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# Mathematics JSS 2 First Term

WEEK 1&2: WHOLE NUMBERS

WEEK 3:  LCM AND HCF OF WHOLE NUMBERS

WEEK 4: FRACTIONS

WEEK 5: APPROXIMATION

WEEK 6: ALGEBRAIC EXPRESSIONS – FACTORS AND FACTORIZATION

WEEK 7: ARITHMETIC IN THE HOME AND OFFICE

WEEK 8&9 DIRECTED NUMBERS – MULTIPLICATION AND DIVISION

WEEK 10: EXPANSION OF ALGEBRAIC EXPRESSIONS

Week 1 & 2

TopicWHOLE NUMBERS

Factors and Prime factors (revision)

40 ÷ 8 = 5 and 40 ÷ 5 = 8

8 and 5 divide into 40 without remainder.

8 and 5 are factors of 40.

prime number has only two factors, itself and 1, 2, 3, 5, 7, 11, 13, … are prime numbers.

1 is not a prime number.

Standard form

Standard form is a way of writing down very large or very small numbers easily. 103 = 1000, so 4 × 103 = 4000. So 4000 can be written as 4 × 10³ . This idea can be used to write even larger numbers down easily in standard form.

Small numbers can also be written in standard form. However, instead of the index being positive (in the above example, the index was 3), it will be negative.

The rule when writing a number in standard form is that first you write down a number between 1 and 10, then you write × 10(to the power of a number). To learn more, click here.

Week 3

Topic: LCM  and HCF of Whole Numbers

Common factors

The number 12, 21 and 33 are all divisible by 3. We say that 3 is a common factor of 12, 21 33.

There may be more than one common factor of a set of numbers. For example, both 2 and 7 are common factors of 28, 42 and 70. Since 2 and 7 are common factors and are both prime numbers, then 14 (= 2 x 7) must also be a common factor of the set of numbers.

1 is a common factor of all numbers.

Lowest Common Multiples (LCM)

L.C.M is least common multiple, the smallest number which is exactly divisible by all the given numbers. To learn more, click here.

Week 4

Topic: Fractions

Expressing Fractions as Decimals, Ratio and Percentages

Converting Fractions to Ratios

To understand the relationship between fractions and ratios, consider a pizza cut into six slices. If you only one slice has pepperoni, then you could say the pizza is 1/6 pepperoni. The ratio between pepperoni and non-pepperoni slices is 1:6.

To convert a fraction to a ratio, first write down the numerator or top number. Second, write a colon. Thirdly, write down the denominator, or bottom number. For example, the fraction 1/6 can be written as the ratio 1:6.

Changing a common fraction to a decimal fraction

Divide the numerator of the fraction by its denominator. To learn more, click here.

Week 5

Topic: Approximation

Rounding Off to Decimal Places

When numbers are rounded off, the digit s 1, 2, 3, 4 are rounded down the and the digits 5, 6, 7, 8, 9 are rounded up.

Round off 124.25 a. to two significant figures b. to one decimal place .

1. 25 = 120 to 2 s.f.
2. 25 = 124.3 to 1 d.p

Rounding off to the nearest whole number

Rules for rounding decimals to the nearest whole number:

• To round a decimal to the nearest whole number analyze the digit at the first decimal place i.e., tenths place.
• If the tenths place value is 5 or greater than 5, then the digit at the ones place increases by 1 and the digits at the tenths place and thereafter becomes 0. To learn more, click here.

Week 6

Topic: Algebraic Expressions – Factors and Factorization

Definition of Algebraic Expression

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number) For example, {displaystyle 3x^{2}-2xy+c} is an algebraic expression. Since taking the square root is the same as raising to the power.

Remember that in algebra, letters can be whole or fractional, positive or negative.

1. Just as 5a is short for 5 x a, so – 5a is short for (-5) x a.{displaystyle {tfrac {1}{2}}}{displaystyle {sqrt {frac {1-x^{2}}{1+x^{2}}}}}
2. Just as m is short for 1 x m, so – m is short for (-1 ) x m.
3. Algebraic terms and numbers can be multiplied together. For Example, To learn more, click here.

Week 7

Topic: ARITHMETIC IN THE HOME AND OFFICE

Personal Arithmetic

Interest

Bankers want people to save money. They give extra payments to encourage saving. The extra money is called interest.

For example, a person saves N10 000 in a bank for a year. If the interest rate is 8% per annum (i.e. 8% per year), the saver will have N10 800 at the end of the year: the original N10 000 plus N800 interest from the bank. Interest that is paid like this is called simple interest.

Example

Find the simple interest on N60 000 for 5 years at 9% per annum.

Yearly interest = 9% of N60 000

= 9/100 X N60 000 = N5 400

Interest for 5 years = N5 400 X 5 = N27 000 To learn more, click here.

Week 9

Topic: DIRECTED NUMBERS – MULTIPLICATION AND DIVISION

Numbers can be shown on a number line which extends above and below zero. This gives positive and negative numbers.

The signs + and – show the direction from 0. Positive and negative numbers are called directed numbers.

To add a positive number, move to the right on the number line.

Example

(+1) + (+3) = +4

Week 11

Topic: EXPANSION OF ALGEBRAIC EXPRESSIONS

Directed algebraic terms

Remember that in algebra, letters stand for numbers. The number can be whole or fractional, positive or negative.

1. Just as 5a is short for 5 x a, so -5a is short for (-5) x a.

2. Just as m is short for 1 x m, so –m is short for (-1) x m.

3. Algebraic terms and numbers can be multiplied together. For example,

4 X (-3x) = (+4) x (-3) X x

= -(4 x 3) X x = -12 X x = -12x

(-2y) x (-8y) = (-2) X y X (-8) X y

= (-2) X (-8) X x X y

= +(2 X 8) X y2