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Math Transformation Assistant

Get help with math transformations, quadratic equations, geometric shapes, and number patterns. Find solutions, rules, and methods for various math problems.

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Math Transformation Assistant

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  1. transformation a + 2b + 3c = 10 3a + b + 2c = 18 2a + 3b + c = 14 what are a, b and c? two lengths: 10cm and 8cm cut a length off one so that it is the mean of the other two David Wells [find two solutions] use the diagram to show that (a – b)2 = a2 + b2 – 2ab y = x2 – 10x + 24 translate this quadratic (parabola) 5 to the left what is the new equation? b a

  2. transformation cut these into two congruent (identical) shapes with one cut – which is connected, dot to dot show how to transform a regular pentagon into an isosceles triangle (of equal area) AB and CD are parallel chords, 6cm apart prove that a number plus its reciprocal is always greater than or equal to 2 10cm C D 1 x x + 1 x x – B A 14cm ? how far is the line AB away from the centre?

  3. generalising 3 4 1 7 a = draw four shapes with an area of 10 squares and a perimeter of 14 what do they have in common? b = find: ab + a + b find fractions for ‘a’ and ‘b’ so that ab + a + b = 1 can you find a general rule? a triangle’s angles are divided in the ratio of 3 consecutive integers what always happens? four consecutive numbers are multiples of 2, 3, 4 and 5 (in this order) what could they be? in general?

  4. generalising in general? 22 + 21 – 20 = 23 + 22 – 21 = 24 + 23 – 22 = 25 + 24 – 23 = (9n – 8) – (7n – 25) is always a multiple of 13 what are the missing numbers? find digits A, B, C and D, all different so that AB + CD = DC + BA e.g. 97 + 24 = 42 + 79 a general rule? a, b, c and d are any four consecutive numbers what is (a2 + d2) – (b2 + c2)?

  5. reversing the question 1 a 1 b 1 6 five numbers have a mean = 4 mode = 3 range = 9 what could they be? [find two solutions] [find five solutions] + = x 4 0 2 7 12 y 14 0 5 35 90 a two-digit number is divided by the sum of the digits what is the smallest result? AB A + B = smallest? what’s the rule?

  6. reversing the question n = 4 n = 3 726 = 462 + 264 a 3-digit number + the reverse of it = 726 find two other solutions draw matchstick patterns for an nth term rule: 6n 6n + 2 6n + 3 6n + 5 766 = PQR + RQP find three solutions example find a quadratic that passes through (6, 0) and (0, 6) with (4, – 2) as a lowest point (vertex) 5 2n + 1 10n + 5 2n – 1 2 4n – 2 10n – 5 4n + 2 find a quadratic that passes through (– 2, 0) and (8, 10) with (2, – 8) as a lowest point (vertex) 8n + 20 see Michael Fenton’s Desmos tasks 18n – 36 12n + 30 12n – 24 two answers

  7. questions on boring topics 1. 2.1 1. • find the volume and surface areas of the two cuboids: • 2 × 2 × 6 • 1½ × 4 × 4 × = 1. 2.1 2. × = 1. 2.1 1. × = 1. 2.1 1. × = × use the digits 1 to 6, once only . . + + • to make: • largest possible • smallest possible • 7.05 • 10.02 • 11.91 • 13.44 • 11.82 use the digits 2 to 7 (once only) in the circles multiply to get the products in the table add these nine products together how do you place the six digits to get the highest possible total?

  8. questions on boring topics M(13) M(8) use any of the digits: 1 , 2 , 3 , 4, 5 , 6 , 7 , 8 but you can’t use a digit twice (or more) in: % of ab – ba = 1 M(13) to get as close as you can to: 400 700 100 500 300 • ab – ba = 7 M(7) • 5a– 2b= 32 • 7a– 10b= 36 ( + ) – ( + ) = 3 solutions possible 2a – 2b = 64 M(7) is a 2-digit multiple of 7, one digit in each box use the four numbers 1 , – 2 , 5 and – 7 once only in a sum: to make the numbers: + 1 – 1 + 9 – 9 + 15 – 15

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