This page will help you prepare for the CHSPE Math test, which is administered by the state of California.
CHSPE Math Practice Problems
Problem 1: (Ordering Numbers by Value)
Which of the following shows the numbers ordered from least to greatest?
A. –1/4 , 1/8 , 1/6 , 1
B. –1/4 , 1/8 , 1 , 1/6
C. –1/4 , 1/6 , 1/8 , 1
D. –1/4 , 1 , 1/8 , 1/6
E. 1 , 1/6 , 1/8 , –1/4
Solution 1:
The correct answer is A. In order to answer questions on ordering numbers from least to greatest or greatest to least, remember these principles:
(a) Negative numbers are less than positive numbers
(b) When two fractions have the same numerator, the fraction with the smaller number in the denominator is the larger fraction.
According to these principles, –1/4 is less than 1/8 , 1/8 is less than 1/6 , and 1/6 is less than 1.
Problem 2: (Math Problems in Narrative Form)
Consider the instructions below, and then answer the question that follows.
Step 1: Begin with a number N.
Step 2: Multiply the number by 3.
Step 3: Subtract 4 from the result.
Step 4: Divide the result by 8.
If the result of the calculation is 4, what is the value of N?
A. 1
B. 2
C. 12
D. 64
E. 0.667
Solution 2:
The correct answer is C. For narrative questions like this one, you are given facts instead of an equation. To solve, you need to work backwards, using inverse operations. So, if you are asked to divide you multiply to get the solution. If you are asked to subtract, you add to get the solution, and so on.
Step 4 says “divide by 8,” so multiply our final result of 4 by 8 to perform the first inverse operation: 4 8 = 32
Step 3 says “subtract 4,” so add 4 to our previous result to perform the inverse operation: 32 + 4 = 36
Step 2 says “multiply by 3,” so divide by 3 to perform the final inverse operation to solve: 36 ÷ 3 = 12
Problem 3: (Open-Ended Questions)
A recent report states that 72.8% of the work for the shopping center is now completed, and it has taken 182 days to do so. If work continues at the same rate, what fraction of the project will be completed after 43 more days? Express your answer as a fraction.
Solution 3:
The correct answer is 9/10.
As mentioned above, divide the percentage by the number of days in order to determine what percentage of the project is being completed each day:
72.8% ÷ 182 days = 0.4 percent completed per day
For the numerator of the fraction, we need to add 43 more days to the current 182 days: 182 + 43 = 225
Then determine how many days are needed to complete the entire project for the denominator of the fraction.
Since a complete project would be 100% complete, we divide the percentage per day into 100% to get the total days needed:
100% ÷ 0.4 = 250 days
Finally, express this as a simplified fraction by dividing the numerator and denominator by the greatest common factor, which is 25:
225/250 = 9/10
Problem 4: (Correcting Erroneous Calculations)
A baker multiplied a recipe by when he should have divided the recipe by 4. Which one of the operations on the erroneous result will correct the error?
A. Divide by 1/2
B. Multiply by 1/2
C. Multiply by 2
D. Divide by 4
E. Multiply by 8
Solution 4:
The correct answer is B. For erroneous calculations that involve division, try to find an equivalent fraction for the division. The baker should have divided by 4. Dividing by 4 is equal to multiplying by what fraction?
In this case, the baker should have divided the recipe by 4. Dividing by four is the same as multiplying by 1/4.
The baker erroneously multiplied by 1/2, so he needs to multiply by 1/2 again since 1/2 × 1/2 = 1/4
Problem 5: (Working with π)
A bridge over a circular pond in the city park passes over the exact diameter of the pond. The circumference of the pond is 176 yards. Approximately how long is the path in feet?
A. 28
B. 56
C. 58
D. 84
E. 168
Solution 5:
The correct answer is E. For this question, you need the formula for the circumference of a circle:
diameter × π = circumference.
If you do not see π in any of the answer choices, use 3.14 for to solve. We are given the circumference, so we need to divide the circumference by or 3.14 to get the diameter in yards:
176 3.14 = 56.05
We round this down to 56 yards. There are three feet in a yard, so multiply to get the final answer:
56 × 3 = 168
CHSPE Math Practice Test Video
The following video has practice test questions for the exam.
CHSPE Math Exam Format
The math section is just one part of the test. You will also have to complete the part on English language skills.
You’ll be allowed three and a half hours for the entire test. There isn’t a separate time limit for the math part. You can spend as much time on the math section as you like, provided that you can finish the other section in the time provided.
The math part of the CHSPE has 50 multiple-choice questions.
There will be nine “Number Sense and Operations” questions.
Fifteen of the problems will be on “Patterns, Relationships, and Algebra” concepts.
You will also see twelve “Data, Statistics, and Probability” problems.
Finally, there will be fourteen “Geometry and Measurement” questions, such as calculating perimeter, circumference, or hypotenuse length.
What specific topics are on the test?
The following topics are assessed on the math section of the CHSPE exam.
Numerical operations with integers, fractions, mixed numbers decimals, and percentages
Practical problem solving and word problems
Ratios and proportions
Algebra and functions
Sequences, patterns, and mathematical relationships
Communication and representation, estimation, mathematical connections, and mathematical reasoning
Coordinate geometry (slope, midpoint and graphing)
Geometric figures (circumference, perimeter, area, angles, and volume)
Data analysis and statistics
Probability
Will the math formulas be provided?
You will be given a sheet with math formulas when you take the CHSPE math test.
But it’s good idea to memorize as many math formulas as you can. That is because some formulas may not be given. In addition, you will be able to solve the questions more quickly if you don’t have to waste time looking the formulas up.
So try to get into the habit of committing the math formulas you need to memory.
Then you can write them out easily when you are doing practice problems for the CHPSE math test.
Please note:
The CHSPE and California High School Proficiency Exam are trademarks of the California Department of Education, which is neither affiliated with nor endorses this website.