Question Explanations For

SAT Practice Test 1 (Math Test: Calculator Section)

1.

The Correct Answer is (B) — The average of a set of numbers can be found by adding all the numbers together and dividing by the number of students. The total number of magazines purchased by the students is 19 + 8 + 9 + 7 + 2 =45. Dividing this number by the number of students (5), we get the answer of 9.

2.

The Correct Answer is (D) — To find the difference between two numbers, we can subtract one term from the other. The two terms in this problem are p – 3 and p + 4, thus the difference is p + 4 - (p - 3) = p + 4 - p + 3 = 7.

3.

The Correct Answer is (A) — First convert the percentages into factors. Since the 12.1% was an increase, we multiply the original population (p) by 1.21. We then multiply this new population by 0.95 to find the final population. Consequently, the final population is p x 1.21 x 0.95 = 1.065p indicating that there was a 6.5% total increase in the population.

4.

The Correct Answer is (C) — The median of a set of numbers if the value of the middle term when the terms are in numerical order. In this case, 5 and 7 are both middle terms, and we must find the average of these two values to find the median. The median is 5 + 7 / 2 = 6.

5.

The Correct Answer is (C) — At the 4th month, the population of lions was around 20, while the population of zebras was around 60. 20 x 3 = 60 so (C) is the correct answer.

6.

The Correct Answer is (C) — We can immediately eliminate choice (D) because adding any number to 900 results in a sum greater than 900. Because 300 + 300 + 300 = 900 we know that 299 cannot be the answer because all three terms would be less than 300. Similarly, we know that 300 cannot be the answer as the other two terms would be less than 300. This leaves us with answer (C).

7.

The Correct Answer is (C) — Using rules for exponents, we can write as . Taking the square root of each side, we get . so the answer is y = 2.

8.

The Correct Answer is (C) — Slope is calculated by dividing the difference between the y-components by the difference of the x-components. Thus the slope is (5 - 1) / (2- ( -10/3)) = 3/4

9.

The Correct Answer is (C) — To find the answer to this problem, we can find the slope of this graph. We first estimate that the number of patients in 1984 is approximately 5000 and that the number of patients in 2011 is approximately 1500. To find the slope we calculate (1500 - 5000)/(2011 - 1984) = -121. The word "decrease" implies the negative sign and the closest answer to this number is (C)120.

10.

The Correct Answer is (B) — We first find the price of the steak before tax by (1.2kg)x($10/kg) = $12. To account for the 6% tax, we calculate ($12)x(1.06) = $12.72. Subtracting $12.72 from $15, we get change of $2.28.

11.

The Correct Answer is (C) — By using cross multiplication, we get 2x - 1 = 21x - 3. When we subtract 2x and add 3 to both sides, we get 2 = 19x. Dividing each side by 19, we get the answer of .

12.

The Correct Answer is (C) — By using points (1,0) and (0,1), we find that the slope of this line is 1. If we plug in the slope and point (1,0) into y = mx + b, we find that b = 1. We can then write the equation of the line as y = x + 1. When we double the slope of this line, we get y = 2x + 1. Plugging in 2 for x, we get y = 4 + 1 = 5.

13.

The Correct Answer is (D) — We can immediately eliminate choices (A) and (B) because adding a new value of 80 or lower cannot make the new average equal to 80. We can test the other two answers by considering a simple case. Because the original average is 70, we know that the sum of the scores of the first four tests is equal to 280. If we add 100 to 280 and divide by 5, we get 76. This is not equal to 80, so we know that (D) is the right answer.

14.

The Correct Answer is (D) — Because we are told the area of the square is 36, we know that each side of the square is 6. This also serves as the diameter for the circle, so the circle has a radius of 3. Therefore, the perimeter of the half circle is 2π(3)/2 = 3π. We are told that the perimeter of the triangle is 24. We can subtract the side it shares with the square to get 24 - 6 = 18. Finally, we add up all the sides to get 3π + 6 + 6 + 18 = 3π + 30.

15.

The Correct Answer is (C) — From the diagram, we know that we are dealing with a 30-60-90 triangle. Using the properties of the triangle, we know that the hypotenuse is twice the length of the side opposite to 30°. Twice of 7 is 14.

16.

The Correct Answer is (D) — Plug in -2 for x. Taking the absolute value of -8, we get 8 - 4 + 2 = 6.

17.

The Correct Answer is (B) — Carlos' walking pace is which means that in 1 minute, Carlos can walk miles. Multiplying this by 35 minutes we get 455 divided by x miles.

18.

The Correct Answer is (D) — For this problem, we can use the Counting Principle found in Chapter 5, Section 6.4. The order of the books matters, so we will be using a permutation. We know that there are 5 possibilities for the first book, and since we cannot have any repeats, 4 possibilities for the second book, and so on. Multiplying all the possibilities, we get 5 x 4 x 3 x 2 x 1 = 120.

19.

The Correct Answer is (A) — We first find the percentage of people who prefer corn cereal for each group by dividing the number of people who prefer corn cereal by the total number of people for that group. Doing this we get for 18 years or younger 3401/8238 = .41 or 41 %. For 19-44 year olds, we get 7325/21078 = .35 or 35 %. For the 45-64 year olds, we get 5643/18713 = .30 or 30%. The highest percentage is 41% so the answer is (A).

20.

The Correct Answer is (B) — We first need to find the portion of 45-64 year olds who like oats cereal. We can do this by dividing 3423/18713 = .183. Multiplying this by 18 million, we get 14.8 million people. 15 million is the closest to this number, so the answer is (B).

21.

The Correct Answer is (C) — We can first find the total number of megabytes that Stefan can download in 10 hours. Because there are 60 minutes in one hour and 60 seconds in one minute, we can convert 10 hours to seconds by (10 hours) x (60min/hour) x (60s/min) = 36,000s. Multiplying this value by 5.4 megabytes/s gives us the total number of megabytes Stefan can download, or (36,000s) x (5.4 megabytes) = 194,400 megabytes. To convert this number to gigabytes, we divide by 1,024: 194,400/1024 = 189.8 gigabytes. Because each film is 10.4 gigabytes, 189.8/10.4 = 18.2, which is 18 full movies.

22.

The Correct Answer is (C) — Because a quadratic function is symmetric, we know that the vertex must fall on in the middle between (-1, 1) and (3, 1). The middle value of -1 and 3 is 1. The question only asks for the value of j, which is the x-component of the vertex, so we know the answer is (C).

23.

The Correct Answer is (B) — This problem is asking us to find the union of two probabilities. When we multiply the chance of rain in Boston by the chance of rain in London, we get (0.33) x (0.62) = 0.20, or 20%.

24.

The Correct Answer is (A) — We find the range of a set of numbers by subtracting the lowest value from the highest value. The range for List 1 is 118 - (-a) = 118 + a. The range for List 2 is 76 - a. When we subtract the range of List 2 from the range of List 1, we get 118 + a - (76 - a) = 118 + a - 76 + a = 2a + 42.

25.

The Correct Answer is (B) — We first recognize that this a 45-45-90 triangle. Because ED is 2, then by the properties of a 45-45-90 triangle, DG and DF must also be 2. We then use the formula for finding the area of triangles by (2 x 4)/2 = 4.

26.

The Correct Answer is (B) — We can use factoring for this problem. Because points (-4, 0) and (c, 0) both have 0 as the value of y, we know that these points must be the zeros of the equation. By factoring a difference of squares, we get that ,which means that the zeros of the equation must be x = 4 and x = -4. We are already given -4, so the answer must be (B).

27.

The Correct Answer is (C) — In Chapter 5, Section 5.1, we learned that the terms of the factors of a polynomial must meet certain criteria. In this case, we know that the last term of each factor must multiply to equal -64. Answers (C) and (D) are the only options where this is possible. We also know that the first terms must multiply to give us . Answer (C) is the only option where this is possible.

28.

The Correct Answer is (C) — We first find the full equation for f(x) by plugging in the point (0,6) which gives us 6 = 0x + c. Therefore, c = 6, so f(x) = 3x + 6. We first find the value of f(11) by 3(11) + 6 = 39, plugging in 39 into g(x), we get -7(39) - 13 = -273 - 13 = -286.

29.

The Correct Answer is (C) — As we learned in section 6.2, the standard deviation of a data set measures the amount of variance in the data. A higher standard deviation means more variance. List A has a higher standard deviation, meaning that it has more variance than List B. The answer is (C).

30.

The Correct Answer is (C) — A system of equations has infinite solutions if you end up with an equation that is true on both sides and has no variables, such as 1=1. If we multiply the first equation by 3, we get 36x + 45y = 318. If we then subtract the second equation from this new equation, we get 0x + 0y = 0 = 318 - 6z. For this equation to be true all the time, 318 - z must also equal zero. Solving for 318 - 6z = 0, we get z = 53.

31.

The Correct Answer is (8) — We can set up the equation as follows: 3x/4 = 6. Solving for x, we get x=8.

32.

The Correct Answer is (4425) — We first convert the 50kg to g by 50kg(1000g/kg) = 50,000g. Because density is equal to mass/volume, we can get the volume by dividing the mass by the density. Doing this we get 50,000g/11.3 = 4424.8 . Rounding to the nearest gives us 4425 .

33.

The Correct Answer is (5/3&lt;x&lt;9/4) — To solve for x, begin by subtracting 6 from all parts of the inequality. -3 - 6 < -4x + 6 -6 < -2/3 - 6, so -9 < -4x < -20/3. Divide all parts of the inequality by -4 to solve for x, and remember to flip the inequality signs because you are dividing by a negative number. 5/3 < x < 9/4 is your answer.

34.

The Correct Answer is (400) — We know that the circumference of a circle is equal to 2πr. If we set this equal to 20π, we find that r = 10. The hypotenuse of the triangle is the diameter of the circle, which is 2r = 20. Using , we know that .

35.

The Correct Answer is (8, 16) — There are two possible solutions for this equation. First, solve for x - 12 = 4 by adding 12 to each sides of the equation. x=16 is one of the possible answers. Since, this is originally an absolute value equation x=8 is the other possible answer because |8-12| = |-4| = 4.

36.

The Correct Answer is (13.5) — We know t = 1.5. When we add x = and y = t - 1 we get x + y = + 5 + 1.5 -1 = 13.5.

37.

The Correct Answer is (13) — We are told that credit card charge of $18.62 includes the 3% conversion fee. This means that before the fee, the charge was 18.62/1.03 = 18.08. We can then set up the equation 235 x (conversion rate) = 18.08. Solving for the conversion rate, we get 0.077. However, this is in the form dollars/peso. Since we want peso/dollar, we take the reciprocal and get 1/0.077 = 13.

38.

The Correct Answer is (5) — Converting $100 to pesos at 13 pesos/dollar gives us 100(13) = 1300 pesos. However, 2.5% of this is taken as a conversion charge, so the actual amount Monique receives is 1300 - 1300(0.025) = 1267.5 pesos. When she converts this back into US dollars at the rate of 13 pesos/dollar, we gets back (1267.5 pesos) X (dollar/13 pesos) = 97.5 dollars. However, once again 2.5% is taken away as a fee so the actual amount Monique receives is 97.5 - (97.5)(0.025)= 95 dollars. The question asks how much money Monique loses in total over the transaction so the answer is 100 - 95 = 5 dollars.