Basic Mathematics Form 1

Yaliyomo

1. 1. Numbers

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   • Hindu-Arabic numerals and place value
   • Roman numerals
   • Types of numbers
   • Factors, multiples, GCF and LCM
   • Operations on integers
   • Squares, square roots and cubes
   • Summary

   What are numbers? Numbers are symbols we use to count, measure and compare. The numbers we use every day are called Hindu-Arabic numerals : the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Each digit has a place value , which depends on its position in the number. In 5,284,016 the digit 2 is in the hundred thousands…

2. 2. Fractions

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   • What is a fraction?
   • Equivalent fractions, simplest form and comparing
   • Adding and subtracting fractions
   • Multiplying and dividing fractions
   • Order of operations and word problems with fractions
   • Summary

   What is a fraction? A fraction shows a part of a whole. In the fraction 3/5, the top number 3 is the numerator (how many parts we take) and the bottom number 5 is the denominator (how many equal parts the whole is divided into). Types of fractions Proper fraction : numerator smaller than denominator, e.g. 4/7. Improper…

3. 3. Decimals and Percentages

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   • Decimals and place value
   • Converting fractions and decimals
   • Operations with decimals
   • Percentages
   • Percentage increase, decrease and applications
   • Summary

   Decimals A decimal is another way of writing a fraction whose denominator is a power of ten. The places after the decimal point are tenths, hundredths, thousandths and so on. For example, 3.247 means 3 + 2/10 + 4/100 + 7/1000. Converting between fractions and decimals Fraction to decimal : divide the numerator by the…

4. 4. Units

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   • Measurement and SI units
   • Length and mass
   • Capacity, area and volume units
   • Time and speed
   • Summary

   Why we need standard units To measure something we compare it with a fixed amount called a unit . If every trader used his own hand or basket as a unit, buyers would be cheated and results could not be compared. For this reason most countries, including Tanzania, use the International System of Units (SI units) . Basic…

5. 5. Approximations

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   • Rounding whole numbers
   • Decimal places
   • Significant figures
   • Estimation and errors
   • Summary

   Why we approximate Many numbers in daily life do not need to be exact. A newspaper may report that 48,000 fans watched a match when the real number was 47,862. Giving a number close to the exact value is called approximation or rounding . Approximations make numbers easier to read, remember and calculate with. Rounding…

6. 6. Algebra

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   • Algebraic expressions
   • Simplifying and substituting
   • Solving linear equations
   • Word problems leading to equations
   • Simultaneous linear equations
   • Linear inequalities
   • Summary

   What is algebra? Algebra uses letters to stand for numbers. A letter that stands for an unknown or changing number is called a variable . Algebra lets us write general rules and solve problems where some numbers are unknown. Key terms Term : a number, a letter or a product of them, e.g. 5x, −3ab, 7. Coefficient : the…

7. 7. Ratio, Profit and Loss

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   • Ratio
   • Sharing in a given ratio
   • Direct and inverse proportion
   • Profit and loss
   • Discount, commission and simple interest
   • Summary

   Ratio A ratio compares two or more quantities of the same kind measured in the same units . If a class has 18 boys and 24 girls, the ratio of boys to girls is 18 : 24. Like fractions, ratios can be simplified by dividing by a common factor: 18 : 24 = 3 : 4. Before comparing 400 g with 2 kg, change both to grams: 400 :…

8. 8. Coordinate Geometry

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   • The Cartesian plane and coordinates
   • Gradient of a straight line
   • The equation of a straight line
   • Intercepts and drawing straight-line graphs
   • Solving simultaneous equations graphically
   • Summary

   The Cartesian plane Coordinate geometry joins algebra and geometry. Two number lines that cross at right angles form the Cartesian plane . The horizontal line is the x-axis , the vertical line is the y-axis , and they meet at the origin O(0, 0). The axes divide the plane into four quadrants , numbered anticlockwise…

9. 9. Perimeters and Area

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   • Perimeter of plane figures
   • Circumference of a circle
   • Area of rectangles, triangles and parallelograms
   • Area of trapeziums, kites and circles
   • Composite figures and applications
   • Summary

   Perimeter The perimeter of a plane figure is the total distance around its boundary. It is a length, so it is measured in units such as cm, m or km. For any polygon, add the lengths of all its sides. Rectangle: P = 2(l + w). Square of side s: P = 4s. Circle: the perimeter is called the circumference , C = 2πr = πd,…