SAT Practice Online- SAT Math Practice Questions -All Math-2022-2023

SAT MathsSAT English SAT Practice Tests -(Full -Length)

Topic 1. Heart of algebra

Topic 2. Passport to advanced mathematics

Topic 3. Problem solving and data analysis

Topic 4. Additional topics in math

SAT Math Section Exam Pattern

The Math section of the SAT is used to analyse the mathematical aptitude of the candidates. With the new changes to the SAT exam pattern, candidates will now be able to use calculators for the entire Math section of an SAT.

Number of Questions	58
Duration	80 minutes
Types of Questions	Multiple Choice Questions
Questions	Heart of Algebra Problem Solving Data Analysis Geometry Trigonometry Complex Numbers

Syllabus Details : Heart of Algebra

Solving linear equations and linear inequalities

Solve linear equations
- Type: $3x-0.6=1.8$ What value of $x$ satisfies the equation above
- Type: If $2x-4=5-x$ what is the value of $x$ ?
- Type: What is the solution to the equation $\frac{1}{2}x+\frac{1}{5}=\frac{1}{7} $
- Type: $-2(x-7)=2$ what is the value of $x$
- Type: $2x+5y=1$ and $x=5$ what is the value of $2y$
- Type: If $3x-1=5$, what is the value of $x-40$ ?
- Type: solve for $\left |2x+1 \right |=10$
Solve linear inequalities
- Type: What values of $x$ satisfy the inequality $5x+1>7$
Recognize the conditions under which a linear equation has one solution, no solution, and infinitely many solutions
- Type: $2x−4=a(x−2)$ If $a=2$, is the equation above, what value of $x$ satisfies the equation?

Understanding linear relationships

basics of linear relationships.
writing linear equations based on word problems
important features of linear functions
- Type: Tobias rented a kayak from a sports equipment store. For the rental, the store charged $$$60 per day plus $$25$ for delivery. If Tobias was charged a total of $$$325, for how many days did he rent the kayak?
- Type: The width of a rectangular vegetable garden is $W$ feet. The length of the garden is 16 feet longer than its width. Which of the following expresses the perimeter, in feet, of the vegetable garden in terms of $W$ ?

linear inequalities

Type : Hammer can harvest at least 48 pounds of honey from her bee colony. If he wants to package the honey harvest in $1.51$ pound jars, what is the minimum number of jars he can fill?
Type : Laila wants to buy at least 40 prizes for rewarding her students throughout the semester. The prize pool will be made of small and large prizes, which cost $3 and $5 each respectively. Her budget for the prizes can be no more than $100. She wants to buy at least 15 small prizes and at least 5 large prizes. Which of the following systems of inequalities represents the conditions described if x is the number of small prizes and y is the number of large prizes?

Graphing linear equations

features of linear graphs from their equations
Write linear equations based on graphical features
Determine the equations of parallel and perpendicular lines
Identify solutions to systems of linear inequalities as regions in the $xy$ plane

Solving systems of linear equations

solve systems of linear equations algebraically: substitution and elimination.
systems of linear equations have one solution, no solutions, or infinitely many solutions: graphically

Syllabus Details : Passport to Advanced Math

Solving quadratic equations

Solve quadratic equations in several different ways
Determine the number of solutions to a quadratic equation without solving

Non-linear expressions

Area of a rectangle
Height versus time
Population growth and decline
Compounding interest

Exponential expressions

change time units
Adding and subtracting exponential expressions
Multiplying and dividing exponential expressions
exponent operations to rational exponents

Radicals and rational exponents

Rational exponents refer to exponents that can be represented as fractions $\frac{1}{3},5,\frac{2}{5}$ etc..
Radicals are another way to write rational exponents. For example, $x^{\frac{1}{2}}\; and\; \sqrt{x}$ are equivalent.
Exponent operations to rational exponents
Equivalent rational and radical expressions

Operations with polynomials

adding and subtracting polynomials
multiplying two polynomials

Polynomial factors and graphs

factors of polynomial functions to the $x$-intercepts of polynomial graphs
polynomial remainder theorem
- The polynomial remainder theorem states that when a polynomial function $p(x)$ is divided by $x-a$, the remainder of the division is equal to $p(a)$, left parenthesis, a, right parenthesis.
determine the zeros of a polynomial function
$x$-intercepts, $y$-intercept and end behavior

Graphing quadratic functions

features of a parabola
function at several different values of $x$
input-output pairs as points in the $xy$-plane.
Sketch a parabola that passes through the points

Graphing exponential functions

Graphing exponential growth & decay
Using points to sketch an exponential graph
y-intercept ,
slope of the graph positive or negative,
value of y as the value of x becomes very large
shift the horizontal asymptote
shift the y-intercept

Linear and quadratic system

graphs of linear and quadratic systems
number of solutions for linear and quadratic systems
solve linear and quadratic systems algebraically
solutions to linear and quadratic systems from graphs

Structure in quadratic expressions

Factoring quadratic expressions
factor by grouping
Special factoring
- Square of sum
- Square of difference
- Difference of squares

Isolating quantities

Using equations and formulas with multiple variables
Manipulating formulas
Translate the word problem or given context into an equation.
Like solving equations, but with more variables

Function Notation

Evaluating functions algebraically and using tables
Determine inputs and outputs using tables
Evaluating composite functions algebraically and using tables $f(g(x))$

Syllabus Details : Problem Solving and Data Analysis

Ratios, rates, and proportions

Identify and express ratios
Part-to-part ratio
Part-to-whole ratio
Word problems using proportions
Applying a per unit rate
- $speed=\frac{distance}{time}$
- $price=\frac{total price}{units purchased}$

Percentages

percentages using part and whole values
equivalent forms of percentages
Calculating a percent value
Finding complementary percentages
Switching between forms of percentages
Calculating percent change

Unit conversion

Applying unit to unit ratios
Converting units within rates

Table data

Read two-way frequency table
calculate proportions and probabilities
Use proportions and probabilities to find missing values
find missing values

Scatterplots

line of best fit to describe scatterplots
Make predictions using the line of best fit
Fit functions to scatterplots

Key features of graphs

Bar graphs, dot plots, and histograms
Reading bar graphs
Reading line graphs
draw line graphs based on verbal descriptions
line graphs

Linear and exponential growth

two variables have a linear or exponential relationship based on their values
Linear
- Changes (i.e., increases or decreases) at a constant rate
- Changes by $c$ per unit of time.
Exponential
- Changes by ,$c%$ percent of the initial value per unit of time
- Changes by a factor of $c$ (e.g., halves, doubles) per unit of time
real-world scenario exhibits linear or exponential growth
Writing equations based on tables

Data inferences

Estimating using sample proportions
- estimate=sample proportion⋅population
margin of error
- range=estimate ± margin of error

Center, spread, and shape of distributions

mean, median, and mode.
range and standard deviation
The effect of outliers
Missing value given the mean

Data collection and conclusion

good and bad sampling methods
Sampling methods and their implications
Correlation and causality
Identifying study types
Sample surveys
correlation and causation.

Probability

$Probability=\frac{desired \: outcome}{all \: possible \: outcome}$
“odds” of any particular event
get tails or head if you flip a coin
Either/Or Probability
Conditional Probability

Syllabus Details : Problem Solving and Data Analysis

Volume word problems

volumes and dimensions of three-dimensional solids
dimension changes affect volume
Volume of a cone
Impact of increasing the radius

Right triangle problems

Pythagorean theorem
Calculating missing side lengths in right triangles
Using trigonometric ratios to find side lengths
Recognizing Pythagorean triples
sine, cosine, and tangent of similar triangles
sine and cosine of complementary angles

Congruence and similarity

Finding angles in triangles
Triangles, vertical angles, and supplementary angles
Triangles and parallel lines
proportional relationships using similarity

Length, perimeter, Area, Angles, arc lengths, and trig functions

Convert between radians and degrees
Special right triangles in circles
Trigonometry using radian measures
unit circle
- $x=rcos\theta =cos\theta $
- $y=rsin\theta =sin\theta$
  $\frac{y}{x}=tan\theta$

Circle theorems

central angle, arc length, and sector area
- $\frac{central \: angle}{360^o} =\frac{arc \: length}{circumference}=\frac{sector \: area}{circle \: area}$
Circumference of a circle $C=2\pi r$
Area of a circle $A=\pi r^2$
Number of degrees of arc in a circle $360$

Circle equations

Standard form equation of a circle
In the $xy$-plane, a circle with center $(h, k)$ and radius $r$ has the equation:
- $(x-h)^2 +(y-k)^2 = r^2$
Rewriting circle equations in standard form

Complex numbers

square roots of negative numbers
complex number $z=a+ib$
add and subtract complex numbers
multiply and divide complex numbers