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Algebra Sequences Equations Sequences Help How many sticks are there in each pattern? Pattern no. n Number of sticks 4 times table 1 2 3 4 5 6 5 9 13 17 21 25 4 8 12 16 20 24 +4 +4 +4 +4 +4 What pattern do you notice in the number of sticks? So the rule for the number of sticks is What must you add to the 4 times table to get the How manyofsticks are there in the next 3 patterns? number sticks? Multiply by 4 then add 1 or x4 + 1 or 4n + 1 1 Back Sequences Help How many tiles are in each shape? Pattern no. n No. of tiles 1 2 3 4 5 3 8 15 24 35 Each shape can be seen as the square of the next Draw theminus next shape. th and 5th shapes? +5 +7 in +9 +11 How many tiles are the 4 pattern number 1. (n + 1)2 – 1 or n2 + 2n What The pattern difference do you increases notice by in the 2 each number time.of tiles? Home Try some on your own. Away Sequences Home • Draw a table of values. • Find the 4th, 5th, and 10th terms. • Find the rule for the following sequences. 1. 2. 7, 10, 13…….. 3. 4. 1, 5, 9 …….. Away Answers Home Answers 1. Pattern no. No. of sticks 2. Pattern no. Sequence no. 3. Pattern no. No. of sticks 4. Pattern no. Sequence no. New topic. 1 2 3 4 5 10 7 12 17 22 27 52 1 2 3 4 5 10 7 10 13 16 19 34 1 2 3 4 5 10 4 9 14 19 24 49 1 2 3 4 5 10 1 5 9 13 17 37 Back to questions Rule: 5n + 2 Rule: 3n + 4 Rule: 5n -1 Rule: 4n - 3 Away Sequences Away • Draw a table of values for the first five results • Work out the 10th term • Find a rule for the sequences 1. 2. 4, 10, 18, 28 ………. 3. Home Answers Away Answers 1. Pattern No. No. white of 1 4 2 3 4 5 12 24 40 60 Rule: 2n2 + 2n 1 4 2 3 4 5 10 18 28 40 Rule: n2 + 3n 1 1 2 6 tiles 2. Pattern No. Sequence no. 3. Pattern No. No. white of 3 4 5 15 28 45 Rule: 2n2 - n tiles New topic. Back to questions Simplification Help Collect together the like terms. 7a + 2c – 3a – 4c = 4a + 2c – 4c But 4a + 2c – 4c = 4a – 2c And 4(2d–+g) f) means – 2(3d – 2f)2means 2 (3c lots of (3c – 1g) 4 lots of (2d + f) OR THEN TAKE (3c AWAY – g) + (3c – g) Which equals 26clots – 2g of (3d – 2f) BUT 4 lots of 2d + f = 8d + 4f AND = – 6d – – 4f = – 6f + 4f So 4(2d + f) – 2(3d – 2f) = 8d + 4f - 6f + 4f THEN TAKE AWAY 2 lots of (3d -2f) = 2d + 8f Solving equations Help 3(c + 5) = 7c - 9 3c + 15 = 7c - 9 We need ‘c’Take on one thesides equation and 3c side from of both numbers on the other 3c +15 = 3c 7c 4c - 9 Add 9 to both sides +9 +11 +24 +20 = 4c - 9 Divide both sides by 4 24 = 4c 4 4 6=c +9 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 Home 2(3) + b = 10 6 + b = 10 So b = 4 Away Algebra Home 1. Simplify: 2 – 4t – 5 + 9t 2. If c = 4 and r = 3, find the value of 6c + r2 11 3. 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. Simplify: 3m2 + 2m – 6m –m2 + m 6. 3(4s – 5) = 9 Away Answers Home answers 1) 2) 3) -3 + 5t 3 y = -1, x = 4 4) D=5 5) 2m2 - 3m 6) s=2 New topic Back to questions Away Algebra Away 1. Solve : 4(3x + 2) – 3(x – 6) = 8 2. Solve: 2x + 3x + 2 = 5 3 6 3. The triangle is not drawn to scale What is the value of each angle in this triangle? 4. Solve: 2x + 3y = 16 3x – 2y = 11 Answers Away Answers 1. X = -2 2. X = 4 3. The angles are 60, 90, 30 4. x = 5, y = 2 Back to questions Home New topic