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A Shaded Isosceles Triangle Is Drawn Inside a Rectangle. Calculate The

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A Shaded Isosceles Triangle Is Drawn Inside a Rectangle. Calculate The 1 A shaded isosceles triangle is drawn inside a rectangle. Calculate the size of angle a. 2 marks 2 The following quadrilaterals all have a perimeter of 36 cm. Here is a table to show the length of each side. Complete the table. One quadrilateral is done for you. Side lengths square 9 cm 9 cm 9 cm 9 cm rectangle 3 cm rhombus 9 cm kite 10 cm 2 marks St+Philip%27s+CE+Primary+School Page 1 of 14 3 Here is a shape on a grid. For each statement, put a tick (✔) if it is true. Put a cross (✘) if it is not true. The shape is a quadrilateral. The shape has 2 lines of symmetry. The shape is a parallelogram. The shape has one right angle. 2 marks St+Philip%27s+CE+Primary+School Page 2 of 14 4 Anna has four different triangles. Complete the table to show the size of the angles in each triangle. Type of triangle Angle 1 Angle 2 Angle 3 Isosceles 90° Right-angled 80° Isosceles 70° Isosceles 70° 2 marks 5 Here is a hexagon. Draw two straight lines across the hexagon to make two triangles and two quadrilaterals. 1 mark St+Philip%27s+CE+Primary+School Page 3 of 14 6 Join dots on the grid to make a quadrilateral that has 3 acute angles. 1 mark St+Philip%27s+CE+Primary+School Page 4 of 14 7 Circle the pentagon with exactly four acute angles. 1 mark St+Philip%27s+CE+Primary+School Page 5 of 14 Adam has this rectangular piece of card. It is marked with grid lines. 8 Adam makes two straight cuts along the grid lines. The two cuts divide the rectangle into 3 shapes: • 2 squares of different size, and • 1 rectangle. Using the grid lines, draw two lines that show where Adam could have made his cuts. Use a ruler. 1 mark 9 Look at the letters below. Circle the letter below that has both parallel and perpendicular lines. 1 mark 10 A bicycle wheel has a diameter of 64 cm. What is the radius of the bicycle wheel? 1 mark St+Philip%27s+CE+Primary+School Page 6 of 14 Two of the angles in a triangle are 70° and 40° 11 Jack says, Explain why Jack is not correct. 1 mark St+Philip%27s+CE+Primary+School Page 7 of 14 Here is a sketch of a triangle. 12 It is not drawn to scale. Draw the full-size triangle accurately below. Use an angle measurer (protractor) and a ruler. One line has been drawn for you. 2 marks St+Philip%27s+CE+Primary+School Page 8 of 14 Mark schemes Award TWO marks for the correct answer of 104°. 1 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g: • 180 − 38 − 38 = a Answer need not be obtained for the award of ONE mark. Up to 2 [2] Completes all three rows correctly, eg: 2 • rectangle 3cm 3cm 15cm 15cm rhombus 9cm 9cm 9cm 9cm kite 10cm 10cm 8cm 8cm ! Measures Accept Side lengths in each row may be given in any order Accept correct values with cm omitted eg, for the rectangle: • 15 3 15 2 or Completes two rows correctly 1 [2] Award TWO marks for all four boxes ticked or crossed correctly as shown: 3 St+Philip%27s+CE+Primary+School Page 9 of 14 If the answer is incorrect, award ONE mark for three boxes ticked or crossed correctly. Accept alternative unambiguous indications eg Y or N. For TWO marks accept: Up to 2m [2] Completes all four rows of the table correctly, eg: 4 90° 45° 45° 80° 90° 10° 70° 70° 40° 70° 55° 55° Accept angles within a row in either order Accept the bottom two rows may be given in either order ! Condone omission of degree signs ! For 2 marks, do not accept correct angles in 3rd row repeated in 4th row, in either order 2 or Completes three rows correctly 1 [2] St+Philip%27s+CE+Primary+School Page 10 of 14 Diagram completed as shown: 5 OR Accept slight inaccuracies in drawing, provided the intention is clear. Diagrams may be completed in any orientation. U1 [1] A quadrilateral with three acute angles, e.g. 6 OR St+Philip%27s+CE+Primary+School Page 11 of 14 OR Accept inaccurate drawing provided the intention is clear. [1] 7 The correct shape circled as shown: Accept alternative unambiguous positive indications, e.g. shape ticked. [1] Rectangle divided, as shown: 8 St+Philip%27s+CE+Primary+School Page 12 of 14 OR OR OR Accept slight inaccuracies in drawing provided the intention is clear. [1] 9 The correct letter circled as shown: Accept alternative unambiguous positive indications, e.g. letter ticked. [1] 10 32 [1] St+Philip%27s+CE+Primary+School Page 13 of 14 An explanation showing an understanding: 11 • that this specific triangle has angles 70, 70 and 40 OR • of the properties of an equilateral triangle − all angles are equal (60°) and therefore that this triangle cannot be equilateral, e.g. • The angles aren’t 60° • There is not a 60° angle • It has two different angles (70° and 40°) so it can’t be equilateral • The angles aren’t the same • An equilateral triangle has 60° + 60° + 60° • All the angles are the same in an equilateral triangle • It’s an isosceles triangle. (In the context of this question, the term isosceles triangle is treated as not including equilateral triangles as a special type, as the national curriculum does not specify this at key stage 2.) Do not accept vague or incomplete explanations, e.g. • The other angle is 70° • They aren’t (all) the same. (No reference to angles) • An equilateral triangle has equal angles. (Does not say all.) Do not accept explanations which include incorrect mathematics or incorrect information that is relevant to the explanation, e.g. • 40 + 70 = 110 + 70 = 180 [1] Award TWO marks for a completed triangle that has all of the following three points: 12 • an angle in the range 33° to 37° inclusive for the angle marked 35° • an angle in the range 88° to 92° inclusive for the right angle • the triangle has been drawn on an 8cm line (either on the given line or a line drawn), provided they have constructed both angles within the tolerance of the line 7.9 cm to 8.1 cm. If the answer is incorrect, award ONE mark for a completed triangle and TWO of the three points correct. Accept drawings where any side has been extended past a vertex. When considering whether the triangle is completed, do not accept: • a quadrilateral or another shape drawn OR • a curved line that is used to complete the shape OR • sides not meeting to form a vertex. Up to 2m [2] St+Philip%27s+CE+Primary+School Page 14 of 14.
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