1. SequencesEquations Algebra

2. Sequences Help Pattern no. n 123456 Number of sticks How many sticks are there in each pattern? 5913 172125 +4 +4 +4 +4 +4 How many sticks are there in the next 3 patterns? What pattern do you notice in the number of sticks? Back 4 times table 4 81216 2024 What must you add to the 4 times table to get the number of sticks? 1 So the rule for the number of sticks is Multiply by 4 then add 1 orx4 + 1 or4n + 1

3. Sequences Help Pattern no. n 12345 No. of tiles How many tiles are in each shape? 38152435 Away Home Try some on your own. Draw the next shape. How many tiles are in the 4 th and 5 th shapes? What pattern do you notice in the number of tiles? +5 +7 +9 +11 The difference increases by 2 each time. Each shape can be seen as the square of the next pattern number minus 1. (n + 1) 2 – 1 or n 2 + 2n

4. Sequences Home Draw a table of values. Find the 4 th, 5 th, and 10 th terms. Find the rule for the following sequences. 1. 2. 7, 10, 13…….. 3. 4. 1, 5, 9 …….. Answers Away

5. Home Answers Pattern no. 1234510 No. of sticks 7121722 2752 Pattern no.1234510 Sequence no.71013 161934 Pattern no.1234510 No. of sticks4914 1924 49 1. Rule: 5n + 2 2. Pattern no.1234510 Sequence no.159 1317 37 Rule: 3n + 4 3. Rule: 5n -1 4.Rule: 4n - 3 New topic.Away Back to questions

6. Sequences Away Draw a table of values for the first five results Work out the 10 th term Find a rule for the sequences 1. 2. 4, 10, 18, 28 ………. 3. AnswersHome

7. Away Answers Pattern No. 12345 No. white of tiles 412244060 1. Rule: 2n 2 + 2n 2. Pattern No. 12345 Sequence no. 410182840 Rule: n 2 + 3n 3. Pattern No. 12345 No. white of tiles 16152845 Rule: 2n 2 - n New topic. Back to questions

8. Simplification Help 7a + 2c – 3a – 4c = 4a + 2c – 4c 4a + 2c – 4c = But 4a – 2c Collect together the like terms.

9. 2 (3c – g) means2 lots of (3c – 1g) OR (3c – g) + (3c – g) Which equals 6c – 2g And 4(2d + f) – 2(3d – 2f) means 4 lots of (2d + f) AND BUT So 4(2d + f) – 2(3d – 2f) = 8 d + 4f – 6f + 4f = ––– 4f6d = 2d + 8f THEN TAKE AWAY 2 lots of (3d – 2f) = = 4 lots of 2d + f THEN TAKE AWAY 2 lots of (3d -2f) 8d + 4f- 6f + 4f

10. Solving equations Help 3(c + 5) = 7c - 9 We need ‘c’ on one side of the equation and numbers on the other Take 3c from both sides +15 = 4c - 93c7c Add 9 to both sides +20 = 4c- 9+11+9 +24 3c Divide both sides by 4 24 = 4c 3c + 15 = 7c - 9 44 6 = c

11. Simultaneous equations Help 3a – 2b = 1 ……… 1 2a + b = 10 ……… 2 Multiply equation 2 by 2 to make the coefficients of ‘b’ the same (ignoring the signs). 3a – 2b = 1 …….. 1 4a + 2b = 20 …… 2 Add equation 1 to equation 2 7a = 21 Divide both sides by 7 a = 3 Substitute a = 3 into either equation 2(3) + b = 10 6 + b = 10 So b = 4 HomeAway

12. Algebra Home 1. 2. If c = 4 and r = 3, find the value of 6c + r 2 11 3. Simplify: 3m 2 + 2m – 6m –m 2 + m Simplify: 2 – 4t – 5 + 9t If y = 3x + 5, and x = -2, what is the value of y? What is the value of x if y =17? 4. Solve 3d + 20 = 7d 5. 6. 3(4s – 5) = 9 AwayAnswers

13. Home answers 1) -3 + 5t 2) 3 3) y = -1, x = 4 4) D = 5 5) 2m 2 - 3m 6) s = 2 New topic Back to questions Away

14. Algebra Away 1. Solve : 4(3x + 2) – 3(x – 6) = 8 2. Solve: 2x + 3x + 2 = 5 3 6 3. 4.Solve: 2x + 3y = 16 3x – 2y = 11 Answers What is the value of each angle in this triangle? The triangle is not drawn to scale

15. Away Answers 1. X = -2 2. X = 4 3. The angles are 60, 90, 30 4. x = 5, y = 2 New topic Back to questions Home