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ALGEBRA: 5. More brackets , more fun: a. 2(4a – 4) + 3(a +1) = b. 4a(3-a) +a(a +1) = c. 5(a -3) +4(a-1)= d. 2(x + 1) + 4(x-4)= Don’t get confused : 1. Solve these: a. a + a + a + a = b. a x a x a x a x a = c. a² + a² + a² = d. a² x a² x a² = e. a² + a⁵ = f. a² x a⁵ = g. 2a + 3a = h. 2a x 3a = 2. a. b. c. d. e. f. g. h. 6. WATCH OUT !Minus before the bracket means: a. 2(a + 3) – 2(4a +4) = b. 4(b + 3) – 4(8-b)= c. 7(5a+4) - 3(a-4) = d. 2(4c + 3) – 4(c-3) = 7. MINUS ATTACK! a. 6(a-2) – 3(a-1) = b. 3(7-b) – 4(b-1)= c. 2(x-6)-(3-x)= More practise: b+b+b= 2b + 3b + b = c + c + 5c = b x c x 2a = 4a x 3a = 4a + 3a = 4a² + 3a² = 4a² x 3a² = 3. Practise with taking away: a. 3a – 5a = b. 7c + 3a – 5a = c. 3a – 5a + 4a – 5c = d. 4a -3b -3a -6a = e. 2x – 4y – 4a +4a= 4. One bracket, a lot of fun: a. 3(a + 2) = b. 3a(3 – b) = c. 3a(a + 3) = d. 7b(b + 3a)= e. 3a(4 - a) = a. b. c. d. e. 8. DOUBLE BRACKETS, DOUBLE FUN (x + 3)(x + 5) = (4 + a)(a +3) = (x – 5) (x+4) = (2x + 4) (3x + 4) = (5x – 4) (3x – 6) = TEST YOURSELF: a. b. c. d. e. f. g. h. i. 5x – 8x = x – 4y – 5x + 3y = 3a -4b + 6a – 6b = 3(a + 4) = c⁵ + c⁵ = 8a x 6a = 2a x 4b = 6c(3 – 5a) = (4 –a)(5 + 4a) = SUBSTITUTION: Find the value of these expressions using substitution: 1. PURE PLEASURE When a = 5 a. 2a = b. 2a+ 6 = c. a² = d. a² + a = e. a -2a = 2. POWERS FIRST ! When a = 3 a. b. c. d. e. 3a + a² = 2a² = a³ = a + a³= a² = 3. TEST YOURSELF when a= 4 and b = 2 a. 2a – 3b = b. ab = c. 2ab = d. 2a² - 3b = e. 3a² + 3b²= 4. BRACKETS ABOVE ALL a. (a+3)² = b. (2a -b)² = c. (a + 5) x (b + 2) = 5. NEGATIVE VALUES: If a = -4 a. 2a = b. 2a + 3 = c. 3a – 4 = d. a² = e. 2a² = f. 2a² - a = g. 3a - a² = LCM AND HCF: 1. CIRCLES WE CALL VENN DIAGRAMS: Find LCM of: a. 15 and 25 b. 16 and 36 c. 105 and 28 d. 56 and 24 e. 60 and 24 FIND HCF of: a. b. c. d. 24 and 56 105 and 84 18 and 27 325 and 125 2. TEXT QUESTIONS WITH LCM AND HCF: 1. Cheese slices are sold in packs of 8. Bread rolls are sold in packs of 6. What is the least number of packs that needs to be bought to have the same number of cheese slices and bread rolls? 2. Sally has her roses in packs of 12 and tulips in packs of 8. a. How many packs of flowers does she need to buy if she wants to plant one rose and one tulip in each pot? b. B. how many pots will she need? 3. Tom has strawberry chewing gums and lollies for his friends. His gums are in packs of 12 and lollies in packs of 9. He gives one lolly and one gum to each friend. What is the smallest number of packs of sweets he will need ? 4. Mary wants to pack 100 roses and 60 lilies into identical baskets with the same arrangement of flowers in each basket. a. How many baskets does she need if she wants to use all the flowers? b. How many of each kind of flowers will fit into each basket ? 5. Shona is organising a trip. She has 90 girls and 36 boys. She wants to divide her students into identical groups. a. How many girls and boys will she put into each group? b. How many groups will there be? 6. Chris is putting desks and chairs together into office rooms. He has 60 tables and 96 chairs. He wants to have the same amount of people sitting in each office and the same amount of tables in each office. a. How many office rooms will he need? b. How many chairs in each office room can he have? 7. Leah is putting packed lunches together. She has 88 packs of carrots and 33 mini rolls (Chinese vegetarian). How many lunches can she do provided each packed lunch is identical? PRODUCT OF THE PRIME FACTORS: 1. Express these as a product of its prime factors: a. 18 – b. 24 – c. 56 – d. 60e. 132 – f. 240 – g. 64 – h. 105 – i. 1225 – POWERS, POWERS, POWERS Write as a single power : a. 3⁵ x 3³ = b. 2⁹ x 2⁹ = c. a³ x a⁵= d. b⁷ x b³ = e. 4⁷ ÷ 4³ = f. 6⁵ ÷6³ = g. 5⁵ ÷ 5 = h. (4³)⁵ = i. (5³)⁷ = j. (x³)³ = k. (a⁵)⁴ = WHEN YOU HAVE TO REMEMBER ABOUT NUMBERS, TOO: a. (3a⁵)² = b. (2a⁴)⁴ = c. (3x⁹)² = d. (4x⁴)² = FACTORISE means FUN WITH BRACKETS: a. 2x + 4= b. 3x + 6 = c. 4x + 8= d. 5x + 15 = e. 9x + 6= f. 12x – 8 = g. 24x – 18= h. 45 +15x = i. x² + 4x = j. 4x² + 8x = k. 5x + 10xy= l. 15xy – 25xyz=