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Problem Set

1. Evaluate the following expressions.

(a) (2 + 3)

5

(15

20

5)

(b) (( 2 + 2 )

4

(10

2) )

(c) (2

3

9 )

3

(d) 2(30

(10

(4 + 12

4)) )

6

2. How much smaller is the sum of 3 and 7 than the product of 4 and 8?

3. If a = b = c = d and a + b + c + d = 16, what is the value of a

b

c

d?

4. *You are a contestant on the popular European game show Countdown. During a

“Numbers Round” you draw six numbers,

75 2 5 6 1 4

and a target.

273

Your goal is to use your numbers and four arithmetic operations (addition, subtraction,

multiplication, and division) in order to reach your target. You can only use each

number once, but you do not have to use all of your numbers. How close can you get?

5. If

is an operation deﬁned as p

q = p + 3pq

2q + 1, what is the value of 7

5?

6. Evaluate the following products without a calculator.

(a) 3

57

(b) 5

371

1

(c)

1256

2

(d) 23

32

(e) 17

142

7. Solve for x. Show all of your work.

x

15

(a) 2x + 3 =

7

(b) x + 4

2x = 3x + 20

(c)

+ 3 =

4

4

8. The product of 2, 4, 6, and x is equal to its sum. What is value of x?

9. Clark scored a total of 36 points in his basketball team’s ﬁrst four games. He scored

1

1

2

of these points in the ﬁrst game,

of these points in the second game, and

of the

4

6

9

points in the third game. How many points did he score in the fourth game?

x

y

10. If x

2y =

12 and

+ y = 8, then what is the value of

?

2

3x + 8

10

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Parent category: Education