Grade 7 Algebra review

Distribution

100

2(a+3)

2a+6

200

(5-s)3

15-3s

300

a(2-6d)

2a-6ad

400

2v(d-4)

2dv-8v

500

2a(4+7a)

8a+14a^2

Combine Like terms

100

2a+7a

9a

200

-3t-5t

-8t

300

3av-4a+6av-2

9av-4a-2

400

6x+7-2x-10

4x-3

500

3xy+7x+8y-4

3xy+7x+8y-4

2 steps equations

100

3x-7=0

x=7/3

200

-2x+9=3

x=3

300

4x-8=8

x=4

400

6=-4x-5

x=-11/4

500

-8+4x=8

x=4

Multi-steps equations

100

3(x-6)=7

3x-24 =7

x=31/3

200

-3(2x-2)=1

-6x+6=1

x=5/6

300

2a²-4=-8

2a²=-4

a² = -2

a = does not exist

400

2(t²-5)=3

2t²-10=3

t²=13/2

t=1.80

500

3.45 = 0.5(3t²)

3.45=1.5t²

2.3 = t²

1.516 = t

Words problem

100

A car is traveling at 35mph for 0.2 hours. Calculate how many miles the car travels

d=vt

35 x 0.2 = 7 miles

200

Alice is running at a speed of 3 mph around a track. Find how long it takes Alice to run 10 miles

d = vt

10 = 3t

t =10/3 = 3.3 hours

300

A bike is traveling at the speed of 6 m/s. As the bike approaches the red light, it starts to slow down at 1.5 m/s². How long does it take to make a complete stop?

V_f=V_i+AT

0 = 6 +(-1.5)T

T = 4s

400

A plane is waiting to take off. It needs to reach the speed of 180 mph in 2.25 miles (Seatac airport). How long does it take to reach that speed? (bonus, convert to seconds)

d = (V_f+V_i)/2 x T

2.25 = 180/2 x T

2.25 = 90T

T = 0.025 h = 90 seconds

500

A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.

d=V_iT + 0.5AT²

110 = 0(5.21) + 0.5(A)(5.21²)

110 = 0 +0.5(A)(27.14)

110 = 13.57A

A =8.11 m/s²