Chapter 4 Practice Paper: Algebraic Expressions and Formulae — question paper (print)

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QQ/S3EM/CH4

Secondary 3 · Elementary Mathematics (G2 / G3)

Chapter 4 Practice Paper

Algebraic Expressions and Formulae

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.
Show all necessary working. Omission of essential working will result in loss of marks.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
Geometrical instruments and an approved calculator may be used.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for each paper is shown on its cover.

Original practice material written for the MOE Elementary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 4 (N5 Algebraic Expressions and Formulae: expansion, factorisation, algebraic fractions, nth term, formulae).

For Examiner’s Use
Section A	/ 30
Total	/ 30

Section A: Structured questions[30 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give non-exact numerical answers correct to 3 significant figures where appropriate.

1
This question is about simplifying and expanding.
1. (a)
  Simplify 4(2x − 3) − 3(x − 5).
  [2]
2. (b)
  By first expanding each product, show that (2x + 1)(x − 3) − 2(x² − 5) simplifies to 7 − 5x.
  [3]
2
Factorise each expression completely.
1. (a)
  8ab − 12a².
  Answer =[1]
2. (b)
  x² − 12x + 36.
  Answer =[1]
3. (c)
  3x² + 10x − 8.
  [3]
3
A canteen arranges tables in a row. Figure 1 seats 6 people, and each new figure in the row seats 4 more people than the one before. The first three figures seat 6, 10 and 14 people.
1. (a)
  Write a formula for C, the number of people seated at figure n.
  [2]
2. (b)
  Find the number of people seated at figure 25.
  Answer =[1]
3. (c)
  Which figure seats exactly 90 people?
  [2]
4. (d)
  Explain why no figure in this pattern seats exactly 91 people.
  [1]
4
This question is about algebraic fractions and formulae.
1. (a)
  Simplify (5x/6) ÷ (10x²/9).
  [2]
2. (b)
  Express 2/(x + 1) + 3/(x − 1) as a single fraction in its simplest form.
  [3]
3. (c)
  The surface area of a sphere of radius r is A = 4πr². Make r the subject of the formula.
  [2]
5
Two mobile plans are compared. Plan A charges an $80 setup fee plus $12 for each month of use. Plan B charges $25 per month with no setup fee. Let n be the number of months and T₁ and T₂ the total costs of plans A and B.
1. (a)
  Write a formula for T₁ in terms of n.
  Answer =[1]
2. (b)
  Find the smallest whole number of months after which plan A becomes cheaper than plan B.
  [3]
3. (c)
  Make n the subject of your formula in (a).
  [2]
4. (d)
  Use your answer to (c) to find how many months of use give a total cost of $236 with plan A.
  Answer =[1]

— End of paper —