Karen Dillard’s College Prep L.P. — MATH WORKSHOP #1108: A2017 © This material is covered by Federal copyright laws that prohibit its reproduction in whole or in part without theexpress, written permission of Karen Dillard’s College Prep, LLC. No rights claimed for original works of outside authors. 1

MATHWORKSHOP

FEATURE PROBLEM Katrina leaves her house and drives to work. For the

first 5 miles of the trip, her average speed is 40 miles per hour. Then, due to an accident clearing on the road ahead, she is stuck in one spot for 10 minutes. Finally, once the accident clears, she is able to go the last 10 miles of the trip at an average speed of 60 miles per hour. To the nearest tenth, what is Katrina’s average speed, in miles per hour, for the entire trip?

STRATEGY Average speed is defined as total distance over total time. Calculate the amount of time that each leg of the trip takes and then make sure that you are using the proper units when you convert to the final rate.

#1108

9 9 9 98 8 8 87 7 7 7

5 5 5 5

6 6 6 6

4 4 4 4

2 2 2 2

3 3 3 3

1 1 1 1

0 0 0

. . . ./ /

Karen Dillard’s College Prep L.P. — MATH WORKSHOP #1108: A2017 © This material is covered by Federal copyright laws that prohibit its reproduction in whole or in part without the

express, written permission of Karen Dillard’s College Prep, LLC. No rights claimed for original works of outside authors.2

STRATEGY IN REVIEW

1

A circle in the xy-plane is defined by the equation (x + 6)2 + (y – 4)2 = 25. Which of the following

statements about the graph of this circle is true?

A. It will intersect the x-axis twice, but it will not intersect the y-axis.

B. It will intersect the y-axis twice, but it will not intersect the x-axis.

C. It will intersect both the x-axis and y-axis twice.D. It will intersect neither the x-axis nor the y-axis.

2

O

Y

X

80°

In the figure above, points X and Y lie on the circle with center O such that angle XOY measures 80° as shown. If the length of minor arc XY! is 24π, what is the area of the circle?

A. 108πB. 729πC. 2,916πD. 11,664π

A B C DA B C D

CIRCLES

On problems that involve circles, consider the relationships in a circle:

When a wheel rolls one full revolution (360°), it moves a distance equal to its circumference.

To solve arc length or sector area problems, set up a proportion.

sector areacircle area (πr 2 )

= arc lengthcircumference (2πr )

= central angle360°

= partwhole

The EQUATION OF A CIRCLE is: (x − h)2 + (y − k)2 = r2, where (h, k) is the center of the circle and r is the radius.

Karen Dillard’s College Prep L.P. — MATH WORKSHOP #1108: A2017 © This material is covered by Federal copyright laws that prohibit its reproduction in whole or in part without theexpress, written permission of Karen Dillard’s College Prep, LLC. No rights claimed for original works of outside authors. 3

A B C D 9 9 9 98 8 8 87 7 7 7

5 5 5 5

6 6 6 6

4 4 4 4

2 2 2 2

3 3 3 3

1 1 1 1

0 0 0

. . . ./ /

STRATEGY IN REVIEW

3

A circle in the xy-plane has a radius of 8 and its center is (−3, 7). Which of the following is the equation of this circle?

A. (x – 3)2 + (y + 7)2 = 8B. (x + 3)2 + (y – 7)2 = 8C. (x – 3)2 + (y + 7)2 = 64D. (x + 3)2 + (y – 7)2 = 64

4

O

A B60°

In the figure above, points A and B lie on the circle

with center O such that ∠OAB measures 60° as shown.

If the radius of the circle is 60π

, what is the length of

minor arc AB! ?

Karen Dillard’s College Prep L.P. — MATH WORKSHOP #1108: A2017 © This material is covered by Federal copyright laws that prohibit its reproduction in whole or in part without the

express, written permission of Karen Dillard’s College Prep, LLC. No rights claimed for original works of outside authors.4

ALGEBRA QUIZ : 10 QUESTIONS, 14 MINUTES

1

a > 4b− 2

b > 114

Given the system of inequalities shown above, which of the following inequalities defines all the possible values of a ?

A. a > 11B. a > 9C. a > 7D. a > 4

2

If x−12 = 8, what is the value of x ?

r

A = �r 2

C = 2�r

V = ℓwh

h

wℓ

A = ℓw

w

ℓ

A = bh12

b

h

rr

h

V = �r 2 h V = �r 343

b

a

c

c 2 = a 2 + b 2

rh

V = �r 2 h13

h

wℓ

V = ℓwh13

2x

x 3

x30°

60°

45°

45°s

s

s 2

Special Right Triangles

The number of degrees of arc in a circle is 360.The number of radians of arc in a circle is 2p.The sum of the measures in degrees of the angles of a triangle is 180.

A B C D 9 9 9 98 8 8 87 7 7 7

5 5 5 5

6 6 6 6

4 4 4 4

2 2 2 2

3 3 3 3

1 1 1 1

0 0 0

. . . ./ /

Karen Dillard’s College Prep L.P. — MATH WORKSHOP #1108: A2017 © This material is covered by Federal copyright laws that prohibit its reproduction in whole or in part without theexpress, written permission of Karen Dillard’s College Prep, LLC. No rights claimed for original works of outside authors. 5

A B C D

3

In the xy-plane, line ℓ passes through the points (−4, 10) and (2, 7). If line m is perpendicular to line ℓ,

what is the slope of m ?

A. −2

B. − 1212

C.

D. 2

4

The function f is defined as f (x) = 2x2 – 5 and the function g is defined as g (x) = −f (x – 3) + 4. What is the value of f (g (5)) ?

A. −3B. −1C. 1D. 3

5

Which of the following expressions is equivalent to (4x + 5)2 + (8x + 11) ?

A. (2x + 9)(8x + 4)B. (4x + 6)2

C. (4x + 7)2 – (8x – 13)D. (5x + 5)2 − (2x – 11)

6

The carriages on a particular amusement park ride can hold either 4 or 6 people. The ride has 40 carriages. If at a given time, every seat in every carriage is occupied and there are 194 people on the ride, how many of the carriages hold 4 people?

ALGEBRA QUIZ

A B C D

A B C D

9 9 9 98 8 8 87 7 7 7

5 5 5 5

6 6 6 6

4 4 4 4

2 2 2 2

3 3 3 3

1 1 1 1

0 0 0

. . . ./ /

Karen Dillard’s College Prep L.P. — MATH WORKSHOP #1108: A2017 © This material is covered by Federal copyright laws that prohibit its reproduction in whole or in part without the

express, written permission of Karen Dillard’s College Prep, LLC. No rights claimed for original works of outside authors.6

7

2x +10 + 7 = x

What is the solution set for the equation shown above?

A. {3}B. {13}C. {3, 13}D. There are no solutions.

8

The equation of a parabola in the xy-plane is given as y = 3x2 – 12x + 18. What are the (x, y) coordinates of

the vertex of this parabola?

A. (−4, 114)B. (−2, 54)C. (2, 6)D. (4, 18)

9

Dalilah stocks a koi pond with fish on the first of the month. The number of fish that can be found in the pond m months later is given by the equation

k = 8m + 50 where k is the number of koi in the pond at that time. In the context of this equation, what is the best interpretation of the number 8?

A. It is the expected monthly increase in the number of koi in the pond.

B. Dalilah initially stocked the pond with 8 koi.C. When 8 more koi are added to the pond, there will

then be 50 koi in the pond.D. In eight months, there will be exactly 50 koi in the

pond at that time.

10

x f (x)−5 −21−2 −120 −64 6

Some of the defined values of the linear function f are shown in the table above. What is the value of f (7) ?

A. 9B. 12C. 15D. 18

ALGEBRA QUIZ

A B C D

A B C DA B C D

A B C D