Summer Success Program Week 5

Algebra & Exponents

100

Without calculating the numerical value, simplify:

Simplify:

(3⁴⋅3^-2)/3

3^(4−2−1)=3¹ = 3

200

Which is larger?

2+3(4)2+3(4) or (2+3)(4)

(2+3)4=20

2+3(4)2+3(4)=38 (larger)

300

Simplify:

((2³)²*2^-4)/2^-1

2³ = 8

400

What kind of dog do I have?

golden retriever

500

Solve for x:

(3x+6)/4 - (x-2)/3 =2x - 5

x = 86/19

Ratios & Units

100

Which quantity has the same units as velocity?

A. m/s²
B. m/s
C. N/m
D. kg/s

m/s

200

A length is multiplied by a scale factor of 3.

By what factor does the area change?

9 because 3²=9

300

Suppose

d=vt

If velocity is measured in m/s and time is measured in seconds, what units must distance have?

m/s * s = m

400

A cube has side length 3 cm. Every side is doubled.

A student says:

"The volume doubles because the side length doubled."

Is the student correct?

No since volume scales cubically.

V_new = 2³V_old

8

500

A runner travels 100 m in 12.5 seconds.

Another runner travels 0.12 km in 14 seconds.

Who has the greater average speed?

Runner 1:

v₁=100/12.5

= 8m/s

Runner 2:

0.12km=120m 

v2=120/14

≈8.57m/s

Therefore:

Runner 2

Graphs & Functions

100

Where am I from?

Orange County

200

An object has a horizontal line on a position-vs-time graph.

Is the object moving?

No because a horizontal line has slope zero.

300

Two objects have position-time graphs.

• Object A has slope +4 m/s.
• Object B has slope −4 m/s.

Which object is moving faster?

They have the same speed:

4m/s but opposite velocities.

400

During which segment is the object moving fastest? What is its velocity during that segment?

• Segment A: t=0 to t=2, position increases from 0 m to 8 m
• Segment B: t=2 to t=5, position remains at 8 m
• Segment C:t=5 to t=7, position decreases from 8 m to 2m

For Segment A:

v=8−0/2−0

=4 m/s

For Segment B:

v=0

For Segment C:

v=2−8/7−5

=−3 m/s

Compare the magnitudes:

∣4∣>∣−3∣>0|4|>|-3|>0

Therefore:

Segment A, with a velocity of +4 m/s

500

A position-time graph is a straight line passing through (2,8) and (6,20). Assume the time is given in seconds and position is given in meters.

• What is the velocity?
• Write the position equation. Written in x(t)=
• What is the position at t=10 seconds

Velocity:

v=20−8/6−2

=3m/s

Equation:

x(t)=3t+b

Using (2,8):

8=2(3)+b

b=2

Therefore:

x=3t+2

At t=10

x=32m

x(10)=32m

Trig & Vectors

100

A vector has: x>0, y<0

Which quadrant does it point toward?

Quadrant IV

200

What college am I from?

Seventh!! 7️⃣

300

A 20 N vector points 30^∘ above the positive x-axis. Which component is larger: F_x or F_y?

F_x=20cos30^∘

≈17.3N

F_y=20sin30^∘

=10N

400

A vector points directly upward.

What are its x- and y-components?

x = 0, y > 0

500

Two forces act on an object:

A=40N at 60^∘ B=25N at 150^∘

Find the x-component of the resultant.

A_x=40cos60^∘=20 

B_x=25cos⁡150^∘≈−21.7

Therefore:

R_x=20−21.7 

R_x=−1.7N

Multi-step algebra for an unknown value

100

A car travels at a constant rate using distance = rate × time. If it travels 150 miles in 3 hours, find its rate.

50 mph

200

An object has an acceleration of 3 m/s² under a net force of 12 N. Find its mass using F = ma.

4 kg

300

A 1,500 g object experiences a net force of 6 N. Find its acceleration in m/s² using F = ma.

 1000g=1kg

1500g=1500/1000=1.5kg

F=ma

a=6N/1.5kg

 mass = 1.5 kg, so a = 4 m/s²

400

An object in equilibrium experiences four forces along the same line: 30 N to the right, 12 N to the left, 8 N to the left, and an unknown force. Find the magnitude and direction of the unknown force.

10 N to the left (-10N), since 30 − 12 − 8 + x = 0

500

Two cars start from rest.

• Car A accelerates at 2m/s².
• Car B accelerates at 4m/s².

After the same amount of time, how do their velocities compare?

v=at

v_B=2v_A

So Car B has twice the velocity of Car A.