Quadratics and Geometry Problem Solving
Explore a mix of algebraic sequences, equations, and geometric challenges including finding terms in sequences, equations of lines, and calculating areas. Enhance your problem-solving skills in quadratics and geometry with these intriguing tasks.
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Quadratics Name Do Now Tracker 1 2 3 Sequences 4 5 6 1 2 3 Straight Line Graphs 4 5 6 1 2 3 Solving Equations 4 5 6 1 2 3 Area and Perimeter 4 5 6
1 Find the ?th term of the sequence 8,2,16,34, Find an equation of the line perpendicular to ? = 3? 2 that passes through the point (2,1). Solve for ?: Draw an unusual triangle with an area of 12 cm2. ? + 4 =? 5 3 Find the equation of the line passing through the points (3, 1) and ( 1, 3). 2 Find the ?th term of the sequence 2, 2,0,4, This shape has perimeter 68 cm. Find the value of ?. Draw a triangle that someone might think has an area of 12 cm2, but doesn t.
3 Find the ?th term of the sequence 0,1,3,6, Find an equation of the line perpendicular to ? = 13? 4 that passes through the point ( 4,1). Solve for ?: Draw a trapezium with an area of 12 cm2 3 =? 2 6 4 Find the ?th term of the sequence 1.5,1.5,6.5,13.5, A line passes through the points ( 2,5) and (3, 4). Find the equation of the line. Draw a trapezium with an area of 12 cm2. Solve for ?: 7? 8 5 =2? + 5 The height must be a decimal. 4
5 What number appears exactly once in the sequence 50,37,26,17, Find an equation of the line parallel to ? =3 4? + 2 that passes through the point ( 4,4). Draw a trapezium with an area of 12 cm2. Solve for ?: ? + 2 ? + 3= 4 All the lengths given must be prime numbers. 6 What is the largest number in the sequence 1,14,25,35, Find an equation of the line parallel to ? = 4? + 2 that passes through the point ( 5,1). Show that ? 8 of the square is shaded. Solve for ?: 5 3? + 1= 12
Task 1: Expanding and Factorising Single Brackets Factorised Expanded Factorised Expanded 4(? 6) 2?4+ 6?3+ 8?2 a n 4? 6 2?2+ 6?3+ 8?4 b o ?(? 6) ?(? + 3) c p 2?(? + 4) d q ?2+ 6? 12?? + 15? e r 4(2? 6) 42? 6 12?2+ 15?? f s ?(2? 6) 12?2? + 15?? g t 2?(? 6) 5?(? 3? + 2?) h u 6?2+ 10? 18?2 12?? i v 6?3+ 10?2 6?? 5?2?2 j w ?(?2+ 3? + 4) 5?2? ??2 k x 2?2+ 6? + 8 ?3?3 ?2?2+ ?? l y 2?(?2+ 3? + 4) 91?2? 119??2 m z Task 2: Introducing Areas and Grids 24 61 29 32 17 11 12 23 Original: (10 + 7)(20 + 4) Brackets: Result: Find four different ways to calculate 23 37
Task 3: Expanding Double Brackets with Grids ? + 5 (? 2) (? 5)(? + 2) (? 5)(? 2) (? + 5)(? + 2) Brackets: Grid: Expanded : Simplified : (? + 5)(? 5) ? + 2 (? 2) Brackets: Grid: Expanded : ?2 9 ?2 100 Simplified : ? 22 ? + 52 ? + 22 Brackets: ? 2 ? Grid: 2 Expanded : ?2 10? + 25 Simplified : Brackets: ? 4 3 ?2 3? ?2 6? 4? Grid: 8 5? 2? 12 Expanded : ?2+ 9? + 14 Simplified :
Task 4 Match them up! A:(? + 20)(? 6) B:(? + 20)(? + 6) C:(? + 6)(? 4) D:(? 6)(? + 4) E:(? + 6)(? + 8) F:(? 8)(? + 6) G:(? + 8)(? 6) H:(? + 10)(? + 12) J:(? + 24)(? + 2) L:(? 10)(? + 12) I: K: ?2+ 14? + 48 ?2+ 26? + 48 ?2+ 26? + 120 ?2+ 14? 120 ?2+ 26? 120 A L I ?2+ 2? 24 ?2 2? 24 ?2+ 22? + 120 ?2+ 2? 48 ?2+ 22? 48 Task 5 Expanding and Factorising Double Brackets - Variation Grids (? + 14)(? + 1) ?(? + 15) (? + 16)(? 1)(? + 17)(? 2)(? + 18)(? 3) ?2+ 15? + 14 ?(? + 6) (? + 7)(? 1) (? + 8)(? 2) (? + 9)(? 3) (? + 2)(? 2) (? + 3)(? 3) (? + 4)(? 4) ?(? 6) (? + 1)(? 7) (? 1)(? 14) ?2+ 7? + 12 ?2+ 6? + 9 ?2+ 5? + 6 ?2+ 4? + 3 ?2+ 3? ?2+ ? 12 ?2 9 ?2 ? 6 ?2 ? 12 ?2 9 ?2 7? + 12
Task 6: Expanding More Double Brackets with Grids 4? + 5 (2? + 1) (2? + 3)(3? + 5) Brackets: 5?10?2 24?232? Grid: 2 6 6? 8 Expanded : Simplified : (3? + 7)(3? 5) 2? + 5 (3? 4) Brackets: 2? 1 Grid: 8? 6? 4? Expanded : 10?2 11? 6 Simplified : (2? 5)(2? + 5) 2? + 52 Brackets: Grid: Expanded : 4?2 20? + 25 25?2 4 Simplified : (? + ?)(? + 2?) (2? + ?)(3? ?) 4? 3?2 Brackets: 3? Grid: 4? 12??9?2 Expanded : ?2+ 5?? + 6?2 Simplified :
Task 7 Match them up! A:(? + 1)(28? + 45) B:(? + 3)(28? + 15) C:(? + 5)(28? + 9) D: E:(2? + 1)(14? + 45) F:(2? + 3)(14? + 15) H:(2? 3)(14? 15) G: I:(4? + 1)(7? + 45) K:(4? + 5)(7? + 9) L:(4? 5)(7? 9) J: 28?2+ 72? + 45 28?2+ 73? + 45 28?2+ 81? + 45 28?2+ 88? + 45 28?2+ 99? + 45 J G 28?2+ 104? + 45 28?2+ 149? + 45 28?2+ 187? + 45 28?2 73? + 45 D Task 8 Expanding and Factorising Double Brackets - Variation Grids (? 5)(6? + 31) ? 1 (6? + 7) ?(6? + 1) (? + 1)(6? 5) (? + 5)(6? 29) (2? 5)(6? + 17) (2? 1)(6? + 5) 2?(6? + 2) (2? + 1)(6? 1) 12?2+ 4? 65 (3? 1)(6? + 13) (3? 1)(6? + 5) 3?(6? + 3) 18?2+ 9? + 1 18?2+ 9? 35 2?2 11? + 12 2?2+ 11? + 12 4?2 11? + 6 4?2+ 11? + 6 3?2 14? + 8 3?2+ 14? + 8 3?2 10? + 8 3?2+ 10? + 8 6?2 11? + 4 6?2+ 11? + 4 12?2 11? + 2 12?2+ 11? + 2 8?2 14? + 3 8?2+ 14? + 3 8?2+ 22? + 15 8?2 2? + 15 8?2+ 2? + 15 8?2 22? + 15 8?2+ 26? + 15 8?2 14? + 15 8?2+ 14? + 15 8?2 26? + 15
Task 9 Difference of Two Squares Expand and Simplify a. (? 2)(? + 2) d. (3? 4)(3? + 4) b. (? + 3)(? 3) e. (? + ?)(? ?) c. (2? + 5)(2? 5) f. (2? + 3?)(2? 3?) Factorise a. ?2 25 j. 0.64 0.25?2 b. 9?2 4 k. ? 22 9 c. 36?2 25?2 l. ?2?4 36 d.49?2 ?2 m.18?2 2 1 4?2 4?2 e. n.320 20?2 f.?2 1 o. ? + 22 ? + 12 9?2 g. ??2 9 p.32?2? 50?3 q.2 ?2 54 1 4?2 16 h. 9 i.?4 16 r. 9 ? + 22 4 ? 32 Calculate cleverly a. 982 22 b. 912 92 c.882 122 d.1042 42 e.9992 12 f.9912 92 g.99 101 h.67 73 i. 9.5 10.5 j.1992 k.2.42 1.42 l.87.72 12.32 m.65.82 34.22 n.16.52 3.52 2 2 2 2 7 10 3 10 p. 84 11 o. 6 3 5 5 2 2 q. 53 41 r. 4. 62 1. 62 4 4 2 2 2 2 s. 23 11 23 6 21 t. 4 4 6 2 3 5 v. 0.6 1 0.7 2 u. 4.42
