7th grade ERB preparation

The math part of thee ERB is divided into 3 sections: Quantitative Reasoning, Mathematics, and Constructed Response. We've already looked at examples of the kinds of quantitative reasoning problems you might get.

The following questions should help you prepare for the Mathematics section. As you will see, you really don't need a calculator to do these. Thinking carefully is the key to success!. Sometimes a problem will use a variable (a letter standing in for an unknown number), just as we've seen in the practice we've done for the Quantitative Reasoning section.

1. x is to 16 as 1 is to 4. What is x?

Hint: A proportion is useful. We used them a lot when we studied percents.

2. If you know the measures of 2 angles of a triangle, can you calculate the measure of the third? _____ If so, how?

(Remember that the 3 angles need to sum to 180 degrees.)

EX: Triangle A has 2 angles measuring 55 and 35 degrees. The degree measure for the third angle will have to be equal to 180 - (55 + 35)

3. I toss a coin 3 times and each time the coin lands with "heads" facing up. What is the probability that I will get heads the next time?

(Remember that each new toss is not affected by outcomes in the past tosses.)

4. You and I each get on a merry-go-round (menage? or carousel) but our merry-go-rounds are making complete turns at different speeds. Mine makes a complete turn every minute and yours makes a complete turn every minute-and-a-half. How many minutes will it be before we are both once again in our original starting positions?

(Hint: Think about multiples! You are doing the same kind of thinking that you do when you find the LCM of two numbers.)

Let's assume that mine makes a complete turn every 60 seconds and yours makes a complete turn every 80 seconds. When will be both be back in our original starting positions?

What would the answer be if mine made a complete turn every 60 seconds but yours made a complete turn every 45 seconds?

5. Each edge of a cube is 3 ft. long. The cube is going to be covered with paper. What is the least amount of paper needed?

If you forget how many faces a cube has, just think of dice: 6! Find the area of one face (3 ft. squared or 3 ft. x 3 ft.) and then multiply that area times 6!!

6. Which of the following numbers is equal to 1/5? a. 0.02 b. 20 c. 0.2

7. Which of the following numbers is equal to 6/12? a. 0.05 b. 0.5 c. 0.6

8. What is the LCM of 2, 6, 8?

Remember to find the multiples of each number. Then look for the lowest shared multiple. Multiples of 6 are 6, 12, 18, 24, 30, 36, etc.

9. What is 100% of 50?

10. What is 10% of 50?

11. What is 20% of 200?

12. I want to balance two items on a scale: one weighs 5 grams and one weighs 100 kg. How many of the smaller items do I need to balance with one of the larger items?

Practice your metric tables. For example, you should know that 1 mm = .1 cm. Know many meters in a km, how many g in a kg, etc.

13. Imagine a clock. What is the measure of the angle formed when the hour hand is at the 12 and the minute hand is at the 10?

14. Imagine a clock, again. What is the measure of the angle formed when the hour hand is at the 12 and the minute hand is at the 11?

Hint for 13 and 14: a complete rotation is equal to 360 degrees.)

15. Solve 2n - 2 = 8 n =


16. The price of a car was reduced from $20,000 to 18,000. By what percent was it reduced?



Hint: To find percent that a price was reduced you first calculate the amount of the price reduction ($200) and then divide the amount of the reduction by the original price and then you multiply that by 100. So: $200/$2,000 x 100

17. A proportion problem:
To estimate species populations, biologists sometimes place tags on a number of animals. Later they take a second sample and count how many in the sample have tags. Then they can use a proportion to estimate the size of the total population.

In a pond, biologists tagged 200 fish and then released them back into the pond. Soon after they took a sample of 500 fish and found that 10 were tagged. What might they estimate the entire population to be?



10/500 = 200/entire population

18. I have 10 cards in a basket. On each card is a letter. If you pick a card, the probability that the letter on the card is an A is 3/5. What is the probability that the card you pick does not have a letter A?

How many of the 10 cards have an A on them?____

19. A dog weighs 5 pounds more than 3/4 of its weight. How much does it weigh?

Hint: 1/4 of its weight will be equal to 5 pounds.

20. 4n = 40 x .1 n= _____

21. 3n = 60 x .001 n = ____

22. 5n = 100 x .001 n=____

To do well on questions like 20-22, it is important to practice multiplying numbers by 10, 100, and 1,000 and .1, .01, and .001. Get comfortable moving around the decimal point! Don't just rely on your calculator to tell you this, but see that multiplying by .1 is the same as dividing by 10.

When you divide by 10, it is the same as moving the decimal one place to the left. When you multiply by .01, it is like dividing by 100 or moving the decimal two places to the left. You can practice with these:

40 x .1 = 4 40 x .01= .4 40 x .001= .04 400 x .001 = .4

23. Imagine that there are ten cards in a basket. The numbers 1-10 are written on them. What is the probability that a card picked at random will have a prime number written on it?___ An odd number?____ An even number? A number divisible by 3?_____ A number divisible by 6?______ A multiple of 4?______
A factor of 8?______A factor of 9?_____A single digit number?______

24. Are all rectangles parallelograms?

25. Are all parallelograms rectangles?

FORMULAS
Know how to use each geometry formula!! I'd like each of you to make up a problem for each formula and provide me with the answer. Remember to be careful to get your units right. Problems for area have answers in square units. Problems for volume have answers in cubic units.

Rectangles

Area = l x w (units will be square units such as square in., sq. ft, etc.)

Perimeter = 2l = 2w (units will be linear units such as in, ft. , etc.)

Squares

A = side x side

Perimeter = 4s

Triangles

A = 1/2 (b x h) or A = (b x h): 2

The base can be any side. The height must be perpendicular to base!

Perimeter = side 1 + side 2 + side 3