# HSPT Math and Quantitative Skills Review Course

## Mathematics Section:

*64 multiple choice questions @ 45 minutes timed test using a #2 pencil; NO calculators allowed*

The mathematics test will focus on arithmetic, problem solving, algebra and geometry (which includes addition, subtraction, multiplication, division, evens and odds, prime numbers, percents, square of a number, exponents, roots and averages). The purpose is to measure how well you can apply math concepts by solving problems and performing arithmetic operations. Understanding basic concepts is absolutely necessary. Most of the arithmetic questions require you to perform more than one step, testing a range of skills. Think about tricks and shortcuts you learned over the years like recalling “order of operations”. The following is a breakdown of this portion of the test: conceptual, procedural and applications.

*Conceptual* – **14 items**; consists of testing your knowledge of certain concepts by asking questions related to the following: numbers/numeration, measurements, geometry, algebra and stats/probability.

*Procedural* – **28 items**; measures your ability to perform in the following areas: numbers/numeration, measurements, geometry, algebra and stats/probability.

*Applications* – **22 items**; how well do you apply math concepts in the following areas: numbers/numeration, measurements, geometry, algebra and stats/probability.

## Quantitative Skills Section:

*52 multiple choice questions @ 30 minutes timed test using a #2 pencil*

Quantitative Skills focuses on your skills in mathematics (including number series, geometric comparison, non geometric comparison and number manipulation), science and other areas that deal with numbers. How well do you solve reasoning problems that involve numbers and quantities?

*Sequence* – **22 items**; when solving sequence problems, focus on identifying and recognizing a pattern. You will be given a set of numbers and asked to choose the one that logically fits the pattern or sequence. Remember, the numbers can include both negative and positive numbers, so concentrate on understanding the question in its entirety.

*Reasoning* – **13 items**; reasoning involves bringing together a series of skills you learned over time to solve a problem. You may find it to be complicated, involving several steps. Take your time to understand and evaluate each problem before choosing the correct answer.

*Geometric Comparison* – **8 items**; you will use your geometry skills to find the best answer in comparing geometric shapes and shaded areas. Pay close attention to each multiple choice answer since it will involve using a multi-step solution to come up with the best answer.

*Non Geometric Comparison* – **9 items**; this section of the test involves using your math skills to compare and solve multi-step equations that do not involve geometry. Both the equations and answers involve complex problem solving, so be sure to take your time to understand what is being asked.

## Below are related videos to these sections of the test.

## Math Basics

### Lesson 1: Operations Basics

- Addition and Subtraction
- Associative Property
- Distributive Property
- Exponents and Roots
- Integers, Decimals, and Fractions
- Multiplication and Division
- Order of Operations

### Lesson 2: Factors and Multiples

- Greatest Common Factor
- Least Common Multiple
- Multiples
- Multiples and Least Common Multiples
- Prime Numbers, Factoring, and Prime Factorization

### Lesson 3: Unit Conversions

## Fractions

### Lesson 1: Fraction Basics

- Changing Mixed Numbers to Improper Fractions
- Converting Improper Fractions to Mixed Numbers
- Fractions of a Whole
- Improper Fractions and Mixed Numbers
- Ordering Fractions

### Lesson 2: Fraction Operations

- Adding and Subtracting Fractions
- Converting Improper Fractions to Mixed Numbers and Decimals
- Converting Mixed Numbers to Decimals and Improper Fractions
- Converting Percentages to Decimals and Fractions
- Multiplying and Dividing Fractions

## Decimals

### Lesson 1: Decimal Basics

### Lesson 2: Decimal Operations

- Adding and Subtracting Decimals
- Changing a Number from Standard Form to Scientific Notation
- Converting Decimals to Fractions and Percentages
- Converting Decimals to Improper Fractions and Mixed Numbers
- Dividing Decimals
- Multiplying Decimals
- Scientific Notation

## Solving Equations

### Lesson 1: Equation Basics

- Absolute Value
- Arithmetic Sequences and their Formulas
- Solving Equations Using All Four Basic Operations
- Solving Equations Using Addition and Subtraction
- Solving Equations Using Multiplication and Division
- Solving Equations with Absolute Value

### Lesson 2: Inequalities

- Equations and Inequalities
- Graphing Solutions to Linear Inequalities
- Linear Inequalities
- Solving Absolute Value Inequalities
- Solving Inequalities Using All Four Basic Operations

### Lesson 3: Linear System of Equations

- Comparison of Methods for Solving System of Equations
- Linear Equations Basics
- System of Linear Equations
- System of Equations Basics

### Lesson 4: Graphing of Linear Equations and Functions

- Changing Constants in Graphs of Functions: Linear Functions
- Changing Constants in Graphs of Functions: Quadratic Equations
- Graphing Absolute Value Equations
- Graphing Linear Equations
- Graphing the Inverse of a Function
- Graphs of Functions
- Solutions of a Quadratic Equation on a Graph
- Using a Graph

### Lesson 5: Word Problems

- Right Triangle Word Problems
- Word Problems and Addition
- Word Problems and Division
- Word Problems and Multiplication
- Word Problems and Subtraction

## Geometry

### Lesson 1: Angle Basics

### Lesson 2: Triangles

- Area and Perimeter of a Triangle
- Measurements for Similar Triangles
- Measurements for Similar Triangles – Continued
- Proof that a Triangle is 180 Degrees
- Similar Triangles

### Lesson 3: Circles

- Area and Circumference of a Circle
- Finding Measurements for Parts of a Circle
- Unit Circles and Standard Position

### Lesson 4: Volume and Surface Area of 3D Shapes

- 3D Geometric Shapes
- Volume and Surface Area of a Cube
- Volume and Surface Area of a Pyramid
- Volume and Surface Area of a Rectangular Solid
- Volume and Surface Area of a Circular Cone
- Volume and Surface Area of a Circular Cylinder
- Volume and Surface Area of a Sphere