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Free Math Worksheets — Over 100k free practice problems on Khan Academy

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Statistics and probability

High school statistics, ap®︎/college statistics, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra.

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  • Add and subtract within 20
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  • Negative numbers: addition and subtraction
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  • Arithmetic properties
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  • Negative numbers and coordinate plane
  • Ratios, rates, proportions
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  • Foundations
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  • Green’s, Stokes’, and the divergence theorems
  • First order differential equations
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  • Laplace transform
  • Vectors and spaces
  • Matrix transformations
  • Alternate coordinate systems (bases)

Frequently Asked Questions about Khan Academy and Math Worksheets

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Khan Academy’s 100,000+ free practice questions give instant feedback, don’t need to be graded, and don’t require a printer.

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Is Khan Academy free?

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Our 100,000+ practice questions cover every math topic from arithmetic to calculus, as well as ELA, Science, Social Studies, and more.

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Math Review

Get a head start on your math review.

Below are different categories of math testing topics. To review a particular category you are interested in or need assistance with studying for, simply click on it.

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Mometrix Academy – Home

by Mometrix Test Preparation | This Page Last Updated: October 31, 2023

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High School Math Review, Tutorials and Problems

Each of our high school math tutorials and math review has worked examples and math problems for you try (with solutions). So if you need help with your math homework or with one of our printable high school math worksheets then this is a good place to start. This a great study site for high school and college students. Parents, too, can use these free resources and problems to help your child learn math .

A note about year levels

Each tutorial is given a year level that it is applicable to. As we're all in different countries the year level corresponds to the number of years at school. So, for example, a tutorial for Year 11 is for students in their 11th year of school. Math reviews for earlier or later years may still be suitable for you.

View High School Math Tutorials and Review ...

Number and basic numeracy tutorials & review.

  • Order of Operations In a math calculation the order you do the operations (add, subtract, multiply, divide and brackets) is important. This tutorial is suitable for students in Year 7 to 9.
  • Directed Numbers Directed numbers are signed numbers i.e. numbers with a positive or plus sign (+) in front of them or a negative or minus sign (-) in front of them  e.g.  +6, -2, +7 etc.  All these whole numbers (and 0) grouped together are called integers. How do you add, subtract, multiply and divide directed numbers? View the tutorial. This tutorial is suitable for students in Year 9 or 10.

Fractions Tutorials & Review

  • An Introduction to Fractions What are fractions? How do you express a diagram as a fraction? What are the parts of a fraction called? This tutorial is suitable for students in Year 8 or 9.
  • Equivalent Fractions What are equivalent fractions, improper fractions and mixed numbers? How to simplify a fraction. This tutorial is suitable for students in Year 9.
  • Fractions, Decimals & Percentages How to convert fractions to decimals and percentages. This tutorial is suitable for students in Year 9.
  • Ratios What are ratios and how to simplify them. This tutorial is suitable for students in Year 9.

Algebra Math Review & Tutorials

  • Solving Linear Equations Learn how to solve simple algebriac equations like 4x - 5 = 3x + 7 Single variable only This tutorial is suitable for students in Year 9 or 10
  • Solving Quadratic Equations What if the variable has a power of 2 or is squared? How to solve simple quadratic equations by square rooting and factorising. The first part of this tutorial is suitbale for Year 10 students. The second part of this tutorial is suitable for Year 11 students.
  • Introduction to Graphing - Cartesian Co-ordinates How to plot points on a graph. This tutorial is suitable for students in Year 9
  • Drawing Straight Line Graphs using the Tabular Method Examples of the general equation ... y = mx + c This tutorial is suitable for students in Year 9 or 10
  • Plotting Straight Line Graphs using the Intercept Method Using the intercept method to obtain an x-intercept and a y-intercept and then plotting a straight line graph. This tutorial is suitable for studentsin Year 10.
  • Drawing a Straight Line Graph using the Gradient Method For the graph y = mx + c we can use the gradient (m) and the intercept (c) to plot a straight line graph. This tutorial is suitable for students in Year 10.
  • Drawing Quadratic and Cubic Graphs An introduction to the quadratic and cubic graphs and using the tabular method to plot them. This tutorial is suitable for students in Year 11.

Geometry Math Review and Tutorials

  • Angles & Straight Lines An introduction to some basic geometry principles - the sum of angles on a straight line, angles around a point and vertically opposite angles. This tutorial is suitable for students in Year 9.
  • Angles & Parallel Lines New defintions - corresponding angles, alternate angle and co-interior angles. This tutorial is suitable for students in Year 9.
  • Angles & Triangles The angles inside and outside triangles have some special rules. Learn about the sum of the angles inside a triangle, exterior angles and special rules for equilateral and isosceles triangles. This tutorial is suitable for students in Year 9.
  • Angles & Polygons Rules for the interior and exterior angles of polygons. And rules for special polygons like squares and kites. This tutorial is suitable for students in Year 10.
  • Angles & Arcs More angle rules - this time for angles on an arc (or part of a circle). This tutorial is suitable for students in Year 11.

A tangent is a straight line touching one point on the circumference of a circle.

  • Cyclic Quadrilaterals Put a quadrilateral inside a circle and you have a cyclic quadrilateral with special rules for interior and exterior angles. This tutorial is suitable for students in Year 11.
  • Pythagoras' Theorem Named after Greek Mathematician, Pythagoras, this theorem is about the relation amongst the three sides of a right angle triangle. So if you know the length of two sides of a right angle triangle you can caculate the length of the other side. This has some wonderful practical applications. This tutorial is suitable for students in Year 10 or 11.
  • Transformation Geometry 1 - Translation What is translation and how to write a translation in vector form. This tutorial is suitable for students in Year 10.
  • Transformation Geometry 2 - Rotation What is rotation of a shape? This tutorial is suitable for students in Year 10.

Trigonometry Review and Problems

  • Trigometric Ratios We can use Pythagoras' Theorem (see above) to calculate the length of an unknown side in a right-angled triangle when we are given information about the lengths of 2 other sides . However, if we are given information about an angle (other than the 90 degrees) and one side and need to calculate the length of another side then we use the trig ratios . This first tutorial takes you through naming the sides of a triangle and an introduction to the trig ratios. This tutorial is suitable for students in Year 10 or 11.
  • Calculating sides using the trigometric ratios. We can use trig ratios to calulate the length of a side on a triangle if we know the length of one side and the size of one angle. You will need a scientific calculator for this tutorial This tutorial is suitable for students in Year 11 or 12.
  • Calculating angles using the trigometric ratios. OK, so probably saw this coming. If you know the length of the two sides of a right-angle triangle then you can caculate the size of the other angles inside the triangle. Nifty huh? We're really getting to know stuff about right-angle triangles. You will need a scientific calculator for this tutorial This tutorial is suitable for students in Year 11 or 12.

Calculus Tutorial, Review and Problems

  • Introduction to Differentiation Definitions, worked examples and exercises with solutions. Your first step to calculus. This tutorial is suitable for students in Year 12.
  • Differentiation of Negative Indices & Rational Powers You should review the differentiation of positive powers first (above) as negative indices are managed in the same way but you need to take care with the signs. This tutorial is suitable for students in Year 12.
  • Applications of Differentiation Using derivatives to find the grandient of a tangent and normal of straight line graphs. This tutorial is suitable for students in Year 12 or 13.
  • Introduction to Integration Sometimes called antidifferentiation, integration is the process of finding the definite or indefinite integral of a function. This tutorial is suitable for students in Year 12.

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Daily Math Review Worksheets - Math Buzz

Help your students build, practice, and retain essential math skills. Each level of Math Buzz daily math review features 150 worksheets - one for each day of the school year.

Daily Math Review Worksheets - Math Buzz

This collection of 150 daily review worksheets was designed to help first graders master basic math skills. Worksheets in this spiraling review set feature problems related to counting, addition and subtraction, shape recognition, measurement, and place value.

This collection of 150 daily review worksheets will help students master a variety of 1st and 2nd grade math skills. Topics include: addition and subtraction of 1 and 2-digit numbers, skip counting, measurement, solid and flat shapes, comparing 2-digit numbers, and solving word problems.

Here is a collection of 150 daily math review worksheets for students in 3rd grade. Skills include multi-step word problems, addition, subtraction, multiplication, place value, geometry, and more.

Practice 4th grade math skills each day with these printables. Topics include operations with fractions and decimals, long division, area and perimeter, multi-step word problems, and much more.

The 5th grade (Level E) Math Buzz series will have your students practicing 4th and 5th grade math concepts on a daily basis. Includes many problems related to operations with decimals, long division, operations with fractions, geometry, measurement, and multi-step word problems.

Daily Word Problems

This is a daily math review with graphical word problems for Kindergarten students. These work well as part of a classroom meeting, learning center review, or morning work.

This set contains a word problem for everyday of the school year. Most problems are basic addition and subtraction. Some problems also review place value and repeated addition.

In the daily word problems for 2nd grade, students will review addition, subtraction, and basic multiplication, as well as place value, time, and money. About half of the problems are single-step; the other half are multi-step.

In the 3rd grade Daily Math Word Problem series, students review multiplication, multi-digit addition and subtraction, elapsed time, money, and more. Approximately half of the problems are multi-step.

In the 4th grade Daily WP series, students will practice multi-digit addition, subtraction, multiplication, and division. They will also review operations with fractions, line plots, and more. About half of the problems presented are multi-step.

These 5th grade daily word problems include operations with decimals and fractions, interpreting charts and graphs, measurement, and more.

This page has daily word problems. Includes single and multi-step problems, covering a variety of topics.

Print task cards for a huge variety of math skills, including: operations, algebra, angles, fractions, area, volume, counting money, time, place value, rounding, comparing numbers, and more.

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An actual ACT Mathematics Test contains 60 questions to be answered in 60 minutes.

  • Read each question carefully to make sure you understand the type of answer required.
  • If you choose to use a calculator, be sure it is permitted, is working on test day, and has reliable batteries.
  • Use your calculator wisely.
  • Solve the problem.
  • Locate your solution among the answer choices.
  • Make sure you answer the question asked.
  • Make sure your answer is reasonable.
  • Check your work.

Calculator Tips

  • Review the latest information on permitted and prohibited calculators.
  • You are not required to use a calculator. All the problems can be solved without a calculator.
  • If you regularly use a calculator in your mathematics work, use one you're familiar with when you take the mathematics test. Using a more powerful, but unfamiliar, calculator is not likely to give you an advantage over using the kind you normally use.

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Sample Test Questions

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Section 1 - 5 of 30

DIRECTIONS:  Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document.

Do not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test.

You are permitted to use a calculator on this test. You may use your calculator for any problems you choose, but some of the problems may best be done without using a calculator.

Note: Unless otherwise stated, all of the following should be assumed.

  • Illustrative figures are NOT necessarily drawn to scale.
  • Geometric figures lie in a plane.
  • The word  line  indicates a straight line.
  • The word  average  indicates arithmetic mean.

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Practice Test

  • Introduction to Prerequisites
  • 1.1 Real Numbers: Algebra Essentials
  • 1.2 Exponents and Scientific Notation
  • 1.3 Radicals and Rational Exponents
  • 1.4 Polynomials
  • 1.5 Factoring Polynomials
  • 1.6 Rational Expressions
  • Key Equations
  • Key Concepts
  • Review Exercises
  • Introduction to Equations and Inequalities
  • 2.1 The Rectangular Coordinate Systems and Graphs
  • 2.2 Linear Equations in One Variable
  • 2.3 Models and Applications
  • 2.4 Complex Numbers
  • 2.5 Quadratic Equations
  • 2.6 Other Types of Equations
  • 2.7 Linear Inequalities and Absolute Value Inequalities
  • Introduction to Functions
  • 3.1 Functions and Function Notation
  • 3.2 Domain and Range
  • 3.3 Rates of Change and Behavior of Graphs
  • 3.4 Composition of Functions
  • 3.5 Transformation of Functions
  • 3.6 Absolute Value Functions
  • 3.7 Inverse Functions
  • Introduction to Linear Functions
  • 4.1 Linear Functions
  • 4.2 Modeling with Linear Functions
  • 4.3 Fitting Linear Models to Data
  • Introduction to Polynomial and Rational Functions
  • 5.1 Quadratic Functions
  • 5.2 Power Functions and Polynomial Functions
  • 5.3 Graphs of Polynomial Functions
  • 5.4 Dividing Polynomials
  • 5.5 Zeros of Polynomial Functions
  • 5.6 Rational Functions
  • 5.7 Inverses and Radical Functions
  • 5.8 Modeling Using Variation
  • Introduction to Exponential and Logarithmic Functions
  • 6.1 Exponential Functions
  • 6.2 Graphs of Exponential Functions
  • 6.3 Logarithmic Functions
  • 6.4 Graphs of Logarithmic Functions
  • 6.5 Logarithmic Properties
  • 6.6 Exponential and Logarithmic Equations
  • 6.7 Exponential and Logarithmic Models
  • 6.8 Fitting Exponential Models to Data
  • Introduction to Systems of Equations and Inequalities
  • 7.1 Systems of Linear Equations: Two Variables
  • 7.2 Systems of Linear Equations: Three Variables
  • 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
  • 7.4 Partial Fractions
  • 7.5 Matrices and Matrix Operations
  • 7.6 Solving Systems with Gaussian Elimination
  • 7.7 Solving Systems with Inverses
  • 7.8 Solving Systems with Cramer's Rule
  • Introduction to Analytic Geometry
  • 8.1 The Ellipse
  • 8.2 The Hyperbola
  • 8.3 The Parabola
  • 8.4 Rotation of Axes
  • 8.5 Conic Sections in Polar Coordinates
  • Introduction to Sequences, Probability and Counting Theory
  • 9.1 Sequences and Their Notations
  • 9.2 Arithmetic Sequences
  • 9.3 Geometric Sequences
  • 9.4 Series and Their Notations
  • 9.5 Counting Principles
  • 9.6 Binomial Theorem
  • 9.7 Probability

For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer.

For the following exercises, evaluate the expression.

2 ( x + 3 ) − 12 ; x = 2 2 ( x + 3 ) − 12 ; x = 2

y ( 3 + 3 ) 2 − 26 ; y = 1 y ( 3 + 3 ) 2 − 26 ; y = 1

Write the number in standard notation: 3.1415 × 10 6 3.1415 × 10 6

Write the number in scientific notation: 0.0000000212.

For the following exercises, simplify the expression.

−2 ⋅ ( 2 + 3 ⋅ 2 ) 2 + 144 −2 ⋅ ( 2 + 3 ⋅ 2 ) 2 + 144

4 ( x + 3 ) − ( 6 x + 2 ) 4 ( x + 3 ) − ( 6 x + 2 )

3 5 ⋅ 3 −3 3 5 ⋅ 3 −3

( 2 3 ) 3 ( 2 3 ) 3

8 x 3 ( 2 x ) 2 8 x 3 ( 2 x ) 2

( 16 y 0 ) 2 y −2 ( 16 y 0 ) 2 y −2

9 x 16 9 x 16

121 b 2 1 + b 121 b 2 1 + b

6 24 + 7 54 − 12 6 6 24 + 7 54 − 12 6

−8 3 625 4 −8 3 625 4

( 13 q 3 + 2 q 2 − 3 ) − ( 6 q 2 + 5 q − 3 ) ( 13 q 3 + 2 q 2 − 3 ) − ( 6 q 2 + 5 q − 3 )

( 6 p 2 + 2 p + 1 ) + ( 9 p 2 −1 ) ( 6 p 2 + 2 p + 1 ) + ( 9 p 2 −1 )

( n − 2 ) ( n 2 − 4 n + 4 ) ( n − 2 ) ( n 2 − 4 n + 4 )

( a − 2 b ) ( 2 a + b ) ( a − 2 b ) ( 2 a + b )

For the following exercises, factor the polynomial.

16 x 2 − 81 16 x 2 − 81

y 2 + 12 y + 36 y 2 + 12 y + 36

27 c 3 − 1331 27 c 3 − 1331

3 x ( x − 6 ) − 1 4 + 2 ( x − 6 ) 3 4 3 x ( x − 6 ) − 1 4 + 2 ( x − 6 ) 3 4

2 z 2 + 7 z + 3 z 2 − 9 ⋅ 4 z 2 − 15 z + 9 4 z 2 − 1 2 z 2 + 7 z + 3 z 2 − 9 ⋅ 4 z 2 − 15 z + 9 4 z 2 − 1

x y + 2 x x y + 2 x

a 2 b − 2 b 9 a 3 a − 2 b 6 a a 2 b − 2 b 9 a 3 a − 2 b 6 a

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The GRE ® General Test

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Overview of the Quantitative Reasoning Measure

The Quantitative Reasoning measure of the GRE General Test assesses your:

  • basic mathematical skills
  • understanding of elementary mathematical concepts
  • ability to reason quantitatively and to model and solve problems with quantitative methods.

View Sample Questions

Become more familiar with the Quantitative Reasoning measure of the GRE General Test. Review sample questions, answers and explanations.

Content areas covered

Some of the Quantitative Reasoning questions are posed in real-life settings, while others are posed in purely mathematical settings. Many of the questions are "word problems," which must be translated and modeled mathematically. The skills, concepts and abilities are assessed in the four content areas below.

  • properties and types of integers, such as divisibility, factorization, prime numbers, remainders and odd and even integers
  • arithmetic operations, exponents and roots
  • concepts such as estimation, percent, ratio, rate, absolute value, the number line, decimal representation and sequences of numbers
  • operations with exponents
  • factoring and simplifying algebraic expressions
  • relations, functions, equations and inequalities
  • solving linear and quadratic equations and inequalities
  • solving simultaneous equations and inequalities
  • setting up equations to solve word problems
  • coordinate geometry, including graphs of functions, equations and inequalities, intercepts and slopes of lines
  • parallel and perpendicular lines
  • triangles, including isosceles, equilateral and 30°-60°-90° triangles 
  • quadrilaterals
  • other polygons
  • congruent and similar figures
  • 3-dimensional figures
  • the Pythagorean theorem
  • angle measurement in degrees

The ability to construct proofs is not tested.

  • basic descriptive statistics, such as mean, median, mode, range, standard deviation, interquartile range, quartiles and percentiles
  • interpretation of data in tables and graphs, such as line graphs, bar graphs, circle graphs, boxplots, scatterplots and frequency distributions
  • elementary probability, such as probabilities of compound events and independent events
  • conditional probability
  • random variables and probability distributions, including normal distributions
  • counting methods, such as combinations, permutations and Venn diagrams

These topics are typically taught in high school algebra courses or introductory statistics courses.

Inferential statistics is not tested.

The content in these areas includes high school mathematics and statistics at a level that is generally no higher than a second course in algebra. It doesn’t include trigonometry, calculus or other higher-level mathematics. The  Math Review (PDF)  provides detailed information about the content of the Quantitative Reasoning measure.

Khan Academy® Instructional Videos: Free Preparation for the GRE Quantitative Reasoning Measure

For more explanations about the concepts covered in the Math Review, view free Khan Academy instructional videos.

Symbols, terminology, conventions and assumptions

The mathematical symbols, terminology and conventions used in the Quantitative Reasoning measure are standard at the high school level. For example, the positive direction of a number line is to the right, distances are nonnegative and prime numbers are greater than 1. Whenever nonstandard notation is used in a question, it is explicitly introduced in the question.

In addition to conventions, there are some important assumptions about numbers and figures that are listed in the Quantitative Reasoning section directions:

  • All numbers used are real numbers.
  • All figures are assumed to lie in a plane unless otherwise indicated.
  • lines shown as straight are actually straight
  • points on a line are in the order shown
  • all geometric objects are in the relative positions shown

For questions with geometric figures, you should base your answers on geometric reasoning, not on estimating or comparing quantities by sight or by measurement.

  • coordinate systems, such as  xy -planes and number lines
  • graphical data presentations such as bar graphs, circle graphs and line graphs 

To learn more about conventions and assumptions, download  Mathematical Conventions (PDF) .

Question types and Data Interpretation sets

The Quantitative Reasoning measure has four types of questions:

  • Quantitative Comparison Questions

Multiple-choice Questions — Select One Answer Choice

Multiple-choice questions — select one or more answer choices.

  • Numeric Entry Questions

Each question appears either independently as a discrete question or as part of a set of questions called a Data Interpretation set. All questions in a Data Interpretation set are based on the same data presented in tables, graphs or other displays of data.

Quantitative Comparison

These questions ask you to compare two quantities — Quantity A and Quantity B — and then determine which of the following statements describes the comparison.

  • Quantity A is greater.
  • Quantity B is greater.
  • The two quantities are equal.
  • The relationship cannot be determined from the information given.

Tips for answering

  • Become familiar with the answer choices . Quantitative Comparison questions always have the same answer choices, so get to know them, especially the last choice, "The relationship cannot be determined from the information given." Never select this last choice if it’s clear the values of the two quantities can be determined by computation. Also, if you determine that one quantity is greater than the other, make sure you carefully select the corresponding choice and don’t reverse the first two choices.
  • Avoid unnecessary computations . Don't waste time performing needless computations to compare the two quantities. Simplify, transform or estimate one or both of the given quantities only as needed to compare them.
  • Remember that geometric figures aren’t necessarily drawn to scale . If any aspect of a given geometric figure is not fully determined, try to redraw the figure, keeping those aspects that are completely determined by the given information fixed but changing the aspects of the figure that are not determined. Examine the results. What variations are possible in the relative lengths of line segments or measures of angles?
  • Plug in numbers . If one or both quantities are algebraic expressions, you can substitute easy numbers for the variables and compare the resulting quantities in your analysis. Consider all kinds of appropriate numbers before you give an answer: e.g., zero, positive and negative numbers, small and large numbers, fractions and decimals. If you see that Quantity A is greater than Quantity B in one case and Quantity B is greater than Quantity A in another case, choose "The relationship cannot be determined from the information given."

These multiple-choice questions ask you to select only one answer choice from a list of five choices.

  • Reread the question carefully — you may have missed an important detail or misinterpreted some information.
  • Check your computations — you may have made a mistake, such as mis-keying a number on the calculator.
  • Reevaluate your solution method — you may have a flaw in your reasoning.
  • Examine the answer choices . In some questions you’re asked explicitly which of the choices has a certain property. You may have to consider each choice separately or you may be able to see a relationship between the choices that will help you find the answer more quickly. In other questions, it may be helpful to work backward from the choices, for example, by substituting the choices in an equation or inequality to see which one works. However, be careful, as that method may take more time than using reasoning.
  • For questions that require approximations, scan the answer choices to see how close an approximation is needed . (This may be helpful for other questions too, as it can help you get a better sense of what the question is asking.) For some questions, you may have to carry out all computations exactly and round only your final answer in order to get the required degree of accuracy. In others, estimation is sufficient and will help you avoid spending time on long computations.

These multiple-choice questions ask you to select one or more answer choices from a list of choices. The question may or may not specify the number of choices to select.

  • Note whether you’re asked to indicate a specific number of answer choices or all choices that apply . In the latter case, be sure to consider all of the choices, determine which ones are correct, and select all of those and only those choices. Note that there may be only one correct choice.
  • In some questions that involve conditions that limit the possible values of the numerical answer choices, it may be efficient to determine the least and/or the greatest possible value . Knowing the least and/or greatest possible value may enable you to quickly determine all the correct choices.
  • Avoid lengthy calculations by recognizing and continuing numerical patterns .

Numeric Entry

These questions ask you either to enter your answer as an integer or a decimal in a single answer box or as a fraction in two separate boxes — one for the numerator and one for the denominator. You’ll use the computer mouse and keyboard to enter your answer.

  • Make sure you answer the question that’s asked . Since there are no answer choices to guide you, read the question carefully and make sure you provide the type of answer required. Sometimes there will be labels before or after the answer box to indicate the appropriate type of answer. Pay special attention to units such as feet or miles, to orders of magnitude such as millions or billions, and to percents as compared with decimals.
  • If you’re asked to round your answer, make sure you round to the required degree of accuracy . For example, if an answer of 46.7 is to be rounded to the nearest integer, you need to enter the number 47. If your solution strategy involves intermediate computations, carry out all computations exactly and round only your final answer in order to get the required degree of accuracy. If no rounding instructions are given, enter the exact answer.
  • Examine your answer to see if it’s reasonable with respect to the information given . You may want to use estimation or another solution path to double-check your answer.

Data Interpretation sets

Data Interpretation questions are grouped together and refer to the same table, graph or other data presentation. These questions ask you to interpret or analyze the given data. The types of questions may be Multiple-choice (both types) or Numeric Entry.

  • the axes and scales of graphs
  • the units of measurement or orders of magnitude (such as billions) that are given in the titles, labels and legends
  • any notes that clarify the data
  • When graphical data presentations such as bar graphs and line graphs are shown with scales, you should read, estimate, or compare quantities by sight or by measurement, according to the corresponding scales . For example, use the relative sizes of bars or sectors to compare the quantities they represent, but be aware of broken scales and of bars that don’t start at 0.
  • Answer questions only on the basis of the data presented, everyday facts (such as the number of days in a year) and your knowledge of mathematics . Don’t make use of specialized information you may recall from other sources about the particular context on which the questions are based unless the information can be derived from the data presented.

Problem-solving steps

In addition to the tips for answering in the question type sections above, there are also some general problem-solving steps and strategies you can employ. Questions in the Quantitative Reasoning measure ask you to model and solve problems using quantitative, or mathematical, methods. Generally, there are three basic steps in solving a mathematics problem:

Step 1: Understand the problem

Read the statement of the problem carefully to make sure you understand the information given and the problem you are being asked to solve.

  • Some information may describe certain quantities.
  • Quantitative information may be given in words or mathematical expressions, or a combination of both.
  • You may need to read and understand quantitative information in data presentations, geometric figures or coordinate systems.
  • Other information may take the form of formulas, definitions or conditions that must be satisfied by the quantities. For example, the conditions may be equations or inequalities, or may be words that can be translated into equations or inequalities.

In addition to understanding the information you are given, make sure you understand what you need to accomplish in order to solve the problem. For example, what unknown quantities must be found? In what form must they be expressed?

Step 2: Carry out a strategy for solving the problem

Solving a mathematics problem requires more than understanding a description of the problem (the quantities, the data, the conditions, the unknowns and all other mathematical facts related to the problem). It also requires determining  what  mathematical facts to use and  when  and  how   to use those facts to develop a solution to the problem. It requires a strategy.

Mathematics problems are solved by using a wide variety of strategies, and there may be different ways to solve a given problem. Develop a repertoire of problem-solving strategies and a sense of which strategies are likely to work best in solving particular problems. Attempting to solve a problem without a strategy may lead to a lot of work without producing a correct solution.

After you determine a strategy, carry it out. If you get stuck, check your work to see if you made an error in your solution. Maintain a flexible, open mindset. If you check your solution and can’t find an error, or if your solution strategy is simply not working, look for a different strategy.

Step 3: Check your answer

When you arrive at an answer, check that it’s reasonable and computationally correct.

  • Have you answered the question that was asked?
  • Is your answer reasonable in the context of the question? Checking that an answer is reasonable can be as simple as recalling a basic mathematical fact and checking whether your answer is consistent with that fact. For example, the probability of an event must be between 0 and 1, inclusive, and the area of a geometric figure must be positive. You may be able to use estimation to check that your answer is reasonable. For example, if your solution involves adding three numbers, each of which is between 100 and 200, estimating the sum tells you that the sum must be between 300 and 600.
  • Did you make a computational mistake in arriving at your answer or a key-entry error using the calculator? Check for errors in each step in your solution. Or you may be able to check directly that your solution is correct. For example, if you solve an equation for x, substitute your answer into the equation to make sure it’s correct.

There are no set rules — applicable to all mathematics problems — to determine the best strategy. The ability to determine a strategy that will work grows as you solve more and more problems. Download the Sample Questions for a list of 14 useful strategies you can employ, along with one or two sample questions that illustrate how to use each strategy.

Calculator use

You’re provided with a basic on-screen calculator on the Quantitative Reasoning measure. Sometimes the computations you need to do to answer a question in the Quantitative Reasoning measure are somewhat time-consuming, like long division, or they involve square roots. Although the calculator can shorten the time it takes to perform computations, keep in mind that the calculator provides results that supplement, but don’t replace, your knowledge of mathematics. You’ll need to use your mathematical knowledge to determine whether the calculator's results are reasonable and how the results can be used to answer a question.

Here are some general guidelines for calculator use in the Quantitative Reasoning measure:

  • Most of the questions don't require difficult computations, so don't use the calculator just because it's available.
  • Use it for calculations that you know are tedious, such as long division, square roots, and addition, subtraction, or multiplication of numbers that have several digits.
  • Avoid using it to introduce decimals if you’re asked to give an answer as a fraction.
  • You may be able to answer some questions more quickly by reasoning and estimating than by using the calculator.
  • If you use the calculator, estimate the answer beforehand so you can determine whether the calculator's answer is "in the ballpark." This may help you avoid key-entry errors.

For more information, download  Guidelines Specific to the On-Screen Calculator (PDF) .

Homeschooling 4 Him

15 Fun Math Review Activities and Games for Active Kids

What if you could help your child remember what they are learning in math more easily? And, what if you could make math fun at the same time? Well, with fun math review activities, you can do just that! Studies show that kids learn more and remember better when they are relaxed and having fun. And that means that using math review games is the perfect way to help your children learn. Here are 15 of my favorites.

These math review activities are a lot of fun and perfect to keep active kids moving, even when they are inside! Your kids will love math review when you ...

Make Math Questions Fun

Forget boring math worksheets. Here are some easy ways to practice the same math questions, while enjoying math with your child.

Scavenger Hunt

An easy way to make math fun is to turn your review questions into a scavenger hunt. Cut up slips of paper and write a review question on each one. Or, cut up a worksheet so each problem is on a different sheet of paper.

Then, hide the questions around the room for your child to find. When your child finds the questions, have them bring you the paper and tell you the answer.

You can turn this into a scavenger hunt by writing a clue on the back of each question to let your child know where to look for the next one.

This is a great activity for families with kids of multiple ages and grades to play together. Use different colors of paper for each different grade level, and assign each child a different color to find.

Scavenger hunts are a great way to practice measurement, too. Kids can look around the house for things to measure with a ruler. Or, they can search for 2 objects that are the same height.

Similar to a scavenger hunt, task cards are a fun way for kids to review the math concepts they are learning. You can hide task cards around the house, and ask your child to complete the tasks as they find each card. There are many different ways to use task cards to make learning fun for kids!

Flashcard Race

Another fun math review activity is to set up a race for your child. Shuffle a deck of flashcards and set up stacks of cards at one end of a room or a long hallway.

Ask your child to run to the stack of cards, grab one, and then run back to you to tell you the answer. Once your child has completed the entire stack of game cards, the race is over.

This is a great way for kids to practice multiplication facts- or any other math skill they need to review. This is also a great way for kids to get some exercise on a rainy day!

Life-Sized Game Board

math review activities life sized game board

One of my kids’ favorite math review games is to create a life-sized board game. To play, we create a board game path on the floor by arranging sticky notes in a line. Then, my kids stand on the first sticky note.

During their turn, they must answer a math review question. If they get the correct answer, they can roll the dice and move forward that number of spaces. We use a large dry erase die which makes the game even more fun.

Older kids can use a recording sheet to write down the questions and answers as they go. This fun game can be used for almost any kind of math, but it works especially well for math facts.

Rolled Up Socks Toss

math review activities rolled up socks toss

This is another game that is great for kids who are stuck inside due to bad weather. To set up, we get out several large baskets or buckets. Then, we tape the answer to a math problem on each bucket.

I say a math problem out loud, and my kids have to try to throw a rolled-up sock into the bucket that has the right answer.

You can assign point values to each bucket, or just give kids a point for each correct answer. After a certain number of questions, or a set amount of time, add up the points and see who is the winner.

This game is especially great for reviewing equivalent fractions.

Practice Math Facts

Math fact fluency is very important and requires a lot of extra review. Here are some fun math review activities that work especially well for practicing math facts.

Addition War

Addition War is a card game that is played much like the regular card game of War. The twist is that each time you would turn over a card, you should turn over 2 cards and add them together instead.

We generally play with 2 decks of cards with the face cards removed. This leaves the numbers 2-10, and we use the aces to represent the number 1.

This is a great game for siblings to play together. Or, you can play it with your child as a fun review and a way to see how they are doing with their math facts in a low-pressure environment.

Another fun way to review math facts is with dice. Kids can roll 2 dice and add or multiply the numbers together.

Then, they can keep track of the answers in a graph. As they color in the graph, they can keep track of which answer is “winning.” This makes a fun lesson in probability as well as a great math fact review.

math review questions

Play Board Games

math review games playing chess

Many common board games are great for math review. Think about what your child needs to learn and then look for a game that will allow them to practice those skills.

Many fun math games provide specific practice in certain concepts. But, some of the best math review comes from playing classic games like Yahtzee or Cribbage.

You can find a list of recommended educational board games or more about gameschooling here.

Use Magnets

A perfect way to practice simple math problems is with a magnet board. Look for a set of magnetic numbers that also includes operation symbols.

Then, you can use the magnets to spell a math problem for your child to solve. They will need to show the answer using a magnet. This is a simple way to make math fun.

You can also try counting with magnetic tiles as manipulatives. This post about how to store magnetic tiles has lots of great ideas for keeping them organized.

Bingo Games

math review activities playing bingo

Playing Bingo is another easy way to add some fun to your math review.

You can create customized Bingo cards for your child that include the answers to their review questions. Ask the questions, and have your child cover up the correct answer on their Bingo card.

Of course, Bingo is more fun when you can use pieces of a favorite cereal or candy, or fun small toys, as the Bingo markers.

Trashketball

This variation on basketball is a fun way for kids in small groups to review together. Get a large trash can to use as the basketball hoop, and find a soft ball (or roll up some socks to use as a ball).

Then, kids can take turns answering math problems. If they answer correctly, they can try to make a basket for their team.

Apply New Skills

A great way to help kids review what they are learning is to try to apply it to a new situation. Here are some fun ways to make those abstract math skills concrete for children.

baking to practice fractions and measurement

Baking is one of the best ways for kids to apply what they are learning in math. This is one of my son’s favorite mother son activities because it’s a great way to spend some quality time together. And of course, baking a pie is one of the best Pi Day activities !

Kids can practice measurement as they add ingredients. This can be a great way to review fractions and learn about equivalent fractions, too.

Older students might enjoy reading the recipe, which is a good way to practice following directions as well.

Use Manipulatives

Manipulatives are a fun way to help kids understand math concepts that they are learning. They are especially important for younger students, and for homeschool math for struggling students . That is because kids have an easier time learning concrete concepts rather than abstract ideas.

Try to find a way to tie in the math manipulatives to one of your child’s interests. For example, you can look for themed counters that your child likes.

A child who likes trucks might enjoy practicing addition by dumping both quantities of counters into the back of a dump truck. Kids who like animals might practice division by sharing the counters between several stuffed animals.

Manipulatives help kids practice new skills in a fun and hands-on way.

Play Store or Restaurant

Playing pretend is a great way for kids to practice their math skills in a real-life environment.

Kids can assign a price to each item in their store, and then practice adding the total and making change. In a restaurant, kids can calculate the percentage for the tip, add the tax to their purchase, or practice writing a check or making change.

math review activities homeschool apps

Many high-quality educational apps provide interactive games and activities to help kids with math review. Many offer fun prizes for kids when the game ends, which might motivate kids to review more. You can see a list of recommended homeschool apps here.

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math review questions

HESI Practice Test

HESI Math Practice Test

HESI Math Test Prep

If you are serious about getting a great score on your HESI Math test, try out this highly rated   HESI Math Prep Course .

The HESI Math test consists of 50 questions which must be completed within 50 minutes. The majority of the questions are multiple choice, but a few are fill-in-the-blank. It covers arithmetic, fractions, decimals, percentages, and basic algebra. Many of the questions are based on math that is commonly used in a healthcare setting. Use our free HESI Math practice test to review your skills. You may use a calculator.

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1 . Question

Subtract: \(\, 2033 − 987 =\), 2 . question, the patient’s daily calorie target needs to be reduced by 400 calories. if it is currently 2100 calories, what will be the calorie target after the reduction.

(Type your answer below as a numeric value only.)

3 . Question

Multiply: \(\, 774 × 68 =\), 4 . question, if each tablet contains 38 mg of diphenhydramine citrate, how many milligrams of this ingredient will there be in 215 tablets, 5 . question, divide: \(\, 8844 ÷ 12 =\), 6 . question, erin drives 156 miles commuting to and from work over the course of 6 days. how many miles does she commute each day, 7 . question, add: \(\, 2.788 + 0.46 + 0.975 =\), 8 . question, subtract: \(\, 4.68 − 0.975 =\), 9 . question, multiply: \((97.3)(0.006) =\).

(If rounding is necessary, round to the nearest thousandth.)

10 . Question

If a nurse sees 1.7 patients per hour, how many patients should she be expected to see in 9.5 hours round to the nearest whole number., 11 . question, divide: \(\, 16.8 ÷ 1.5 =\).

(If rounding is necessary, round to the nearest tenth.)

12 . Question

A hospital pays $21.36 for a pack of 24 surgical masks. what is the cost of each mask, 13 . question, add: \(\, \dfrac{2}{5} + \dfrac{1}{3} =\).

  • \(\dfrac{7}{15}\)
  • \(\dfrac{11}{15}\)
  • \(\dfrac{7}{8}\)
  • \(\dfrac{3}{8}\)

14 . Question

Add: \(\, 2 \dfrac{5}{6} + \dfrac{4}{15} =\).

  • \(2 \dfrac{9}{21}\)
  • \(2 \dfrac{1}{10}\)
  • \(3 \dfrac{9}{21}\)
  • \(3 \dfrac{1}{10}\)

15 . Question

Subtract: \(\, \dfrac{5}{6} − \dfrac{1}{4} =\).

  • \(\dfrac{2}{3}\)
  • \(\dfrac{15}{24}\)
  • \(\dfrac{13}{18}\)
  • \(\dfrac{7}{12}\)

16 . Question

Subtract: \(\, 3 \dfrac{1}{6} − 1 \dfrac{3}{4} =\).

  • \(1 \dfrac{11}{12}\)
  • \(2 \dfrac{1}{12}\)
  • \(1 \dfrac{5}{12}\)
  • \(2 \dfrac{7}{12}\)

17 . Question

Multiply: \(\, \dfrac{3}{8} × \dfrac{4}{9} =\).

(Express your answer in the simplest form.)

  • \(\dfrac{59}{72}\)
  • \(\dfrac{7}{17}\)
  • \(\dfrac{12}{17}\)
  • \(\dfrac{1}{6}\)

18 . Question

What is \(\dfrac{2}{3} \text{ of } \dfrac{1}{5} \).

  • \(\dfrac{2}{15}\)
  • \(\dfrac{5}{8}\)
  • \(\dfrac{13}{15}\)

19 . Question

Divide: \(\, \dfrac{4}{9} ÷ \dfrac{3}{8} =\).

  • \(\dfrac{84}{27}\)
  • \(\dfrac{12}{27}\)
  • \(\dfrac{12}{72}\)
  • \(\dfrac{32}{27}\)

20 . Question

Divide: \(\, 8 ÷ 2 \dfrac{2}{5} =\).

  • \(\dfrac{9}{7}\)
  • \(\dfrac{29}{9}\)
  • \(\dfrac{10}{3}\)
  • \(\dfrac{13}{5}\)

21 . Question

A tablet contains 0.45 mg of an active ingredient. how would this decimal be written as a fraction be sure to write it in its simplest form..

  • \(\dfrac{3}{7}\)
  • \(\dfrac{9}{50}\)
  • \(\dfrac{9}{20}\)

22 . Question

Express 0.125 as a fraction in its simplest form..

  • \(\dfrac{1}{25}\)
  • \(\dfrac{1}{8}\)
  • \(\dfrac{1}{12}\)
  • \(\dfrac{1}{15}\)

23 . Question

At a long-term care facility, 4 out of the 15 nursing staff are registered nurses. how could this be represented as a decimal.

(If rounding is necessary, round to the nearest hundredth.)

24 . Question

Express the improper fraction \(\dfrac{72}{5}\) as a whole number with decimal., 25 . question, convert the decimal 0.3 to a percentage., 26 . question, express 35% as a fraction in its simplest form..

  • \(\dfrac{1}{3}\)
  • \(\dfrac{5}{14}\)
  • \(\dfrac{3}{10}\)
  • \(\dfrac{7}{20}\)

27 . Question

Ratio and proportion:, \(x : 30 :: 16 : 120\), solve for \(x\)., 28 . question, \(60 : x :: 12 : 7\), 29 . question, how can \(\dfrac{7}{40}\) be expressed as a percentage, 30 . question, in the typical hospital, 3 out of every 25 beds are icu beds. what percentage of hospital beds are icu beds, 31 . question, of all the patients that visited the er yesterday, 5% required admission. if 6 patients were admitted yesterday, how many total patients visited the er yesterday, 32 . question, for a patient on a low-sugar diet, a maximum of 8% of the total calories consumed should come from sugar. if the patient consumed 1800 total calories today, what is the maximum number of calories from sugar she should have consumed, 33 . question, covert the following military time to regular time: 20:30, 34 . question, a staff member clocked in at 19:30 and clocked out 9.5 hours later. what time did he clock out if the attendance system uses military time, enter your answer using hh:mm format., 35 . question, solve for \(x : −5x + 100 = 65\), 36 . question, evaluate the following:, \(r × (220 − a) \)\(\text{ if } r = 0.8 \text{ and } a = 50\), 37 . question, how would 350 milligrams be expressed in grams, 38 . question, how tall in inches is a patient that has a height of 4 feet 7 inches, 39 . question, a patient is receiving pain relief via iv. the 1000 ml iv bag contains 8 mg of morphine. how many milligrams of morphine has the patient received when 400 ml of the iv solution remains in the iv bag, 40 . question, dosing instructions for a prescription oral pain medicine call for 0.3 milligrams per kilogram of body weight 3 times per day. if a patient weighs 180 pounds (1 pound = 0.45 kilograms), how many mg of the pain medicine should they be taking in total each day.

(Round to the nearest whole number of milligrams and enter your answer in a numeric value only.)

41 . Question

A patient needs to take pain medicine every 8 hours. if the first dose was taken at 22:00 (military time), when will they receive the third dose, 42 . question, a hospital worker worked a total of 45 hours over the course of 5 days last week (they stay clocked in during all of their breaks, including lunch). if they had the same schedule each day and clocked out at 18:00 (military time), at what time did they clock in each day enter your answer using hh:mm format., 43 . question, a patient’s height is \(1.8\) meters. how much should they weigh (in kilograms) in order to have a bmi of \(22 \text{kg/m}^2\), use the formula: \(\text{bmi} = \text{mass/height}^2\) where the mass is in kilograms and the height is in meters (note: the height is squared in the bmi formula)..

(Round to the nearest whole kilogram and enter numeric value only.)

44 . Question

An inpatient received 800 mg of a drug on monday. the dosage was decreased by 20% on tuesday. on wednesday it was reduced an additional 30% from tuesday’s dosage. how many milligrams of the drug was received on wednesday.

(Round your answer to the nearest whole number of milligrams and enter numeric value only.)

45 . Question

A 0.9% nacl (sodium chloride) solution contains 0.9 mg of nacl per 100 ml of solution. how many liters of such a solution would be needed in order to contain 7.0 mg of nacl.

(Round your answer to the nearest hundredth of a liter and enter numeric value only.)

46 . Question

An iv solution is set for 30 drops per minute. there are 15 drops per milliliter of iv solution. over the course of 4 hours, how many milliliters of the iv solution will have been delivered, 47 . question, a prescription medicine has a dosage of 0.8 mg/kg/day divided into two doses per day. if a patient is prescribed 21 mg per dose, how much would that patient be expected to weigh.

(Round to the nearest tenth of a kilogram and enter numeric value only.)

48 . Question

A patient used 12 ml of medicine 3 times per day for 30 days. in total, how many milliliters of medicine did they take.

(If rounding is necessary, round to the nearest whole milliliter and enter numeric value only.)

49 . Question

A doctor saw 17 patients during his shift which began at 9:00 am and ended at 5:00 pm. he took a 45 minute lunch break. on average, how many minutes did he spend with each patient.

(If rounding is required, round to the nearest minute, and enter numeric value only.)

50 . Question

Insulin is being dosed at 1.5 units per kilogram per day. if a patient weighs 200 pounds, what would be the expected dosage (in units) per day there are 2.2 pounds per kilogram..

(If rounding is required, round to the nearest whole number, and enter numeric value only.)

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