The Math Test of the SAT is compromised of 58 questions broken into two sections one is non-calculator with 20 questions (25 minutes) and the second is calculator with 38 questions (55 minutes). These 2 sections are designed to assess students’ ability to solve real world problems in the following four key areas:
The Heart of Algebra
Problem Solving and Data Analysis
Passport to Advanced Mathematics
Additional Topics in Mathematics.
The test is mostly multiple-choice; students may select from four possible choices. Correct answers award one-point and incorrect answers or leaving a question blank will neither award nor deduct points.
There are free response questions at the ends of both sections- five non-calculator questions and eight calculator questions.
Students should take their time on easy questions to earn as many points as possible. If students are unsure of an answer the best course of action is to keep moving forward and return to the problem later if time allows them to do so.
Here is an example SAT question:
How many solutions are there to the system of equations above?
A) There are exactly 4 solutions. 4个
B) There are exactly 2 solutions. 2个
C) There is exactly 1 solution. 1个
D) There are no solutions. 没有答案
There are many ways to solve systems of equations, we will use a method called substitution as it is effective in almost all cases. This method is fast and effective and we can do it without a calculator.
To solve this system of equations, we must first rearrange the second equation into a form where y is the subject of the equation.
We have done this by adding 5x to both sides of the equation and taking away 8 from both sides of the equation.
We can then replace y in our first equation with the new expression we have just found.
From here, we will rearrange the equation into a clearer form. We do this by taking 5x away and adding 8 to both sides of the equation.
We will then use factorisation to allow us to solve the equation. We are looking for numbers which multiply together to make +1 and they must also add together to make -2. The only numbers which satisfy these two conditions are -1 and -1.
From here we can solve the equation by setting each individual bracket equal to zero.
As you can see, these are the same.
We can then see that the equation will only have one solution. And by solving the equation we can see the solution will be: