Section A Pythagoras Theorem Grade C
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1 Name: Teacher ssessment Section Pythagoras Theorem Grade 1. support for a flagpole is attached at a height of 3 m and is fixed to the ground at a distance of 1.2 m from the base. Not to scale x 3 m 1.2 m alculate the length of the support (marked x on the diagram) nswer... m (Total 3 marks) St Paul s atholic School 1
2 2. rectangular field D is shown. The length of the field, = 160 m. The width of the field, = 75 m. 160 m 75 m alculate the length of the diagonal D. D Not to scale Give your answer to a suitable degree of accuracy. 3. is a right-angled triangle. = 15 cm and = 17 cm nswer...m (Total 4 marks) 15 cm 17 cm alculate the length of the side. nswer...cm (Total 3 marks) St Paul s atholic School 2
3 4. (a) The diagram shows a right-angled triangle. = 10 cm and = 15 cm 15 cm Not drawn accurately alculate the length of. Leave your answer as a square root. 10 cm PQRS is a quadrilateral. ngles RQS and QSP are right angles. PS = 4 cm, QR = 12 cm and RS = 13 cm. nswer... cm (3) (Total 3 marks) Q 12 cm R 13 cm P 4 cm S Not to scale Success: Show that the length of PQ is 41 (Total 4 marks) Target: St Paul s atholic School 3
4 Teacher ssessment Section o-ordinates Grade / 1. The diagram shows the points (1, 3) and (10, 5). y x alculate the distance. Give your nswer to 2 decimal places nswer... units (Total 5 marks) St Paul s atholic School 4
5 2. The square PQRS is drawn on a centimetre square grid. y 5 P 4 Q S R x (a) The coordinates of P are (1, 5). Write down the coordinates of Q, R and S. nswer Q (, ) R (, ) S (, ) (2) (b) alculate the area of square PQRS. You must show your working. State the units of your answer. nswer... (4) (Total 6 marks) St Paul s atholic School 5
6 3. The parallelogram D is drawn on a centimetre square grid. y O x 1 (a) The coordinates of are ( 2, 2). D Write down the coordinates of, and D. nswer (...,...) (...,...) D (...,...) (2) (b) Emma says that the perimeter of the parallelogram is more than 18 cm. Explain why Emma is correct. (1) (c) alculate the area of the parallelogram. Success: nswer... cm 2 Target: (2)(Total 5 marks) St Paul s atholic School 6
7 Teacher ssessment Section Trigonometry Finding Lengths Grade 1. is a right-angled triangle. = 81 cm ngle = 48 81cm 51 cm Not to scale 48 Find the length of. Give your answer to a suitable degree of accuracy. 2. is a right-angled triangle. = 60 m ngle = 32 nswer... cm (Total 4 marks) 60 m Find the length of. 32 nswer... m (Total 3 marks) St Paul s atholic School 7
8 3. is a right-angled triangle. = 5.1 cm = cm x 48 Find the length of (marked x in the diagram). Give your answer to a suitable degree of accuracy The diagram shows a triangle. ngle = 20 and angle = 90 = 32 m nswer... cm (Total 4 marks) 32 m 20 alculate the height. nswer... m (Total 3 marks) St Paul s atholic School 8
9 5. is a right-angled triangle. = 125 m. ngle = 33. x 125 m 33º Find the length of (marked x in the diagram). Give your answer to an appropriate degree of accuracy nswer... m (Total 4 marks) cm 38 alculate the length y. y..... nswer.. cm (Total 3 marks) Success: Target: St Paul s atholic School 9
10 Teacher ssessment Section D Trigonometry Finding ngles Grade 1. PQR is a right-angled triangle. PQ = 11 cm and QR = 24 cm. P Not to scale 11 cm Q 24 cm R alculate the size of angle PRQ nswer... degrees (Total 3 marks) P 2. PQR is a right-angled triangle. PR = 10 cm and PQ = 5 cm 5 cm 10 cm alculate the size of angle QPR. Q R nswer... degrees (Total 3 marks) St Paul s atholic School 10
11 3. right-angled triangle has the dimensions shown. y x 40 cm 45 cm (a) alculate the length x. Give your answer to a suitable degree of accuracy. nswer... cm (4) (b) alculate the size of angle y. Show your working. nswer... degrees (3) (Total 7 marks) St Paul s atholic School 11
12 4. PQ is the surface of a ramp laid on level ground. The ramp is 230 cm long and 20 cm high, as shown in the diagram. Q 230 cm 20 cm Not to scale P x R Work out the size of angle x nswer... degrees (Total 3 marks) 5. In the diagram, PQ = 14 cm and QR = 8.6 cm. ngle PSQ = angle SQR = 90 ngle PQS = 25 alculate angle R. P cm S 25 Q cm... R... Success: nswer... degrees (Total 5 marks) Target: St Paul s atholic School 12
13 Teacher ssessment Section E Trigonometry in 3D Grade / * 1. DEFGH is a cuboid with sides of 5 cm, 5 cm and l2 cm as shown. D 5 cm Not to scale E 5 cm H F G 12 cm alculate angle DFH nswer... degrees (Total 5 marks) St Paul s atholic School 13
14 2. The diagram shows a door-wedge with a rectangular horizontal base PQRS. The sloping face PQTU is also rectangular. PQ = 3.8 cm and angle TQR = 6 The height TR is 2.5 cm. S 6 U T 2.5 cm R Not drawn accurately P 3.8 cm Q alculate the length of the diagonal PT. nswer... cm (Total 5 marks) St Paul s atholic School 14
15 3. VD is a right pyramid on a square base. V is vertically above the centre of the square. V = V = V = VD = 20 cm = 15 cm V 20 cm D 15 cm alculate the angle between the edge V and the base D. nswer... degrees (Total 5 marks) St Paul s atholic School 15
16 4. VD is a right pyramid on a rectangular base. V = V = V = VD = 16 cm. = 20 cm and = 14 cm. V 16 cm D 14 cm 20 cm alculate the angle between the edge V and the base D nswer... degrees (Total 5 marks) St Paul s atholic School 16
17 5. VD is a right pyramid on a rectangular base. V = V = V = VD = 11 cm. 0= 12 cm and = 7 cm. VO is the perpendicular height. V 11 cm not drawn accurately D O 12 cm 7 cm alculate the angle between the edge V and the base D. nswer...degrees (Total 5 marks) St Paul s atholic School 17
18 6. The diagram shows a cuboid. = 3 cm, E = 4 cm, = 12 cm. H G E D 4 cm F 3 cm x y 12 cm (a) Find the length of H. nswer... cm (2) (b) The angle between H and D is x and the angle between H and is y. Which angle is bigger, x or y? You must show your working. nswer... (3)(Total 5 marks) Success: Target: St Paul s atholic School 18
19 Teacher ssessment Section F Problem Solving Grade / * 1. (a) ramp is 4 metres long and 29 centimetres high. If the ramp is safe for wheelchair users the angle marked x must be 4 or less. not drawn accurately 4 m 29 cm x Is this ramp safe for wheelchair users? You must show your working nswer... (4) 2. The point is 50 metres from the base of a tower. The angle of elevation of the top of the tower from is 74. Tower not drawn acc (i) m alculate the height of the tower.give your answer to a suitable degree of accuracy nswer... m (4) (ii) What is the angle of depression of the point from the top of the tower?... nswer... degrees (1)(Total 5 marks) St Paul s atholic School 19
20 3. For a ladder to be safe it must be inclined at between 70 and 80 to the ground. (a) The diagram shows a ladder resting against a wall m 1.5 m Not to scale Is it safe? You must show your working. (3) (b) nother ladder rests against a wall. 4 m Not to scale Work out the closest distance that the bottom of the ladder can be from the wall so that it is safe. nswer... m (3)(Total 6 marks) St Paul s atholic School 20
21 4. (a) Sadhia stands 25 in from the base of a tree. The angle of elevation of the top of the tree is 17. T not drawn accurately S m G alculate the height of the tree, TG. nswer...m (3) (b) Max is holding the string of a kite which is flying 3O metres above the ground. His height is 1.5 metres. The string is straight and its length is 35 metres. K 35 m 30 m x 1.5 m M L not drawn accurately alculate the angle x between the string and the ground. Success: nswer x =... degrees (3)(Total 6 marks) Target: St Paul s atholic School 21
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