Grade 9 - Mathematics Review ( Trimester3 )

Find sin , cos and tan in these triangles (as a simple fraction). : ( )

sin

cos

tan Find the value of x, given that :

A: cos 25 = sin x b: sin 60 cos x c : cos 10 = sin x

.. Find the unknown side using Pythagoras theorem and then find sin and cos in decimal form. :

. . . Find x and y. ( Note: DE = x and CE = y. ) : By finding tan in two different triangles, find the value of m. m tan .. .. ( 1 ) Using the degrees/minutes/seconds button on your calculator, write each of the following in degrees and minutes, giving answers correct to the nearest minute.

( ) : = a : 165 = b : 3825 = c : 739 = Write in degrees, correct to 3 decimal places where necessary

( )

: = a : 1745 = b :4816 = .c : 12543 =

Find the size of ( to the nearest degree ) where is acute.

cos tan sin shift : ( ) : = a : sin = 0259 , = . b : sin = 0934 , = c : tan = 12 , = d : cos = 0222 , =

( ) . ..Find the value of the pronumeral in each triangle, correct to 1 decimal place. : ( ) . A ladder leans against a wall so that the angle it makes with the ground is 52 and its base is 4 m from the wall. How far does the ladder reach up the wall (to the nearest centimetre) 52 4 ( ).. A boat is anchored in a river that is 32 m deep. If the anchor rope makes an angle of 52 with the surface of the water, how long is the rope from the surface of the water ? (Answer to the nearest centimetre.) 3.2 52 ( ) .... The base of an isosceles triangle is 96 cm long and each of the base angles is 38 42. Find the length of each of the equal sides. (Answer correct to 3 significant figures.) 9.6 38 42 . ( ) .. Find the size of the angle marked in each triangle. Give your answers correct to the nearest degree. ( ) ..

Find the angle in each of the following. (Answer correct to the nearest minute.) ( ) . Find the apex angle of an isosceles triangle, if the length of each of the equal sides is 143 cm and the length of the base is 208 cm. Give your answer to the nearest degree. 14.3 20.8 ( ) ......Find the angle in each of the following. (Answer correct to the nearest degree.) ( ) ...The angle of elevation of the top of a tower is observed to be 23 from a boat 180 m from the base of the tower. What is the height of the tower ? (Answer correct to 1 decimal place.) 180 23 ( ) ... An observer stands on the top of a tower the height of the tower is 40-metre to observe a boat that is 650 metres out from the base of the tower. What is the angle of depression from the observer to the boat ? ( Answer to the nearest minute 40 650 .... The angle of depression of a boat 800 m out to sea from the top of a vertical cliff is 9. Find the height of the cliff, to the nearest metre. 800 9 ( ) ..

A wire is stretched from point A on the top of a building 213 m high, to point B on the top of a shorter building, 156 m high. The angle of depression from A to B is 2015 21.3 15.6 20 52 What is the horizontal distance between the buildings ( to the nearest centimeter ) : ....

Two points, P and Q, are in line with the foot of a tower 25 m high. The angle of depression from the top of the tower to P is 43 and to Q is 57. How far apart are the points? (Answer to the nearest metre.) Q P 25 ( ) ( ) .Find x in the diagram shown. Give answers correct to 2 decimal ( ) .. A plane is flying at an altitude of 900 m. From a point P on the ground, the angle of elevation to the plane was 6830 and 20 seconds later the angle of elevation from P had changed to 2512. How far had the plane flown in that time, and what was its speed, to the nearest kilometre per hour ? ( Find the distance to the nearest metre. 900 ( ) 68 30 20 25 12 . ( ) ....

Use Pythagoras theorem to calculate the unknown length , x, correct to 1 decimal place , and then calculate the surface area ( ) .......... Find the surface area of the following prisms. All measurements are in centimetres. ( ) .....................

For each of the following cylinders find : : A: the curved surface area b : the area of the circular ends

c :the total surface area ....The following solids have been formed from cylinders. Find the surface area of each correct to 1 decimal place. (All measurements are in metres.) ( ).............

For the following nets find :

a : its area ...... b : the name of the solid that it produces when folded along the dotted lines .. c : if the prism is open or closed .. Each of the following solids has been built from 1 cm cubes. What is the surface area of each solid? 1 3 ......... ..

The volume of all prisms is given by the formula V Ah , where V volume , A cross-sectional area and h height of the prism. ......................... ....................................... ........................................................ ....................................................................... =................................................................................................. =........................................................................................................ The following prism has been made by joining rectangular and triangular prism. Find the volume of the prism. . ... Calculate the volume of the following solid correct to three significant figures. ( ) ....

In the following, find the volume of the prism and then divide by 3 to find the volume of the pyramid. 3 : ......... A square pyramid has a volume of 18 000 cm3. If the side of the square is 30 cm, what is its height? 18000 30 .... Find the volume of the following cone correct to one decimal place. ( ) . Find the volume of sphere with the radii 3 cm. Give answers correct to one decimal place 3 ( ) .....

A sphere has a volume of 2000 cm3. Calculate its radius correct to one decimal place. 2000 ( ) . Calculate the volume of the following solid. All measurements are in centimetres. Give answers to the nearest cubic centimetre. : ( ) ...... The direction of a point Y from an original point X is known as the bearing of Y from X. This is mainly expressed in one of two ways. Examine the diagram below : x y ...

The angle of depression of a boat 800 m out to sea from the top of a vertical cliff is 9. Find the height of the cliff, to the nearest metre 800 9 ( ) ....22