# Year 9 Term 1 Foundation (Unit 1) INTEGERS, Year 9 Term 1 Foundation (Unit 1) INTEGERS, ROUNDING AND PLACE VALUE Key Concepts Integers are whole numbers. Order the following numbers starting with the smallest: 1) a) 1 decimal place 3.527 5, -3, 4, 7, -2 -3, -2, 4, 5, 7 Rounding rules: A value of 5 to 9 rounds the 2) 0.067 0.6 0.56 0.65 0.605 number up. Rewrite 0.067, 0.600, 0.560, 0.650, 0.605 A value of 0 to 4 keeps the 0.067 0.56 0.6 0.605 0.65 number the same. 1 3, 31 32 Integer Even Digit Odd Decimal place Significant figures 3.5 b) 2 decimal places 3.527 3.53 c) 1 significant figure 3.527 4 A) Order the following numbers starting with the smallest: 1) 6, -2, 0, -5, 3 2) 0.72, 0.7, 0.072, 0.07, 0.702 B) 1) Round the following numbers to the given degree of accuracy 14. 1732 (1 d.p.) 2) 0.0568 (2 d.p.) 3)3418 (1 S.F) A1) -5, -2, 0, 3, 6 2) 0.07, 0.072, 0.7, 0.702, 0.72 B1) 14.2 2) 0.06 3) 3000 Key Words Round 3.527 to: ANSWERS: Digits are the individual components of a number.

Examples Year 9 Term 1 Foundation (Unit 1) DECIMALS Th H T U . t h th When adding and subtracting decimals we must ensure the decimal places are underneath each other when setting up. When multiplying decimals, calculate without the decimal point and use estimation to help replace it. 345.461 1 thousandths 42.8 5.3 Forty or 4 tens 6 hundredths 5 units 4 tenths 4 2 42.8 5.32 42.80 + 5.32 48.12 Key Words 102 110 Examples 3 hundreds Decimal Tenths Hundredths Thousandths 42.8 5.32 31 71 42.80 - 5.32 37.48 2 2 8 2 0 1 0 4 0 1 2 0 6 2 4 6 4 8 5

3 226.84 Estimated answer 40 5 = 200 A) What is the value of the 4 in each number? 1) 498 2) 8746 3) 6.243 4) 1.004 B) Work out: 1) 3.1 + 5.27 2) 16.4 9.18 3) 0.03 500 5) 4.79 6.8 4) 3.4 5.6 ANSWERS: A 1) 4 hundred 2) forty 3) 4 hundredths 4) 4 thousandths B 1) 8.37 2) 7.22 3) 15 4) 19.04 5) 32.572 Key concepts Place value: Year 9 Term 1 Foundation (Unit 1) INDICES AND ROOTS Key Concepts Examples Simplify each of the following: 1) 6) 4) 7) 2) 5) = = 9) 3) d d 4) m m2 5) n n 10) 9) 9 or 9 10) 6) 2) b b 5) 1 6) 7) 8) Powers Roots Indices Reciprocal Simplify: 1)

a a 3) 4) 102 110 = 2) Key Words 8) ANSWERS: 1) 3) Year 9 Term 1 Foundation (Unit 1) FACTORS, MULTIPLES AND PRIMES Examples Find the highest common factor and lowest common multiple of 60 and 75: Prime factor decomposition Breaking down a number into its prime factors Highest common factor Finding the largest number which divides into all numbers given Lowest common multiple Finding the smallest number which both numbers divide into 60 2 75 3 30 15 2 3 2 25 5 2 3 5 5 5 5 2 2 3 5

22 3 5 Key Words 29 32,34,35 75 60 Factor Multiple Prime Highest Common Factor Lowest Common Multiple 3 5 5 3 5 2 1) 2) 3) Questions Write 80 as a product of its prime factors Write 48 as a product of its prime factors Find the LCM and HCF of 80 and 48 ANSWERS: 1) 2) 3) LCM = 240 and HCF = 16 Key Concepts Year 9 Term 1 Foundation (Unit 2) EXPRESSIONS/EQUATIONS/IDENTITIES AND SUBSTITUTION Examples Key Concepts A formula involves two or more letters, where one letter equals an expression of other letters. An expression is a sentence in algebra that does NOT have an equals sign. An identity is where one side is the equivalent to the other side. When substituting a number into an expression, replace the letter with the given value. 1) 5(y + 6) 6y + 30 is an identity as when the brackets are expanded we get the answer on the right hand side 2) 5m 7 is an expression since there is no equals sign 3) 3x 6 = 12 is an equation as it can be solved to give a solution 4) C = is a formula (involves more than one letter and includes an equal sign) 5) Find the value of 3x + 2 when x = 5 (3 5) + 2 = 17 6) Where A = b + c, find A when b = 2 and c = 3 A = 2 + 3 A=4+3 A=7 Questions

(c) identity (d) equation Substitute Equation Formula Identity Expression (b) expression 153, 189 1) Identify the equation, expression, identity, formula from the list (a) v = u + at (b) (c) (d) 5b 2 = 13 2) Find the value of 5x 7 when x = 3 3) Where A = d + e, find A when d = 5 and e = 2 ANSWERS: 1) (a) formula 2) 8 3) A = 27 Key Words Year 9 Term 1 Foundation (Unit 2) ALGEBRAIC EXPRESSIONS Key Concepts When collecting like terms involving addition or subtraction, add/subtract the numbers in front of the letters. If the like terms are multiplied, multiply the numbers in front of the letters and put the letters next to each other. If the like terms are divided, divide the numbers in front of the letters. Examples Simplify the following expressions: 1) 4p + 6t + p 2t = 5p + 4t 2) 3 + 2t + p t + 2 = 5 + t + p 3) f + 3g 4f = 3g 3g 4) f + 4f - 2f = 3f 5) 6a 3b 2c = 36abc 6) = 3b Questions 2) 5 + 4t + 3p 2t + 7 4) b 7b + 2b 6) 8m 3n 2m 8) ANSWERS: 1) 8p 2) 12 + 2t + 3p 5) 40abc 6) 48mn 7) 3p 3) -4m 8g 8) 4) -4b

151 152, 156 157 Key Words Simplify Term Collect Simplify: 1) 7p + 3q + p 3q 3) m 8g 5m 5) 2a 5b 4c 7) Year 9 Term 1 Foundation (Unit 2) EXPAND AND SIMPLIFY BRACKETS AND INDICES Examples Key Concepts Expanding brackets Multiply the number outside the brackets with EVERY term inside the brackets Factoring expressions Take the highest common factor outside the bracket. Expand and simplify where appropriate 1) 7 (3 + a) = 21 + 7a 2) 2(5 + a) + 3(2 + a) = 10 + 2a + 6 + 3a = 5a + 16 3) Factorise 9x + 18 = 9(x + 2) 4) Factorise 6e 3e = 3e(2e 1) Questions 1) Expand and simplify (a) 3(2 7f) (b) 5(m 2) + 6 (c) 3(4 + t) + 2(5 + t) 2) Factorise (a) 6m + 12t (b) 9t 3p (c) 4d 2d ANSWERS: 1) (a) 6 21f (b) 5m 4 (c) 22 + 5t 2) (a) 6(m +2t) (b) 3(3t p) (c) 2d(2d 1) 160, 161, 168, 189, 105, 106 Key Words Expand Factorise Simplify