Sample SAT Math Questions

The math section of the SAT test is a mix of hard and easy questions. Some major topics of the math section of the tests are:

• Heart of algebra
• Problem-solving and data analysis
• Passport to advanced math

Heart of Algebra

The majority of the math questions come from the topic of Heart of Algebra. 19 questions come under the various topics covered by Heart of Algebra. It includes topics like

• Linear Equations and Expressions
• Linear Inequalities
• Systems of Linear Equations and Inequalities
• Interpreting Linear Functions
• Direct and Inverse Variation
• Arithmetic with Linear Expressions
• Slope and Rate of Change

Examples:

Linear Equations: Regular tees are available for $15 apiece and deluxe shirts are available for $25 each in a store. The shop made $1,600 last Saturday after selling 80 shirts in total. How many plain shirts were sold in total?

• A) 20 basic shirts
• B) 40 standard shirts
• C) 50 standard shirts
• D) 70 standard shirts

Answer:

Let's fix this issue using a set of equations. Let P stand for the sale of premium shirts, and R for the sale of regular shirts.

R + P = 80 (because 80 shirts were sold in total).

Given that the revenue from ordinary shirts at $15 apiece and premium shirts at $25 each is $1600, 15R + 25P = 1600.

The first equation, R + P = 80, can be used to express one variable in terms of the other. Let's figure out P: P = 80 - R.

Now, change P in the second equation to the following expression:

15R + 25(80 - R) = 1600

Now, condense and find R's solution:

15R + 2000 - 25R = 1600

combining similar terms

-10R + 2000 = 1600

2000 from both sides subtracted:

-10R = 1600 - 2000 -10R = -400

To find R, divide by -10 now: R = -400 / -10 R = 40

40 standard shirts were sold.

1. B) 40 ordinary shirts is the right response.

Explanation: This issue can be resolved by constructing an equation system depending on the quantity of shirts sold and the total amount of money made. We can solve for the value of the variable (in this case, the number of regular shirts sold) by expressing one variable in terms of the other using the equations. We can determine that 40 ordinary shirts were sold using this technique.

Linear Inequalities: To rent a car, Emily must follow the equation C = 40d 50, where C stands for the cost in dollars and d is the number of days. Emily has a maximum budget of $300 allocated for the car rental. How many days, d, can she rent the car for? Which inequality below accurately describes the situation?

 50 ≤ 40d in the range of 300.

 700 must be less than or equal to 40d 50.

50. C) 200 is greater than or equal to the difference between 40 times p and 50.
51. D) ≥ 340 is the solution for 40p – 50 when solving for p.

 Answer: 

By taking the given equation of 40d + 50 for the cost of car rental, Emily's maximum spending limit of $300 can be represented using an inequality.

 We can say that Emily's spending limit is $300, knowing that.

 300 is the limit of C.

 The equation in C can now be altered to the following expression:

 ≤ 300, 40d 50 - rearranged

 The 40d word can be found by subtracting 50 from both sides, as per the equation.

 -50+300 is greater than or equal to 40p.

 250 is the maximum value for 40p.

 To calculate d, divide 250 by 40 to get the answer. Keep in mind that d has to be less than or equal to 6.25.

Rounding down to the nearest whole number is necessary when renting a car since fractional rental times are impossible. This means that the number of days, represented by d, must be a whole number.

 6 ≥ d

Inequality correct, the declared:

is so

300 is greater than or equal to 40d 50.

Explanation: 

By basing an inequality on the equation for rental car costs, we were able to resolve the issue. Emily's budget limit of $300 was reflected by the difference C of 300. After inserting the equation into formula C and stabilizing the inequality, we calculated the value of d. Answer A was correct, due to the rounding down to the nearest whole number requirement since the number of rental days has to be a whole number. Emily will be able to stay within her $300 budget by renting a car for six days at most.

Systems of Linear Equations and Inequalities: Pigs and chickens are the two animal species that a farmer raises on her farm. There are 60 animals in all on the farm, and there are 180 legs altogether. Pigs have four legs while chickens have two. How many pigs and chickens does the farmer own?

1. A) 30 chickens and 30 pigs
2. B) 50 chickens and 80 pigs
3. C) 10 chickens and 40 pigs
4. D) 55 chickens and 25 pigs

Answer:

Let's fix this issue using a set of equations. Let P stand for the number of pigs and C for the number of chickens.

The following details are available to us:

Given that there are 60 animals total on the farm, C plus P equals 60.

Due to chickens having two legs apiece and pigs having four legs each, there are a total of 180 legs on the farm.

These equations allow us to find the values of C and P.

First, let's make equation (2) easier to work with by multiplying both sides by 2:

C + 2P = 90

Let's now translate C into P using equation (1):

C = 60 - P

Now, enter the following expression in place of C in the abbreviated equation (C + 2P = 90):

(60 - P) + 2P = 90

Now, condense and find P:

60 - P + 2P = 90 P + 60 = 90

60 is deducted from both sides:

P = 90 - 60 P = 30

After determining the value of P (number of pigs), we can use equation (1) to determine C (number of chickens):

C + 30 = 60 C = 60 - 30 C = 30

The farmer therefore keeps 30 pigs and 30 poultry.

The right response is A) 30 pigs and 30 chickens.

Explanation:

Depending on the number of legs and the production animals, we devised a set of equations as a solution. The equations were manipulated to determine a value for either C or P. With these calculations, it was determined that the farmer had 30 chickens and 30 pigs on the property, aligning with the total number of animals and number of feet.

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Problem Solving & Data Analysis

Your problem-solving abilities are tested in this section of the SAT math exam. It includes various topics like:

• Ratio
• Percentages
• Data Interpretation
• Probability
• Descriptive Statistics

Examples

Ratio: For this fruit salad recipe, you'll need 2 parts apples, 3 parts oranges, and 4 parts grapes. If you want to make a fruit salad with a total of 45, how many oranges should you use?

1. A) 9 parts oranges
2. B) 15 servings of oranges
3. C) 28 parts oranges
4. D) 20 servings of oranges

 Answer:

You must first determine the proportion of oranges to the total portions before you can use that proportion to calculate the total portions of oranges used in the 45 servings of fruit salad.

The ratio of oranges to total ingredients in the recipe is 3 parts oranges 2 3 4 = 9 ingredients total (2 parts apple, 3 parts orange, 4 parts grape).

Now you can determine the proportions to determine the number of 45 parts of oranges:

3 oranges) divided by 9 is equal to (x oranges) divided by 45.

Multiply 3*45 by 9*x135 to get 9x. Divide 135 by 9 to get 15 and get x: x = 135/9

 So, out of a total of 45 servings of fruit salad, you should use 15 servings of oranges.

1. B) 15 servings of oranges is the correct answer.

Explanation: 

To determine how many orange slices to use in a fruit salad, first determine how many orange slices are on the plate. Then determine the ratio and determine how many oranges are in the 45 servings. After solving that part, you decide you need 15 servings of oranges (choice B).

Percentages: You can save 25% off the list price by purchasing the jacket in store, with an additional 20% off during the sale. If the purchase price is $80, and taking into account both discounts, what is the final retail price of this jacket?

1. A) $48
2. B) $50
3. C) $64
4. D) $74

Answer:

Taking these two discounts into consideration, we can take the following steps to determine the final selling price of the jacket:

Calculate the first discount, which is 25% of the starting price of $80:

First-time discount: 0.25 times $80 ($80 x 25%) equals $20.

To get the price after the first markdown, subtract the original price from it.

The price after the first discount is $80-$20 or $60.

After the first discount, 20% of the price will be deducted to obtain the second discount.

Second discount = 20% of $60 = 0.20 times $60 or $12.

To determine the final selling price, subtract the second discount from the original price.

The final retail price is $60 minus $12, or $48.

Therefore, after applying both discounts, the total retail price of this jacket is $48.

The correct answer is A) $48.

Explanation:

To solve this issue, we first need to find out the discount. The first discount is 25%, and then we need to find the price after the discount. We can do this by subtracting 25% from the original cost. Then, we need to calculate the second discount. The second discount is 20%, and the final selling price is $48, (choice A). So, we need to subtract the 2nd discount after the 1st discount from the $48 price.

Probability: In the lottery, there are ten balls numbered from 1 to 10. As a player, you need to choose five balls without changing your selection. To win you must select the five balls with the numbers (6 10). Now let's calculate the likelihood of winning the lottery.  

1. A) 1/252 
2. B) 1/126 
3. C) 1/210 
4. D) 1/2520 

Answer: 

To estimate this probability we need to determine how ways there are to select the five numbered balls out of all ten. We can use a combination formula for this calculation. There are a total of 10 balls. We want to choose 5 of them;

C(10, 5) = 10! / [5!(10 5)!] = (109876) / (54321) = 252

So there are 252 ways to select the five highest numbered balls from all ten available options.

Now that we know this information lets calculate the probability of winning. Since you have to pick all five balls in order to win, C(5, 5) equals one possibility. Therefore the probability is calculated as; 

Probability = (number of chances to win) / (total number of outcomes

So in this case the odds are determined as being 1, in every 252 attempts.

Explanation: 

To determine the number of options, for selecting the five balls containing numbers ranging from 6 to 10 we initially utilized a combination formula. This allowed us to calculate the ways in which five balls can be chosen out of a pool of ten. By dividing the number of outcomes by the number of potential results we obtained a winning probability of 1/252 (variant A) in the lottery.

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Passport to Advanced Math

The "Passport to Advanced Math" category assesses your ability to work with more advanced mathematical concepts, including algebraic expressions, equations, functions, and more. Here are some of the specific topics that fall under the "Passport to Advanced Math" category on the SAT:

• Algebraic Expressions and Equations
• Radicals and Exponents
• Functions
• Rational Expressions
• Operations with polynomial
• Rewriting expressions
• Quadratic function
• Quadratic equation
• Trigonometry

Examples:

Operations with polynomial: What is the degree of the polynomial 2x^3y^2 - 4xy^3 7x^2 - 9y? 

 Choices: 

1. A) 3 
2. B) 6 
3. C) 8 
4. D) 5 

 Answer: B) 6 

Explanation: 

The degree of the polynomial is equal to the largest power of the polynomial's variables. This polynomial contains: 

 2x3y2, 4xy3, 7x2, and 9x 

You must locate the term with the biggest combined exponent of x and y to calculate the degree of a polynomial. 

The maximum degree of x is indicated by the phrase 2x3y2, while the highest degree of y is shown by the word -4xy3. The exponents of the variables in the highest degree term are added to get the degree of a polynomial with two variables. In order to calculate the degree, you mix the two highest powers. Polynomial 3 has a degree of 3, which equals 6.

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Conclusion

To succeed on the SAT math exam, you must have a solid understanding of these topics and rehearse answering problems related to each one. Knowing the format and content of the SAT math questions can help you perform at your peak on test day.