Understand the Mathematical Reasoning Section of the California High School Exit Exam: Math

There are eight problems involving number sense on the CAHSEE. These problems are grouped together and incorporate skills from number sense, statistics, data analysis, probability, measurement and geometry, and algebra. The areas covered include:

Samples with Suggested Approaches

  1. Andrea rode her bike for 3 hours at a rate of 15 miles per hour. What is the correct method to find the total miles that Andrea traveled?

    1. Add 15 and 3.

    2. Divide 15 by 3.

    3. Multiply 15 by 3.

    4. Multiply 60 by 15.

    Circle or underline the words total miles traveled. To find her total miles traveled, multiply 15 by 3. The actual total of miles traveled is 45 miles. Does this method give you a reasonable answer? Yes, if she travels 15 miles in one hour, then she travels 30 miles in 2 hours and 45 miles in 3 hours. The correct answer is C.

  2. If x is an even number, then which of the following is true about x/2?

    1. It is an even number.

    2. It is an odd number.

    3. It is a multiple of 2.

    4. It can be odd or even.

    When given a situation using types of numbers (odd, even, negative, and so on), try some simple numbers. If x is 2 (which is an even number), then x/2 is 1, which is an odd number. If x is 4, then x/2 is 2, which is an even number. The correct answer is D.

  3. Manuel purchases tickets to an amusement park for his family. Children's tickets cost half price, and adult tickets cost the full price of $8.00 each. Which of the following expressions represents the total dollars spent for tickets if there are 2 adults and 6 children in Manuel's family?

    1. 2(8) + 3(4)

    2. 2(4) + 6(6)

    3. 2(8) + 4(4)

    4. 2(8) + 6(4)

    In this question you are being asked to set up an expression. Focus on key words and information given. From the information given you can figure out the total spent for adult and children's tickets:

    2 adults X $8 for each ticket

    6 children X $4 for each ticket (Note: Half the price of $8 = $4.)

    So, the total spent for tickets was 2(8) + 6(4). The correct answer is D.

  4. Union High School is planning to order yearbooks for the student body. The following shows the percent of students in each class that usually order yearbooks.

    40% of Freshmen buy a yearbook

    60% of Sophomores buy a yearbook

    85% of Juniors buy a yearbook

    95% of Seniors buy a yearbook

    Considering the preceding information, if there are 500 sophomores and 600 juniors in the school, what additional information is necessary to find out how many more sophomores than freshman will probably order yearbooks?

    1. The number of seniors in the school

    2. The number of juniors not ordering yearbooks

    3. The number of freshman in the school

    4. The number of sophomores not ordering yearbooks

    Since the question asks for the additional information necessary, and focuses on the difference between freshman and sophomores, you need to know the number of freshman in the school. The correct answer is C.

  5. How many numbers are less than 100 and are divisible by 2, 3, and 7?

    1. 2

    2. 3

    3. 4

    4. 5

    For a number to be divisible by 2, 3, and 7, it must be a multiple of 2, 3, and 7. Simply multiply 2, 3, and 7, and you get 42, which is a multiple of these three numbers. Double 42 and you get 84, another multiple of 2, 3, and 7. So there are two numbers less than 100 that are divisible by 2, 3, and 7. The correct answer is A.