EVERYTHING YOU NEED TO KNOW TO GET A GRADE C GEOMETRY & MEASURES (FOUNDATION)

Transcription

1 EVERYTHING YOU NEED TO KNOW TO GET A GRADE C GEOMETRY & MEASURES (FOUNDATION)

2 Rhombus Trapezium Rectangle Rhombus

3 Rhombus

4 Parallelogram Rhombus Trapezium or Rightangle Trapezium

5 Base angles in a kite are equal Opposite angles in a rhombus are equal Angles around a point sum to 360 Angles in a kite sum to

6 Kite Trapezium

7 Replace a with 3 and b with 5.2 P = 2 x x 5.2 P = Total areas of both shapes are equal to one as shown.

8 Equilateral triangle Rhombus 2 (Fits on top of itself twice through a full turn)

9 5cm 9cm 5cm 3cm 3cm Can choose either as your answer 5cm Any two of rectangle, parallelogram, kite or arrowhead The 3cm and 5cm rods would not meet when joined with the 9cm rod.

10 In an isosceles triangle, the base angles are the same Angles in a triangle sum to Each angle is 60 in an equilateral triangle 120 because angles on a straight line add to because angles in a right angle add to 90 Base angles are both 30 so ABD is an isosceles triangle

11 Isosceles Triangle Angles in a triangle add to because angles on a straight line add up to = = y = = No, because 38 is not equal to 35. Therefore, it is not an isosceles triangle

12 Angles in a triangle add to = = because angles on a straight line add up to

13 80 Base angles are the same in an isosceles triangle Means work out angle A in triangle ABC Angles in a triangle add to = Angles in a triangle add to = 40 A right angle is = 50 Both base angles are equal = = 65 Means work out angle R in triangle PQR Base angles are the same in an isosceles triangle 65

14 = = 66 Angles on a straight line add to = A quadrilateral is made up of two triangles Angles is a triangle add up to = 360

15 LEARN OFF BY HEART (because the exterior angles add up to 360 ) Exterior angle = 72 As worked out in part (a) Two exterior angles joined together 144

16 Exterior 72 angle 108 Interior angle 36 Exterior 72 angle 36 Exterior angle 72 All the angles and sides are the same in a regular pentagon LEARN OFF BY HEART Exterior 72 angle Exterior 72 angle = 72 Angles on a straight line add up 180 Interior angle = = 108 Base angles in a isosceles triangle are the same = 72 36

17 Interior angle LEARN OFF BY HEART Exterior angle Angles on a straight line add up 180 Exterior angle = = 18 = 20 20

18 Decagon 144 Interior 144 angle Pentagon Interior 108 angle LEARN OFF BY HEART Sum of interior angles = (number of sides 2) x 180 Sum of interior angles of an decagon = (10 2) x 180 = 8 x 180 = 1440 = 144 Sum of interior angles of a pentagon = (5 2) x 180 = 3 x 180 = 540 = 108 Angles around a point add up to = 108 Base angles in a isosceles triangle are the same = = = 180 (Angles on a straight line add up to 180 ) Therefore, ABC lie on a straight line

19 LEARN OFF BY HEART Hexagon Sum of interior angles = (number of sides 2) x 180 Interior angle 120 Square Square Sum of interior angles of an hexagon = (6 2) x 180 = 4 x 180 = 720 = 120 Angles around a point add up to = 60 Base angles are the same = = 60 Therefore, as all angles are 60 AHJ is equilateral

20 Sum of interior angles of an octagon = (8 2) x 180 = 6 x 180 = 1080 = 135 LEARN OFF BY HEART Sum of interior angles = (number of sides 2) x = 135 As worked out in part (a) Angles around a point add up to = 90 Therefore, as all angles are 90 PQRS is a square

21 2.5-1

22 Alternate angles are equal Angles on a straight line add up = 70 Angles in a triangle add up = 70 As both base angles are 70, triangle BEF is isosceles.

23 55 55 Alternate angles are equal Angles in a triangle add up = 55 As both base angles are 55, triangle ABC is isosceles.

24 Interior angles add up to =

25 2 4cm 3cm 4cm 3cm OTHER ANSWERS 2cm 6cm 2cm ALSO ALLOWED 6cm Perimeter of rectangle A 14cm = Perimeter of rectangle B = 16cm Difference = 16cm - 14cm 2 Perimeter is the length around a shape

26 6cm 4cm 4cm Perimeter is the length around a shape 6cm Perimeter of rectangle = 6cm + 4cm + 6cm + 4cm 20 Square has 4 equal sides 3cm for each side

27 x x OTHER ANSWERS ALSO ALLOWED x x Because two lengths of 12cm makes 24cm which is more than the perimeter As evident from the rectangle drawn for part (a)

28 40cm 20cm 1cm 1cm 2cm 2cm 40cm 10cm 20cm 8cm 4cm 4cm 5cm 5cm 10cm 8cm Find the only rectangle which has a perimeter of 26cm 8 5

29 Rectangle A Kilo means a thousand 1km = 1000m 1000m Area = Length x Width = 1000m x 10m Split compound shape into two rectangles 200m Rectangle B Area of rectangle A = 100 x 30 Area of rectangle B = 200 x a 200a = a = 7000

30 Count the number of squares to find the area C B E

31 Shaded Area = Area of square Area of circle Area of square = length x width = 80cm x 80cm LEARN THE FORMULAE OFF BY HEART Area of circle = = 3.14 x 30cm x 30cm Area shaded =

32 equal to less than (because the length around the shape is the same) (because more than half the rectangle is unshaded)

33 10cm 10cm Shaded Area = Area of big square ABCD Area of the 4 congruent (identical) triangles Area of big square length x width = 10cm x 10cm Area of one triangle = Area of one triangle = Area of one triangle = Area of four triangles = 82 Shaded area =

34 Area of small square = 30cm x 30cm 900 Length of large square = 50 Area of floor = 300cm x 180cm Number of small tiles needed = Number of small tiles needed = 60

35 Perimeter A = 10cm Perimeter B = 9cm Perimeter is the length around a shape Perimeter C = 10cm Perimeter of D = 2cm + 2cm + 2cm + 2cm 8 A and C C and D Area is the space inside a shape

36 Shaded Area = Area of big square Area of two smaller squares Area of big square = length x width = 12cm x 12cm Area of one small square = length x width = 4cm x 4cm Area of both squares = Shaded Area = Area of big square = length x width Area of one small square = length x width Area of both squares = Shaded Area = Shaded Fraction shaded =

37 6

38 A, B and E

39

40

41

42 8 cubes 8 more cubes required to fill box Volume is the space inside the box (number of centimetre cubes that will fit in) 8 cubes + 8 cubes = 16 cubes 16 3

43 Height Length Width Volume = length x width x height 48 = length x width x height 8 x 2 x 3 8 x 74 2 x 74 3 x Round the answers

44 4cm 5cm Volume of a cuboid = length x width x height Volume of cuboid = 5 x 3 x 4 Volume of cube= 2 x 2 x 2 = 7.5 7

45 Volume of a cuboid = length x width x height Volume of cuboid = 30 x 12 x Amount of paint = 10 x 30 93

46 LEARN LEARN Volume of cylinder = area of circle x length Volume of cylinder = 3.14 x 3 x 3 x 10 Amount of glasses filled =

47 Cuboid A Cuboid B Volume of cuboid A = length x width x height Volume of cuboid A = 20 x 20 x 15 d x 20 x 20 = d = 7000 d =

48 radius 0.5cm Volume of cylinder = area of circle x length

49 x x x

50 6 RIGHT 6 RIGHT 6 RIGHT 6 RIGHT 6 DOWN 6 DOWN 6 DOWN 6 DOWN 6 (-6) 180 either clockwise or anticlockwise from the origin (0,0)

51 2 RIGHT 2 RIGHT 2 RIGHT 4 DOWN 4 4 DOWN DOWN (because it s half the size) -2-1

52 Rotation 180 either clockwise or anticlockwise from the origin (0,0)

53 A 2 RIGHT 2 RIGHT 2 RIGHT 2 RIGHT 3 DOWN 3 DOWN 3 DOWN 3 DOWN 2 RIGHT B 3 DOWN y = 1 C

54 Identical B F A 2 (because shape A is twice the size of shape C) Three times bigger

55 = 2.4 = 2.5 The scale factor of enlargement for both respective sides must be equal.

56

57 PYTHAGORAS THEOREM Hypotenuse 6.5

58 90 Angles in a triangle add up to A Pythagoras Theorem only works in right angles triangles.

59 PYTHAGORAS THEOREM 3.2

60 8.7m 45 Angles in a triangle add up to 180 1m 45 angle forms an isosceles triangle. Both base length and height length of the triangle are the same. Height of pole =

61 Not the hypotenuse PYTHAGORAS THEOREM

62 (a) (Any value from )

63 1 100p So p = 500 Weight of all the 2p coins = 500 x 7 = 3500g 1kg = 1000g 3.5

64 = = = 2 87

65 cm or mm litres tonnes

66 LEARN Distance = Speed x Time Distance = 80 x hours 140 2h 15mins 135mins Stage 2 Distance = = 50km Stage 2 Time = 2h 15mins 1h 45mins = 30mins = 0.5hour 0.5 is the same as multiplying by 2 100

67 LEARN 45 3h 30mins 3.5hours LEARN 57.1

68 LEARN Time = 5.2 hours 0.2 hour = 0.2 of 60mins x = 12mins 5 12

69 NW N C x Must be written as 3 figures

70 S cale: 1 cm represents 10 kilom etres A B

71 cm 6.2 cm x 5 31

72 C

73

74

75 L M equidistant from two fixed points.

76

77 6.5cm 43

78

79 Shade in the area in side the curves but out to sea (not many boats in distress on land!)

80 Circumference is the full length around a circle Diameter Circumference = π x diameter Circumference = 3.14 x 8 Circumference = 25.12cm Length of arc (semi-circle) = = 12.56cm Perimeter = 12.56cm + 8cm = 20.56cm (2 d.p.) (Total 3 marks)

81 Volume of prism = area of cross-section x length Volume of prism = area of triangle x length base x height Volume of prism = x length 2 4 x 3 Volume of prism = x 20 2 Volume of prism = 6 x