Question Explanations For

SAT Practice Test 1 (Math Test: No Calculator Section)

1.

The Correct Answer is (C) — When we subtract -3 + 3x from 4 - x, we get .

2.

The Correct Answer is (C) — If there is a 1 in 12 probability that a dime is selected from this bag, it means that 1/12 of the coins must be dimes. To find the number of dimes, we multiply 1/12 by the total number of coins giving us 1/12 × 132 = 11.

3.

The Correct Answer is (D) — We can first notice that this function is not a quadratic function, meaning that we can eliminate answer choice C. Because k is a positive integer, we know that the slope of the line must be positive, allowing us to eliminate choice B. Finally, we know that the line passes through the origin because point (0, 0) satisfies the equation. D is the correct answer.

4.

The Correct Answer is (C) — We can first multiply the ratio of y to z by 5, giving us 5:10. Because x to y is 4:5 and y to z is 5:10, we can conclude that x to z is 4:10. We can then simplify this ratio by dividing by 2, giving us 2:5.

5.

The Correct Answer is (A) — Let’s first consider the monthly charge. We can multiply 100 by m to find the amount of money charged for the monthly fee. However, we must multiply this term by 1.05 to account for the 5% tax. This gives us the term 1.05(100m). We can then add the flat fee of $1000 giving us 1.05(100m)+1000.

6.

The Correct Answer is (C) — Squaring each side of the second equation gives us . We can then plug in into the top equation giving us . We can then solve for , which equals 5.

7.

The Correct Answer is (D) — We can tell from the graph that the x-intercepts are -2 and 2. So p must be -2 × 2 = -4. Then we can plug in this p to get -4/6 = -2/3.

8.

The Correct Answer is (B) — Units on both sides of an equation must be the same. We know the right side has units of number of pies, so the left side must also be in number of pies. This allows us to eliminate answer choices A and D. Since we are told that Daphne eats 3 times more than Velma, we can conclude that the 3/x term represents the number of pies eaten by Daphne. The correct answer is B.

9.

The Correct Answer is (B) — First, multiply all parts of the inequality by -2, making sure to remember to flip the inequality signs. Doing this we get, 10/3 > 4x + 2 > -2/5 so 4x + 2 must be greater than -2/5 but smaller than 10/3. 0 fits this criteria, giving us answer choice B.

10.

The Correct Answer is (C) — We can find the area of the shaded region by subtracting the area of Circle A from the area of Circle O. The area of Circle O is π = 81π. Line AB which is the radius of Circle A, is a third of the length of line OC so line AB = 3. We can then find the area of Circle A which is π = 9π. Subtracting Circle A from Circle B, we get 81π - 9π = 72π. The question asks for the answer in terms of π, so the answer is C.

11.

The Correct Answer is (A) — When we multiply the first equation by 4 we get x - 2y = 16. We need to find a value for a which makes ax - 2y = 16 equal to x - 2y = 16. The only value that fits this criteria is 1. If we use a=1 and subtract the second equation from the first, we get 0 = 0, which means the system of equations has an infinite number of solutions.

12.

The Correct Answer is (D) — Since Fred’s motorcycle can run for 1 hour on 1 gallon of gas, we can use t, the number of hours, to also represent the number of gallons he uses. We subtract this value from the initial amount of gas to get

13.

The Correct Answer is (B) — First, subtract from each side to get . We can factor out a 2 from the numerator of the left side of the equation to get .

Using difference of squares, we can further the numerator into . Cancelling x-1 from the top and bottom we get 2(x+1) = A which is equal to 2x + 2 = A.

14.

The Correct Answer is (C) — When we draw the line QT, we can see that triangle QRT is a right triangle. From the Pythagorean Theorem we know that which means that . The hypotenuse, QT, is the radius of the circle, or 1. We are given the length of RT. We can plug in these values to get . Taking the square root of each side gives us . We can simply multiply this by 2 to get the full length of QS giving us .

15.

The Correct Answer is (B) — Adding π to a given angle simply reflects it across the y-axis. This would mean that for any x with a non-zero cosine, the cosine of x will simply switch signs. The interval 0 < x < π/2 excludes any value for x which would have a cosine of zero, so the correct answer is B: cos(x+π) = - cos(x)

16.

The Correct Answer is (6) — We can first find all the factors of 48 to see all our options: [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. We can eliminate 16, 24 and 48, because using any of these values would immediately make the sum greater than 13. We also can’t use 12 because we would need the product of the other two integers to equal 4, and there is no way to do this without causing the sum to be greater than 13. Similarly, if we use 8, the only possibilities are [2, 3, 8] and [1, 6, 8] and both of these sets of numbers add to greater than 13. When we use 6, we can see that [2, 4, 6] satisfies all the conditions. The answer is 6.

17.

The Correct Answer is (5) — Any number taken to the 0th power equals 1 by definition. So .

We can then plug this x in and get .

so n = 5.

18.

The Correct Answer is (14) — Since 10 = |x-4|, x - 4 can equal 10 or -10. Solving for x - 4 = 10 and x - 4 = -10, we find that x = 14 or -6. 14 is the greater of these two values, so the answer is 14.

19.

The Correct Answer is (6) — From the information given, we can see that triangle BEF is a 45-45-90 triangle. From the properties of a 45-45-90 triangle, we know that line BE and line EF both have lengths of 1. From this information, we know that line AD and line CF also have lengths of 1. Since 2 x BE = DF, DF = 2, which means that AC = 2. Adding up all the sides of the rectangle ACFD we get 1 + 1 + 2 + 2 = 6.

20.

The Correct Answer is (120) — We can first consider all the ways that we can manipulate so that it will look like 5x + 4y. One way to do this is to multiply the whole equation by 20 giving us,. So the answer is 120.