Sacramento Area Competitions in Mathematics

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Test Details and Samples

SACMATH contests use tests from MATHLEAGUE.ORG, an organization running and supporting math contests nationwide. Full descriptions of each test can be found on the MATHLEAGUE.ORG site, in the Junior High School section or the High School section.

This page gives a quick summary of each Test, talks about other similar tests, and provides links to sample tests/questions.

In the Sprint Test, individual students get a 30 question test and 40 minutes to solve as many problems as they can. For Elementary School and High School, the questions are multiple-choice, and the student provides the letter of the correct answer. For Middle School, the questions are short answer (exact answer required).

A calculator may not be used on the Elementary and Middle School Sprint Tests. A calculator may be used on the High School Sprint Test.

For Elementary and High School, a student's score on the Sprint Test is 4 points for each correct answer, minus 1 point for each incorrect answer. For Middle School, a student's score is the number of problems correct (MathCounts scoring). A skipped problem (blank on the answer sheet) is *not* counted as incorrect (ie, no points deducted for blank answers).

For example, if on a Sprint Test a student got 15 problems correct, missed 7 and skipped 8, the student's score (for Elementary and High School) would be (4 x 15) - (1 x 7) = 53. A Middle School student's score would be 15 (fifteen).

- Sample Elementary School Sprint Test Questions (solutions)
- Sample Middle School Sprint Test Questions
- Sample High School Sprint Test Questions
- Math Magic (PSIA)

Full sample Sprint Tests maybe be obtained from MATHLEAGUE.ORG, through signing up for their email list (note that very few emails are sent to their mailing list).

The Sprint Test is similar to the following tests:

- MathCounts Sprint Test (Middle School)

- Math League (Middle School)

- AMC-8/10/12

- UIL Mathematics Test

The Target Test consists of 8 questions requiring an exact answer. The questions are given 2 at a time. The amount of time for each pair of questions depends on the contest level (6 minutes for Elementary and Middle, 10 minutes for High School). Students may use scratch paper and a calculator.

A student's score on a Target Test (for ELementary and High School) is 10 points for each correct answer. For Middle School, the score is the number correct. No points are deducted for incorrect answers.

- Sample Elementary School Target Test Questions (solutions)
- Sample Middle School Target Test Questions
- Sample High School Target Test Questions

Full sample Target Tests maybe be obtained from MATHLEAGUE.ORG, through signing up for their email list (note that very few emails are sent to their mailing list).

The Target Test is similar to the following tests:

- MOEMS (Elementary and Middle School)

- Math Counts Target Test (Middle School)

- Math League (High School)

- Rocket City Math League (all levels)

- ARML

Number Sense Test

The Number Sense Test is a fun test of students' ability to do math in their heads! Individual students are given 80 basic math questions and 10 minutes to solve as many as they can. All questions are solved mentally, with the student writing down only the answer. Students may *not* use scratch paper or calculators.

Number Sense is unique because any question that the student skipped, erased, scratched out, or overwrote is counted as incorrect, up to the last question attempted. The "last question attempted" is considered the last question where the student attempted to provide an answer, correct or incorrect.

When SACMATH volunteers coach students for Number Sense, we tell them to try to do the questions in order and try to avoid skipping.

A student's score on a Number Sense Test is 5 points for each correct answer, minus 4 points for each incorrect answer. For example, if a student attempted 25 questions and got 18 correct, the score would be (5 x 18) - (4 x 7) = 62. For students first learning how to do Number Sense Tests, a score in the range of 40 to 60 is very typical. A score over 100 is an extremely good score!

To learn how to do Number Sense Tests, including some tricks and tips, see the "Number Sense Magic" document (on this page), which is a document produced by PSIA (Private Schools Interscholastic Association). The UIL Number Sense site (link below) provides basic information about Number Sense tests. Also, look at the sample Test (provided in both blank and scored versions).

- Sample Elementary School Number Sense Test (SACMATH)
- Sample Elementary School Number Sense Test (PSIA), (Answers)
- Sample Middle School Number Sense Test (PSIA)
- Sample Middle School Number Sense Test (SACMATH)
- Sample High School Number Sense Test (UIL)
- Sample High School Number Sense Test (SACMATH)
- Sample Number Sense Test with Scoring (Elementary PSIA)
- Number Sense Magic (PSIA)
- Number Sense Contest (UIL)

Science Test

The Science Test is designed to test a students science ability in three main areas: knowledge of scientific fact, understanding of scientific principles, and the ability to think through scientific problems.

The science test is used at Elementary, Middle and High School levels.

At Elementary School, the test is 50 multiple-choice problems for which the student has 30 minutes. The questions cover various aspects of elementary school science eduction including Earth Science, Planetary Science, Sound, and Light.

At Middle School, the test is 50 multiple-choice problems for which the student has 30 minutes. Approximately 40% of the items consist of Earth Science questions; 40% are about Life Science; and 20% are about Physical Science. Some overlapping of these scientific areas may be within the test questions as well.

At the High School level, the test is 60 multiple-choice problems for which the student has 40 minutes. 20 of the problems are Biology, 20 are Chemistry, 20 are Physics. Students can use a calculator, and are provided with a periodic table and a list of scientific constants.

At all levels a student's score is 5 points for each correct answer, minus 2 points for each incorrect answer. There is no penalty for skipping a question. At the High School level, awards are usually given for either the top scorers in the Biology, Chemistry, and Physics part of the test or the top overall scorers (depending on test format).

- Sample Elementary School Science Test (answers coming soon)
- Sample Middle School Science Test
- Sample High School Science Test (coming soon)

Maps/Graphs/Charts Test

Maps. Graphs and Charts is a test of a student's ability to understand information presented in the form of a map, a graph or a chart (or a combination of two or more), and to solve mathematical problems based on information presented in the map, graph or chart.

The Maps, Graphs, and Charts test is very similar to the Maps, Graphs and Charts event run by PSIA (Private School Interscholastic Association) in Texas. The test has 50 short-answer questions. Students are allowed to use a calculator.

A student's score on the Maps, Graphs and Charts Test will be 5 points for each correct answer, minus 2 points for each incorrect answer. No points are deducted for a skipped answer.

NOTE: Some PSIA questions require the use of an Atlas. There will not be any questions of this type on the SACMATH tests. All information needed for the questions will be provided in the SACMATH test itself.

Countdown Round

The Countdown Round is a fun, thrilling, head-to-head Contest held using the top-scoring Individual students in a Contest. The Countdown Round is done before the full audience of students, volunteers, teachers and parents attending a Contest.

Depending on the size of the Contest, the top 8 or 16 scoring students will be put into the Countdown Round. They will be paired up in brackets based on Individual score standings (ie, #1 v #16, #2 v #15, etc).

The pair of students will be presented with three questions, one at a time. After each question is presented, the first student to "buzz in" with the correct answer will be given a point. After the three questions the student with the most points advances to the next round. If the students are tied after three questions a "sudden victory" tiebreaker will be conducted. Once there are four students left, the number of questions presented will increase to 5.

Countdown Round is used as part of Elementary School and Middle School contests. The questions presented are appropriate for the grade levels involved. Students may use scratch paper and calculators. The Countdown Round

is similar to the Countdown Round used in MathCounts contests.

A full sample Countdown Round maybe be obtained from MATHLEAGUE.ORG, through signing up for their email list (note that very few emails are sent to their mailing list).
Team Test

In the Team Test, teams of students receive a 10 question test and 20 minutes to solve as many problems as they can. (In Elementary and Middle School, the team is four students. At High School, the team is three or six students).

A team's score on the Team Test (in the Elementary and High School contests) is 10 points for each correct answer. At the Middle School Contest, the score is the number of questions correct. No points are deducted for incorrect answers.

- Sample Elementary School Team Test Questions (solutions)
- Sample Middle School Team Test Questions
- Sample High School Team Test Questions

Full sample Team Tests maybe be obtained from MATHLEAGUE.ORG, through signing up for their email list (note that very few emails are sent to their mailing list).

The Team Test is similar to the following tests:

- MathCounts Team Test (Middle School)

- ARML Team Test (High School)

In a Relay Test, a group of students is given a set of questions where the questions are "linked", meaning that the answer to one question is used in the next question. Only the answer to the final question is turned in. Students may use scratch paper but not calculators.

In the Elementary and Middle School contests, the group of students is the full team. In the High School contest, the team is split into two groups of no more than three students. In all contests, the group of students is allowed to collaborate on the questions. (In true Relay format, each student in a team receives one question, then hands their answer answer back to the next student in line. The final student in line turns in an answer to the final question.)

An answer may be turned in after 3 minutes and after 6 minutes. A correct answer at three minutes is worth 10 points, a correct answer at 6 minutes is worth 5 points. No points are deducted for an incorrect answer. The last answer turned in is considered the team's final answer.

In a Relay Test, there are either four (Elementary School) or five (High School) sets of questions. A team can score a maximum of 40 (ES) or 50 (HS) points in the Relay Test.

The Relay Test at the High School Level is similar to the ARML Relay Test. At the Elementary School level, the questions are similar in difficulty to Target Test questions.

GUTS Test

The GUTS (Group United Towards Solving) Test is a fun contest where a group of students works to solve various difficult math problems under special conditions.

The GUTS Test consists of 12 problems with different point values. There are 3 problems worth 1 point each, 3 worth 2 points each, 3 worth 3 points each, and 3 worth 4 point each, for a grand total of 30 points. (At some contests, the point values are doubled).

A four-person group of students has 30 total minutes to solve as many problems as they can. However, there is a hitch! The problems are broken up into four three-question "packets", with each packet holding a different total point value (4, 6, 9 and 11 points). At some contests, the point values are doubled. The group of students starts with a packet of their choice, and they can __only__ get another packet __after__ they turn in answers for their current packet.

Some contests will add one more catch: Each four-person "GUTS Group" is chosen randomly, with an attempt made to avoid putting students into the same "GUTS Group" who from the same registered team or the same school.

The GUTS Test will be done live in the testing room. Teachers and parents may attend and watch the competition (but, of course, may not help the "GUTS Groups").

The questions on a GUTS Test are similar in difficulty to the Target and Team questions.

Math Bowl

Math Bowl is a thrilling head-to-head ladder-format contest involving teams, paired against one another. It is the Team equivalent of the Countdown Test. The Math Bowl is done in the full attendance of parents, teachers, students and volunteers attending a contest.

Depending on the size of the contest, a number of top teams (usually four) will be selected for the Countdown round based on their score on the Team Test and/or the average of the Individual Math Scores of the students on the team.

A question will be read out loud. When believes they have the answer, the team should buzz in. A team that gets a question correct receives one point. At the end of the set number of questions (9 or, in the final, 15) the team with the most questions correct advances to to th next round. If the two teams are tied, a "sudden victory" phase will start, where the first to provide a correct answer advances.

Questions on the Math Bowl are similar to questions on the Countdown round, or on the Sprint Test. Check those section of this page for questions.

Calculator Test

In the Calculator Test, students use handheld calculators to solve mathematical problems. The questions are usually of three types (the percentage is the percent of questions that are the given type):

- Problems where the student must correctly input a complex calculation (50%)

- Problems where the student must solve a word question (similar to other math contest problems), but one that involves complicated numbers (30%)

- Problems where the student is given a geometry problem with complicated numbers (20%).

In SACMATH Calculator tests, there will be 38 questions and the student will have 15 minutes to complete as many as she or he can. Students must answer the questions in order. Any problem skipped, before the last question attempted, will be counted as incorrect.

Students must provide answers to three significant digits, and can provide an answer as the numerical value or in scientific notation. For example, the following answer formats would be accepted (where '^' indicates exponents): 1.23, 1.23x10^0, 0.123, 1.23x10^(-1), 12.3, 1230, 1.23x10^3.

An error of plus or minus one in the third significant digit is allowed. For example, if the answer is 1.23, then 1.22 and 1.24 would both be accepted as correct. If the student provides the correct answer but provides too many significant digits, the answer is counted as correct but points are also deducted for the significant digit error.

In the Elementary School Calculator Test, all answers will be between 9.99 and -9.99. Students must provide answers to the hundredths digit (or the nearest cent). An error of plus or minus one in the hundredths digit (or cent) is allowed. (NOTE that the Elementary School Calculator Test is no longer given at contests).

The score is calculated as follows: 5 points for each correct answer, minus two points for each incorrect/skipped problem, minus two points for each significant digit error.

Calculators do not need to be expensive or fancy. Jeff has solved all problems on the calculator tests with a TI 30X purchased at Target for $10.

The Calculator Test is used in the Middle and High School contests. The SACMATH Calculator Test is based on the UIL Calculator Test. The below link contains more information about the UIL Calculator Test, along with practice problems. A sample UIL Calculator Test is also provided below.