1. Number and Operations
NextAcademic Skills
A typical student in this score band can do the following:
- SKILL 1: Solve problems using ideas from basic set theory and basic number theory
- SKILL 2: Recognize and apply ratio, proportion, or percent in solving problems
- SKILL 3: Use properties of real number operations, ordering, and the zero-product property
- SKILL 4: Solve problems involving counting techniques
Suggestions for Improvement
To prepare for the next score band, try the following:
- Determine values or properties of numbers in a sequence when given a description of the sequence
- Create and use ratios, fractions, or percents in solving problems
- Solve more-complex counting problems (e.g., permutations, combinations, and inclusion/exclusion)
Skill Examples
The example questions below demonstrate the Academic Skills found in this score band. Without looking at the answers, try out the questions to see how comfortable you feel with the skills they test.
Skill 1—Example
Solve problems using ideas from basic set theory and basic number theory
X = set of positive integer factors of 6.
Y = set of positive integer factors of 9.
Z = set of positive integer factors of 15.
X, Y, and Z represent three sets of numbers, as defined above. What is the set of numbers that belong to set Z but to neither set X nor set Y ?
- {1, 3}
- {1, 5}
- {5, 15}
- {2, 3, 5}
- {1, 3, 5, 15}
Skill 2—Example
Recognize and apply ratio, proportion, or percent in solving problems
There are 150 teachers at a meeting, 40 percent of whom are male. Of the male teachers at the meeting, 35 percent teach elementary school. How many of the male teachers at the meeting teach elementary school ?
- 21
- 35
- 69
- 72
- 129
Skill 3—Example
Use properties of real number operations, ordering, and the zero-product property
If (p + 1)(t - 3) = 0 and p is positive, what is the value of t ?
- -3
- -1
- 0
- 1
- 3
Skill 4—Example
Solve problems involving counting techniques
If n is a positive 2-digit integer and both digits of n are the same, how many different values are possible for n ?
- 9
- 10
- 12
- 16
- 18