Year 10 Mathematics British outline.pptx

A brief overview of required topics for year 10 Maths

1. YEAR 10: MATHEMATICS Muhammed Abiodun Akanji 1

2. Hi, {}! Welcome to class. 2

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4. NUMBER THEORY

5. Arithmetic: Number theory and Operations with Numbers Number tree Natural Numbers : Counting numbers, viz. {1, 2, 3, 4, ……} Denoted by N: NB: 0 is NOT a Natural number Whole Numbers : Invention of 0 gave rise to set of Whole Numbers. Denoted by W. The set of Natural numbers including Zero viz. {0, 1, 2, 3, 4, ……} Integers : Invention of positives and negatives gave rise to set of Integers. Negative and Positive Natural numbers and 0 viz. {……, –3, –2, –1, 0, 1, 2, 3, ……} Properties of Integers Even Integers : Any integer that is divisible by 2 without a remainder is an even integer ; the set of even integers is {. . . -4, -2, 0, 2, 4, 6, 8, . . .} Odd integer : Integers that are when divisible by 2 leaves no remainder are odd integers ; {. . . -3, -1, 1, 3, 5, . . .} is the set of odd integers. N.B: Even numbers are represented by 2n, where n = 0, 1, 2, …… Zero is also an Even number Odd numbers are represented by 2n+1, where n = 0, 1, 2, …… Prime Number : A prime number is a positive integer that has exactly two different positive divisors, 1 and itself. For example, 2, 3, 5, 7, 11, and 13 are prime numbers, but 15 is not, since 15 has four different positive divisors, 1, 3, 5, and 15.

6. 1 is not a prime number since it has only one positive divisor. Every integer greater than 1 either is prime or can be uniquely expressed as a product of prime factors. For example, 14 = (2)(7), 81 = (3)(3)(3)(3), and 484 = (2)(2)(11)(11). Composite numbers : Natural numbers that have more than two distinct factors. All non-prime numbers are composite numbers e.g., 4, 6, 8,9 etc. Multiples and Factors : A factor is an integer that can divide another number without a remainder Fraction : Any number in the form of n/d. n is the numerator and d is the denominator. The denominator of a fraction can never be 0, because division by 0 is not defined. Two fractions are said to be equivalent if they represent the same number e.g. 8/36 and 14/63 In each case, the fraction is reduced to lowest terms by dividing both numerator and denominator by their greatest common divisor/highest common factor (GCD/HCF) Rational number : All integers, decimals and fractions together form the set of Rational Numbers and is denoted by Q. By definition, it is the set of all numbers that can be expressed in the form, p/q, where p and q are integers and obviously q ≠ 0 Irrational Number : Decimals that are not rational are those that are non-terminating and non-recurring/repeating.

7. NUMBER TREE Real Number The set of Rational and Irrational numbers together is the set of Real Numbers and is denoted by R. Real Numbers are numbers that can be plotted on a number line. All real numbers except zero are either positive or negative.

8. Indices and Surds A positive integer exponent of a number or a variable indicates a product, and the positive integer is the number of times that the number or variable is a factor in the product. For example, x 5 means ( x )( x )( x )( x )( x ); that is, x is a factor in the product 5 times. Some rules about exponents follow. Let x and y be any positive numbers, and let m and n be any positive integers.