Pythagoras theoremIB MYP Maths Extended: Subtopic test

1. 1
   A ladder $5$ m long leans against a vertical wall. The foot of the ladder is on level ground, $1.4$ m from the wall.

   (a)

   How high up the wall does the ladder reach?

   [1 mark]

   • A$5.2$ m
   • B$3.6$ m
   • C$4.8$ m
   • D$23.04$ m

   (b)

   The ladder is moved so that its top reaches a point $3$ m above the ground. How far is its foot from the wall?

   [1 mark]

   • A$2$ m
   • B$4$ m
   • C$5.83$ m
   • D$16$ m

   (c)

   With the foot $1.4$ m from the wall, the top of the ladder slips down $0.6$ m. Find how far the foot of the ladder moves away from the wall. Give your answer to $3$ significant figures.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A rectangular box measures $12$ cm long, $9$ cm wide and $8$ cm high.

   (a)

   Find the length of the diagonal of the base of the box.

   [1 mark]

   • A$21$ cm
   • B$225$ cm
   • C$3$ cm
   • D$15$ cm

   (b)

   Find the length of the longest straight rod that fits inside the box.

   [1 mark]

   • A$17$ cm
   • B$29$ cm
   • C$289$ cm
   • D$15$ cm

   (c)

   Find the length of the diagonal of one of the $12$ cm by $8$ cm faces. Give your answer to $3$ significant figures.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A rectangular football pitch is $100$ m long and $64$ m wide.

   (a)

   Find the length of the diagonal of the pitch. Give your answer to $3$ significant figures.

   [3 marks]

   (b)

   A player runs from one corner to the opposite corner. Running along the two sides is one route and running along the diagonal is another. Find how much shorter the diagonal route is, in metres and as a percentage of the route along the sides. Give each answer to $3$ significant figures.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A flagpole stands vertically on level ground. A support cable of length $13$ m joins the top of the pole to a point on the ground $5$ m from the foot of the pole. Cable costs AED $18$ per metre.

   (a)

   (i) Find the height of the pole.
   (ii) A second cable joins a point on the pole $9$ m above the ground to a point on the ground $12$ m from the foot of the pole, on the opposite side. Find the length of this second cable.
   (iii) Find the cost of the two cables.

   [6 marks]

   (b)

   The pole is replaced by a taller pole $15$ m high. The cable is attached to the top of the new pole and to the same point on the ground. A pupil says: 'The new pole is $25\%$ taller than the old one, so the new cable will be $25\%$ longer than the old $13$ m cable.'
   (i) Find the length of the new cable.
   (ii) Cable is sold only in whole metres. Find the cost of the cable that must be bought.
   (iii) Show that the pupil is wrong.

   [6 marks]

   Total for question 4: 12 marks

End of questions