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More Lessons for SAT Math

More Resources for SAT

**Video Walkthroughs and solutions for the math sample questions in the Test Specification Document (pdf) from the CollegeBoard.**

**Example 1:**

If 1/2 x + 1/3 y = 4, what is the value of 3x + 2y?

**Tip:** This is a question from the Heart of Algebra. Notice the structure of the given equation and see that multiplying both sides of the equation by 6 will give us the answer 3x + 2y = 24. Video Walkthrough and solutions

**Example 2:**

4x - y = 3y + 7

x + 8y = 4

Based on the system of equations above, what is the value of the product xy?

A) 3/2

B) 1/4

C) 1/2

D) 11/9

**Tip:** This is a question from the Heart of Algebra.Since the question asks for xy, you will not be able to plug in the given answers to find the correct one. Instead, you have to make use of the methods to solve simultaneous linear equations: by substitution, by elimination.

Rearrange the equations in standard form and then use either the substitution or elimination method to solve for x and y. Video Walkthrough and solutions

**Example 3:**

The function f is defined by f(x) = 2x^{3} + 3x^{2} + cx + 8, where c is a
constant. In the xy-plane, the graph of f intersects the x-axis at the three
points (–4, 0), (1/2, 0), and (p, 0). What is the value of c?

A) –18

B) –2

C) 2

D) 10

**Tip:** This is a question from the Passport to Advanced Math. You need to understand that a point on the graph of a polynomial would also be a solution for the function or equation of the polynomial.

Choose one of the given points. (-4, 0) will be the easiest. Substitute x = -4 into the function to get 0 = 2(–4)^{3} + 3(–4)^{2} + c(–4) + 8 and solve for c. Video Walkthrough and solutions

**Example 4:**

The scatterplot above shows counts of Florida manatees, a type of sea mammal, from 1991 to 2011. Based on the line of best fit to the data shown, which of the following values is closest to the average yearly increase in the number of manatees?

A) 0.75

B) 75

C) 150

D) 750

**Tip:** You need to know that the slope of the line of best fit in this graph is the number of manatees increased per year. Video Walkthrough and solutions

**Example 5:**

A researcher places two colonies of bacteria into two petri dishes that each have area 10 square centimeters. After the initial placement of the bacteria (t = 0), the researcher measures and records the area covered by the bacteria in each dish every ten minutes. The data for each dish were fit by a smooth curve, as shown above, where each curve represents the area of a dish covered by bacteria as a function of time, in hours. Which of the following is a correct statement about the data above?

A) At time t = 0, both dishes are 100% covered by bacteria.

B) At time t = 0, bacteria covers 10% of Dish 1 and 20% of Dish 2.

C) At time t = 0, Dish 2 is covered with 50% more bacteria than Dish 1.

D) For the first hour, the area covered in Dish 2 is increasing at a higher average rate than the area covered in Dish 1.

**Tip:** You need to synthesize the information given in the graph and the question
and determine which pieces of information in the graph will help
provide you with a correct statement about the data. You will need to go through the given answers and check with the information on the graph. Video Walkthrough and solutions

**Example 6:**
(This is a student-produced response question. You will need to grid in your own answer.)

An international bank issues its Traveler credit cards worldwide. When a customer makes a purchase using a Traveler card in a currency different from the customer’s home currency, the bank converts the purchase price at the daily foreign exchange rate and then charges a 4% fee on the converted cost.

Sara lives in the United States, but is on vacation in India. She used her Traveler card for a purchase that cost 602 rupees (Indian currency). The bank posted a charge of $9.88 to her account that included the 4% fee.

Part 1

What foreign exchange rate, in Indian rupees per one U.S. dollar, did the bank use for Sara’s charge? Round your answer to the nearest whole number.

Part 2

A bank in India sells a prepaid credit card worth 7,500 rupees. Sara can buy the prepaid card using dollars at the daily exchange rate with no fee, but she will lose any money left unspent on the prepaid card. What is the least number of the 7,500 rupees on the prepaid card Sara must spend for the prepaid card to be cheaper than charging all her purchases on the Traveler card? Round your answer to the nearest whole number of rupees.

**Tip:** This is a difficult question. You need to read the question properly. Write down the important information and with the help of some diagrams figure out how you would get to the required solution from the given information. Video Walkthrough and solutions

**Example 7:** (This is an example of a question from the no-calculator portion)

What is one possible solution to the equation 24/(x + 1) - 12/(x - 1) = 1?

**Tip:** Look at the structure of the expressions. Multiply both sides of the equation by a common denominator. Factorize the quadratic equation. Solve for x and check your answers with the original equation. Video Walkthrough and solutions

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for SAT Math

More Resources for SAT

If 1/2 x + 1/3 y = 4, what is the value of 3x + 2y?

4x - y = 3y + 7

x + 8y = 4

Based on the system of equations above, what is the value of the product xy?

A) 3/2

B) 1/4

C) 1/2

D) 11/9

Rearrange the equations in standard form and then use either the substitution or elimination method to solve for x and y. Video Walkthrough and solutions

The function f is defined by f(x) = 2x

A) –18

B) –2

C) 2

D) 10

Choose one of the given points. (-4, 0) will be the easiest. Substitute x = -4 into the function to get 0 = 2(–4)

The scatterplot above shows counts of Florida manatees, a type of sea mammal, from 1991 to 2011. Based on the line of best fit to the data shown, which of the following values is closest to the average yearly increase in the number of manatees?

A) 0.75

B) 75

C) 150

D) 750

A researcher places two colonies of bacteria into two petri dishes that each have area 10 square centimeters. After the initial placement of the bacteria (t = 0), the researcher measures and records the area covered by the bacteria in each dish every ten minutes. The data for each dish were fit by a smooth curve, as shown above, where each curve represents the area of a dish covered by bacteria as a function of time, in hours. Which of the following is a correct statement about the data above?

A) At time t = 0, both dishes are 100% covered by bacteria.

B) At time t = 0, bacteria covers 10% of Dish 1 and 20% of Dish 2.

C) At time t = 0, Dish 2 is covered with 50% more bacteria than Dish 1.

D) For the first hour, the area covered in Dish 2 is increasing at a higher average rate than the area covered in Dish 1.

An international bank issues its Traveler credit cards worldwide. When a customer makes a purchase using a Traveler card in a currency different from the customer’s home currency, the bank converts the purchase price at the daily foreign exchange rate and then charges a 4% fee on the converted cost.

Sara lives in the United States, but is on vacation in India. She used her Traveler card for a purchase that cost 602 rupees (Indian currency). The bank posted a charge of $9.88 to her account that included the 4% fee.

Part 1

What foreign exchange rate, in Indian rupees per one U.S. dollar, did the bank use for Sara’s charge? Round your answer to the nearest whole number.

Part 2

A bank in India sells a prepaid credit card worth 7,500 rupees. Sara can buy the prepaid card using dollars at the daily exchange rate with no fee, but she will lose any money left unspent on the prepaid card. What is the least number of the 7,500 rupees on the prepaid card Sara must spend for the prepaid card to be cheaper than charging all her purchases on the Traveler card? Round your answer to the nearest whole number of rupees.

What is one possible solution to the equation 24/(x + 1) - 12/(x - 1) = 1?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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