics Paper-1: Specimen Questions 136 - 138 of 175

Question number: 136

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The diagram shows a regular pentagon and a square. Calculate the values of x0andy0 .

A regular pentagon and a square

A regular pentagon and a square

Find the angles x0and y0 by using the theory of regular pentagon and square

Explanation

Here, pentagon is regular.

So, we can find it’s exterior angle by using the formula 3600n , where n = number of sides.

In pentagon number of sides = 5, so exterior angle = 36005=720.

So, as shown in figure, its interior angle x0=1800720=1050 .

Now, for angle y0 :

As shown in figure, total angle is 3600 , so x0+y0+squares900=3600

1050+y0+900=3600

y0=36001950

y0=1650 .

Question number: 137

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olve 58÷334

Give your answer as a fraction in its lowest terms. You must show all your working.

Explanation

Here, 58÷33458÷154

Now, if we inverse denominator of it will give multiplication: 58×415=20120=16

Or

Now, by multiplying in cross numbers: 20120=16

Question number: 138

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(a) (35)x=81625 Write down the value of x.

(b) a2=81 Write down the value of a.

Explanation

Here,

(a) (35)x=81625 , so here, we need same fraction in right side as left side.

So, (35)x=3×3×3×35×5×5×5(35)x=(35)4x=4.

(b) Here, a2=81 is given, so we need to convert 81 into exponent form with 2.

So, here a2=92, so a=9.

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