## Sample Problems

## Grade 2

How many times does the digit 6 appear when you write all the numbers from 15 to 71?

## Grade 2

Pam, Kate, and Wendy each have a nickel, a dime, or a quarter. Kate's coin is worth the most. Pam's coin is worth more than Wendy's. Which coin does each girl have?

## Grade 2

Gina collected 1 more sticker than Lina. Lina collected 10 less than Bina. Bina collected 100 more than Dina. Dina collected 297 stickers. How much did Gina collect?

## Grade 2

The distance between the first house and the fourth house is 120 m. If all the houses are equally spaced, what is the distance from the fifth house to the seventh house?

## Grade 3

Jim has 58 batteries. After giving an equal number to each of his 4 friends, he still has 14 batteries left. How many batteries did he give each friend.

## Grade 3

Arjun cuts the square into two congruent rectangles. Each rectangle has a perimeter of 36. What is the perimeter of the original square

## Grade 3

Mrs. Smith has 9 albums and 72 pictures in each. She rearranges all the pictures equally into 6 larger albumns. How many pictures will there be in each of the larger albums?

## Grade 4

Jill divides 27 by a number and gets a remainder of 3. What are all the possible numbers Jill used to divide?

## Grade 4

A group of students plan to buy a gift for their teacher. If each of them pay $2, they will be short of $4. If each of them pays $3, there will be an extra $3. How much does the gift cost?

## Grade 4

Place a decimal point between two digits of the number 707808 so that the digit in the hundreds place is the same as the digit in the tenths place

## Grade 4

The sum of two decimals is 71.5. Their difference is 21.9. What are the two decimals?

## Grade 5

Laurel earned $0.60 more than Harry per hour. If they worked 5 hours each and earned $120 in all, how much did Hardy earn per hour?

## Grade 5

Mr. A and Mr. B have $130 in all. Mr. A and Mr. C have $115 in all. If Mr.A has 1 1/2 times as much money as Mr.C, how much does Mr. B have?

## Grade 5

Amy glues 165 unit cubes to form a rectangular prism. The perimeter of the base is 28 units. What is the height of the prism?

## Grade 5

Elaina and Lynn hasve marbles in the ratio 8:3. After Eliane gave 15 marbles to Lynn, They each had the same number of marbles. How many marbles did Lynn have at first?

## Grade 6

1/4 of Joanne's pens is equal to 2/3 of Penny's pens. The difference in the number of pens each of them has is 135. How many pens do they have in all?

## Grade 6

There were 400 visitors at the art center. 35% of them were children and the rest were adults. When 100 more visitors entered, the percentage of adults increased to 70%. How many new children visitors were added?

## Grade 6

If the value of 52x - 13y = 65. What is the value of 28x -7y?

## Grade 7

Three years ago, I was two-thirds as old as I will be 8 years from now. How old am I now?

## Grade 7

The johnsons family drove to Florida for vacation. On their way back, they traveled 10 m/h faster and took 12.5% less time to complete the journey. Find the speed at which they drove to Florida.

## Grade 7

A large pizza costs twice as much as a small pizza. The diameter of a large pizza is 1.5 times as wide as that of a small pizza. Is it better deal to buy two small pizzas or one large pizza?

## Algebra 1

If f is a function, can the graphs of y = f(x) and y = f(x-2) intesect?

## Algabra 1

How can deg(f+g) be less than both deg f and deg g?

## Algebra 1

How much money should I invest at an annually comounded interest rate of 6% so that I have $100,000 in 3 years?

## Geometry

The sides of a triangle have lengths 18, 24 and 30. Find the length of the shortest altitude of the triangle

## Geometry

One of the angles of a rhombus is 1200. If the shorter diagonal is 4, what is the area?

## Geometry

I am riding in a hot air balloon 1 mile above the surface of the earth. Approximately how far is the horizon? (diameter of the earth = 8000 miles)

## Algebra 2

Find an equation whose graph is a parabola with vertex and focus .

## Algebra 2

The first term of an arithmetic sequence is 4 and the tenth term is 85. Find the sum of the first hundred terms in the sequence.

## Algebra 2

Find the remainder when x13+1 is divided by x-1