Mathematics

Simplification

100

5a+6a

11a

200

11a-7a+3b

4a+3b

300

-12b+3x+3b-x

-9b+2x

400

7c+7s-3s-12c+4s

-5c+8s

500

53n-7x+3n=5x+4n-15x

56n-7x=-10x+4n

Factorisation

100

3x+3

3(x+1)

200

6p²+9p

3p(2p+3)

300

12ab-8ac

4a(3b-2c)

400

4(x+6)+2(3x-2)

-0.333

500

2(2x+9)-4(3+2x)

x= -1.5

Angle of Elevation and Depression

100

A ramp to a building has a height of 4 feet and the angle of elevation is 33⁰. How long is the ramp? 

7.344

200

A 15 foot ladder is leaned against the house. If the base of the ladder is 4 feet from the house, what angle does the ladder make with the ground?

74.5⁰

300

A kite is flown with 240 yards of string. The angle of elevation of the string is 55⁰. How high above the ground is the kite?

196.6

400

Elise is standing on top pf a 50 foot building and sees her friend Molly. If molly is 30 feet away from the base of the building What is the angle of depression from Elise to Molly? Elise's eye height is 4.5 feet.

61.2⁰

500

An inquisitive math student is standing 25 feet from the base of the Washington Monument The angle of elevation from her horizontal line of sight is 87.4. If her eye height is 5 ft how tall is the monument?

550.54

trigonometry

100

Where is the hypotenuse found on a right-angle triangle?

opposite the right angle.

200

where can the adjacent be found on a right-angle triangle?

Next to the theta

300

Find the value of hypotenuse 'x' if the adjacent is 12cm and the theta is 34⁰ to 2 d.p.

14.47cm

400

Find the value of the adjacent 'x' with the hypotenuse as 7 cm and the theta being 62⁰ to 2 d.p

6.18cm

500

Find the value of opposite 'x' if adjacent is valued at 4cm and the theta is 52⁰ to 2 d.p

5.12cm

Simultaneos Equation

100

5a+2b=14

6a+2b=16

a=2

b=2

200

4x+3y=14

5x+7y=11

x=5

y= -2

300

2x+4y=6

3x+6y=5

x=20

y= -5

400

6x-4y=21

4x+4y=24

x=4.5

y=1.5

500

10a+4b=30

3a-2b=2

a=2.125

b=2.1876