12 IB MAA SLHW28 CALCULUS ALGEBRA SEQUENCES AND SERİES PDF

Preview

Summary

Download 12 IB MAA SLHW28 CALCULUS ALGEBRA SEQUENCES AND SERİES PDF

Description

12 IB MATHEMATICS ANALYSIS AND APPROACHES SL HOMEWORK:

GEOMETRY AND TRIGONOMETRY

Due Date: 28.12.2021

1) The following diagram shows triangle ABC.

diagram not to scale AB = 7 cm, BC = 9 cm and ABˆ C = 120°.

(a)

Find AC. (3)

(b)

ˆC. Find BA (3) (Total 6 marks)

1

ˆ C and ADˆ C . 2) The diagram below shows a quadrilateral ABCD with obtuse angles AB

diagram not to scale ˆ C = x°, AD ˆ C = y°. AB = 5 cm, BC = 4 cm, CD = 4 cm, AD = 4 cm, BAˆ C = 30°, AB

(a)

Use the cosine rule to show that AC =

41 40 cos x . (1)

(b)

Use the sine rule in triangle ABC to find another expression for AC. (2)

(c)

(i)

Hence, find x, giving your answer to two decimal places.

(ii)

Find AC. (6)

(d)

(i)

Find y.

(ii)

Hence, or otherwise, find the area of triangle ACD. (5) (Total 14 marks)

2

3) The following diagram shows the triangle ABC.

diagram not to scale The angle at C is obtuse, AC = 5 cm, BC = 13.6 cm and the area is 20 cm2.

(a)

ˆB. Find AC (4)

(b)

Find AB. (3) (Total 7 marks)

3

4) The circle shown has centre O and radius 3.9 cm.

diagram not to scale Points A and B lie on the circle and angle AOB is 1.8 radians.

(a)

Find AB. (3)

(b)

Find the area of the shaded region. (4) (Total 7 marks)

4

5) The diagram below shows a triangle ABD with AB = 13 cm and AD = 6.5 cm. Let C be a point on the line BD such that BC = AC = 7 cm.

diagram not to scale

(a)

Find the size of angle ACB. (3)

(b)

Find the size of angle CAD. (5) (Total 8 marks)

5

6) The diagram below shows triangle PQR. The length of [PQ] is 7 cm, the length of [PR] is ˆ R is 75. 10 cm, and P Q

(a)

Find PRQ . (3)

(b)

Find the area of triangle PQR. (3) (Total 6 marks)

7) In the triangle PQR, PR = 5 cm, QR = 4 cm and PQ = 6 cm. Calculate (a)

ˆ R; the size of P Q

(b)

the area of triangle PQR. (Total 6 marks)

6

8) The following diagram shows a pentagon ABCDE, with AB = 9.2 cm, BC = 3.2 cm, BD = 7.1 ˆ E = 52 and ABˆ D = 60. cm, A Eˆ D =110, AD

(a)

Find AD. (4)

(b)

Find DE. (4)

(c)

ˆ C. The area of triangle BCD is 5.68 cm2. Find DB (4)

(d)

Find AC. (4)

(e)

Find the area of quadrilateral ABCD. (5) (Total 21 marks)

7

9) In triangle PQR, PQ is 10 cm, QR is 8 cm and angle PQR is acute. The area of the triangle is ˆ R. 20 cm2. Find the size of angle P Q

(Total 6 marks)

10)

In a triangle ABC, AB = 4 cm, AC = 3 cm and the area of the triangle is 4.5 cm2.

ˆC. Find the two possible values of the angle BA (Total 6 marks)

8

11)

The following diagram shows a triangle ABC, where BC = 5 cm, Bˆ = 60°, Cˆ = 40°. A

B

(a)

Calculate AB.

(b)

Find the area of the triangle.

60°

40° 5 cm

C

ˆ = 48°, as shown in the diagram. 12) In triangle ABC, AC = 5, BC = 7, A C 5 A

48°

7

diagram not to scale

B

ˆ , giving your answer correct to the nearest degree. Find B (Total 6 marks)

9

13) The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm.

5

7

Diagram not to scale

8

Find (a)

the size of the smallest angle, in degrees;

(b)

the area of the triangle. (Total 4 marks)

14)

The diagrams below show two triangles both satisfying the conditions ˆ C = 50°. AB = 20 cm, AC = 17 cm, AB

Diagrams not to scale Triangle 1

Triangle 2

A

A

B

C

(a)

ˆ B in Triangle 2. Calculate the size of AC

(b)

Calculate the area of Triangle 1.

B

C

(Total 4 marks)

15)

A triangle has sides of length 4, 5, 7 units. Find, to the nearest tenth of a degree, the size of the largest angle. (Total 4 marks)

10...