Chapter 7 Practice Paper: Pythagoras’ Theorem and Irrational Numbers — question paper (print)

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QQ/S2MATH/CH7

Secondary 2 · Lower Secondary Mathematics (G2 / G3)

Chapter 7 Practice Paper

Pythagoras’ Theorem and Irrational Numbers

Duration: 40 minutes

Total: 30 marks

Name:

Class:

Date:

READ THESE INSTRUCTIONS FIRST

Write your name, class and register number in the spaces at the top of this page.
Answer all questions.
Section A: write the letter (A, B, C or D) of the correct answer in the brackets provided.
Section B: write your answers in the spaces provided.
Show all working. Marks may be awarded for correct working even if the final answer is wrong.
Give units with your answers where appropriate.
The number of marks is given in brackets [ ] at the end of each question or part question.

Original practice material written for the MOE Lower Secondary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 7.

For Examiner’s Use
Section A	/ 10
Section B	/ 20
Total	/ 30

Section A: Multiple-choice questions[10 marks]

Answer all questions. For each question, write the letter (A, B, C or D) of the correct answer in the brackets provided.

1
The two shorter sides of a right triangle measure 9 and 12. The longest side is
1. A21
2. B√63
3. C15
4. D10.8
( )
2
From a hypotenuse of 17, one leg of 8 is known. The remaining leg measures
1. A15
2. B√225
3. C19
4. D12
( )
3
Which of these is irrational?
1. A16
2. B0.25
3. C5/8
4. D√7
( )
4
The exact hypotenuse of a right triangle with legs 5 and 7 is
1. A12
2. B√74
3. C√12
4. D35
( )
5
In which triple does the converse test succeed?
1. A(5, 6, 7)
2. B(7, 24, 25)
3. C(9, 16, 20)
4. D(10, 24, 27)
( )
6
Estimate the position of √40: it sits between the whole numbers
1. A6 and 7
2. B5 and 6
3. C7 and 8
4. D3 and 4
( )
7
The exact diagonal of a square of side 8 is
1. A16
2. B64
3. C4√2
4. D8√2
( )
8
A ramp 10 m long rises 6 m. Its horizontal run is
1. A4 m
2. B8 m
3. C√136 m
4. D12 m
( )
9
If a triangle’s sides satisfy a² + b² = c², then we can conclude
1. Ait finds the longest side of any triangle
2. Bit proves all triangles contain a right angle
3. Ca triangle whose sides satisfy a² + b² = c² has a right angle
4. Dit works only for isosceles triangles
( )
10
The decimal 0.101001000100001… is
1. Airrational — no fixed block ever repeats
2. Brational — it is a decimal
3. Crational — the digit 1 keeps appearing
4. Dirrational — it is less than 1
( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show your working clearly. Give exact answers unless told to round.

1
Two right triangles are given.
1. (a)
  Triangle X has legs 9 and 12. Find the hypotenuse.
  [2]
2. (b)
  Find the perimeter of triangle X.
  perimeter =[1]
3. (c)
  Triangle Y has legs 20 and 21. Find its hypotenuse.
  [2]
2
A triangle has sides 11, 60 and 61.
1. (a)
  Name the theorem that tests whether such a triangle has a right angle.
  theorem =[1]
2. (b)
  Show that the triangle is right-angled.
  [2]
3. (c)
  Which side is the hypotenuse?
  hypotenuse =[1]
4. (d)
  Is the triangle isosceles as well? Give a reason.
  [1]
3
A rectangular TV screen has a 50-inch diagonal and stands 30 inches tall.
1. (a)
  Find the width of the screen.
  [2]
2. (b)
  Find the area of the rectangular screen.
  area =[1]
3. (c)
  Another model is 48 by 20 inches. Give the exact length of its diagonal.
  [2]
4
A right triangle has one leg of 9, and a hypotenuse of 15. The other leg is x.
1. (a)
  Write an equation for x using Pythagoras’ theorem.
  [2]
2. (b)
  Solve the equation for x.
  [2]
3. (c)
  Explain why the value x = −12 is rejected in this context.
  [1]

— End of paper —