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Basic 7 · Mathematics · Term Revision

Term Revision in Mathematics

In this topic you will recall and summarise the term's work on numeration, number operations, powers and fractions, and practise answering end-of-term questions.

By the end of these notes you should be able to:

  • Recall key ideas on numeration systems and number operations
  • Recall key ideas on powers and fractions
  • Answer revision questions accurately with clear working

What you already know

  • All topics covered in Mathematics this term

Copy everything that has a blue line on its left into your notebook. The other parts are for reading.

Lesson 1

Strand
Revision
Sub-strand
Term Revision

Introduction

Mathematics builds step by step. Revising the first half of the term helps you see how place value, rounding and operations fit together.

1. Key Ideas

Numeration and operations
TopicKey points
large numbersperiods of three digits; billions; expanded form with powers of ten
comparingcount digits, then compare from the left; >, <, =
roundinglook at the digit to the right; 5 or more rounds up
decimal places and significant figuresd.p. counts after the point; s.f. counts from the first non-zero digit
powers of ten× 10ⁿ moves digits left; ÷ 10ⁿ moves digits right
mental strategiespartitioning, compensation, doubling and halving
propertiescommutative, associative, distributive, identity
operationscolumn methods, long multiplication and division; check with inverses

2. Revision Examples

Mixed revision

(a) Round 7,486,215,903 to the nearest hundred thousand. (b) Correct 0.004568 to 2 s.f. (c) Calculate 25 × 44 mentally.

  1. (a) Hundred-thousands digit 2; next digit 1, round down → 7,486,200,000.
  2. (b) First significant digits 4, 5; next 6, round up → 0.0046.
  3. (c) 25 × 44 = 50 × 22 = 100 × 11 = 1,100.

Answer: 7,486,200,000; 0.0046; 1,100

Students revising together with books open
Figure 1: Revision Make a mind map of the numeration topics.

3. Linking Ideas

The topics connect. Rounding uses place value. Significant figures and decimal places are special kinds of rounding. Mental strategies rely on number properties. Estimation, which uses rounding, helps check long multiplication and division.

New words

revision
Studying again what has been learned.
estimation
Finding an approximate answer.
inverse
An operation that undoes another.
place value
The value of a digit's position.

Summary

  • Large numbers are read in periods and modelled in expanded form.
  • Rounding, decimal places and significant figures use the digit to the right.
  • Mental strategies, number properties and inverse operations make calculations easier and help check answers.

Class activity: Revision Stations

  1. Rotate through stations on large numbers, rounding, mental maths and operations.
  2. Solve two problems at each station.
  3. Check answers with the station card.

You need: Bottle tops, Number cards, Graph paper

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. 4,000,000,000 is read as…

    • A. four billion
    • B. four million
    • C. forty million
    • D. four hundred million
    Show answer
    Answer: four billionBillions period.

  2. 2. 3.0456 correct to 3 s.f. is…

    • A. 3.05
    • B. 3.04
    • C. 3.046
    • D. 3.0
    Show answer
    Answer: 3.053, 0, 4 then 5.

  3. 3. Subtraction can be checked by addition.

    • A. True
    • B. False
    Show answer
    Answer: TrueInverse.

  4. 4. 6 × (10 + 3) = 60 + 18 uses the ______ property.

    Show answer
    Answer: distributiveSplitting.

  5. 5. Calculate 2,345 × 13.

    Show answer
    Answer: 30,4852,345 × 3 + 2,345 × 10.

  6. 6. A hall seats 48 people per row. How many rows are needed for 1,000 people?

    Show answer
    Answer: 21 rows; 1,000 ÷ 48 = 20 remainder 40, so one more row.Round up.

Lesson 2

Strand
Revision
Sub-strand
Term Revision

Introduction

The second half of the term covered powers, prime factors and fractions. These skills are used throughout JHS mathematics.

1. Key Ideas

Powers and fractions
TopicKey points
powersbase and index; 2³ = 2 × 2 × 2
product of powers72 = 2³ × 3²
prime factorsfactor trees or repeated division; unique result
zero indexa⁰ = 1 for a ≠ 0
BODMASbrackets, orders, division and multiplication, addition and subtraction
HCFcommon primes with lowest powers
benchmark fractions½ = 0.5 = 50%; ¼ = 0.25 = 25%; ⅕ = 0.2 = 20%
adding and subtracting fractionscommon denominator using the LCM; regroup mixed numbers
multiplying fractionsmultiply tops and bottoms; cancel first
fraction of a quantitydivide by denominator, multiply by numerator

2. Revision Examples

Mixed revision

(a) Find the HCF of 84 and 126. (b) Evaluate 3² + 4⁰ × 5. (c) Calculate 2⅓ − 1¾.

  1. (a) 84 = 2² × 3 × 7, 126 = 2 × 3² × 7; HCF = 2 × 3 × 7 = 42.
  2. (b) 9 + 1 × 5 = 9 + 5 = 14.
  3. (c) 2 4/12 − 1 9/12 = 1 16/12 − 1 9/12 = 7/12.

Answer: 42; 14; 7/12

An open mathematics textbook with exercises
Figure 2: Mathematics textbook Make a mind map of the fraction topics.

3. Linking Ideas

Prime factors help find the HCF, which is used to simplify fractions to their simplest form. The LCM, found from multiples or prime factors, gives common denominators for adding and subtracting fractions. Percentages are fractions out of 100. Seeing these links makes revision easier.

New words

index
The power to which a base is raised.
HCF
Highest common factor.
LCM
Lowest common multiple.
simplest form
A fraction with no common factor except 1.

Summary

  • Powers, prime factors and the zero index describe numbers compactly.
  • The HCF uses common primes with the lowest powers; the LCM gives common denominators.
  • Fractions can be added, subtracted, multiplied and found of quantities.

Class activity: Revision Relay

  1. Each member solves one step of a multi-step problem and passes it on.
  2. Problems cover powers, HCF and fractions.
  3. The group checks the final answer together.

You need: Bottle tops, Number cards, Graph paper

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. 5⁰ =

    • A. 1
    • B. 0
    • C. 5
    • D. 50
    Show answer
    Answer: 1Zero index.

  2. 2. ⅔ × 9/10 =

    • A. ⅗
    • B. 18/30
    • C. 3/10
    • D. ⅔
    Show answer
    Answer: ⅗18/30 = 3/5.

  3. 3. 60% = ⅗.

    • A. True
    • B. False
    Show answer
    Answer: True60/100 = 3/5.

  4. 4. 2⁴ = ______.

    Show answer
    Answer: 162 × 2 × 2 × 2.

  5. 5. Find ⅜ of GH₵480.

    Show answer
    Answer: GH₵180480 ÷ 8 × 3.

  6. 6. Express 180 as a product of primes and find its HCF with 252.

    Show answer
    Answer: 180 = 2² × 3² × 5; 252 = 2² × 3² × 7; HCF = 36.Prime factors.

Lesson 3

Strand
Revision
Sub-strand
Term Revision

Introduction

Practice questions help you prepare for the examination. Show all your working so that you can earn marks even if the final answer has a small error.

1. Examination Tips

  1. Read each question carefully and underline key words.
  2. Show every step of your working clearly.
  3. Estimate first to check that your answer is reasonable.
  4. Write units, such as GH₵, m or kg, where needed.
  5. Leave time to check your answers.

2. Sample Questions

Practice question 1

Write 3,050,402,007 in words.

  1. Billions: three billion.
  2. Millions: fifty million.
  3. Thousands: four hundred and two thousand.
  4. Ones: seven.

Answer: Three billion, fifty million, four hundred and two thousand and seven.

Practice question 2

Simplify (4 − 1)² × 2⁰ + ½ of 18.

  1. Brackets: 3² = 9.
  2. 2⁰ = 1, so 9 × 1 = 9.
  3. ½ of 18 = 9.

Answer: 9 + 9 = 18

Practice question 3

A trader had 2½ crates of eggs. She sold 1⅔ crates. What fraction of a crate is left?

  1. 2 3/6 − 1 4/6: regroup to 1 9/6 − 1 4/6.

Answer: 5/6 of a crate

Crates of eggs stacked at a market
Figure 3: Egg crates Write and solve a practice question about crates of eggs.

3. Holiday Practice

During the holidays, practise mental maths when shopping, round prices to estimate totals, and help family members calculate fractions of recipes or money. Short daily practice keeps your skills sharp for next term.

4. Checking Your Paper

Before you hand in, check each answer against your estimate, make sure fractions are in simplest form, see that rounded answers use the place value asked for, and confirm that units are written. Many marks are lost through small slips that a quick check would catch.

New words

working
The steps shown in solving a problem.
reasonable
Making sense.
units
Labels for quantities, such as kg.
practice
Repeating an activity to improve.

Summary

  • Show all working, estimate, and include units.
  • Practise with sample questions to build confidence.
  • Use mathematics in daily life during the holidays.

Class activity: End-of-Term Quiz

  1. Answer ten questions covering all topics of the term.
  2. Mark your work using the teacher's model answers.
  3. Write two topics you need to practise more.

You need: Bottle tops, Number cards, Graph paper

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. The HCF of 15 and 25 is…

    • A. 5
    • B. 3
    • C. 75
    • D. 15
    Show answer
    Answer: 5Common factor.

  2. 2. 0.25 × 0.4 =

    • A. 0.1
    • B. 1
    • C. 0.01
    • D. 0.65
    Show answer
    Answer: 0.125 × 4 = 100.

  3. 3. 3⁴ = 81.

    • A. True
    • B. False
    Show answer
    Answer: True3 × 3 × 3 × 3.

  4. 4. 7,860 rounded to the nearest hundred is ______.

    Show answer
    Answer: 7,900Tens digit 6.

  5. 5. Find 45% of GH₵600.

    Show answer
    Answer: GH₵270600 × 45/100.

  6. 6. Order from least: ⅜, 0.4, 35%, ⅓.

    Show answer
    Answer: ⅓, 35%, ⅜, 0.40.333, 0.35, 0.375, 0.4.

Homework

  1. Make a summary sheet of formulas and rules from the term.
  2. Solve ten practice questions without a calculator.
Term Revision in Mathematics – Basic 7 Mathematics Notes | sirbus