SAT Section 1 - Group 5

20 Questions | By Mmmaxwell | Last updated: Oct 9, 2017 | Total Attempts: 349

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We’ve made it to the fifth group of our first section of mathematical quizzes in our ongoing SAT series, and in this instalment we’ll be looking at algebra, with reference to integers, averages, geometry, fractions and degrees.

Questions and Answers

1.

When 70,000 is written as 7.0 x 10ⁿ , what is the value of n ?
- A.
  
  1
- B.
  
  2
- C.
  
  3
- D.
  
  4
- E.
  
  5
2.

On a car trip Sam drove m miles, Kara drove twice as many miles as Sam, and Darin drove 20 fewer miles than Kara. In terms of m, how many miles did Darin drive?
- A.
  
  2m + 20
- B.
  
  2m - 20
- C.
  
  (m/2) + 20
- D.
  
  (m + 20) / 2
- E.
  
  (m-2) - 20
3.

If x and y are positive integers, what are all the solutions (x, y) of the equation 3x + 2y = 11 ?
- A.
  
  (1, 4) only
- B.
  
  (3, 1) only
- C.
  
  (1, 4) and (2, 2)
- D.
  
  (1, 4) and (3, 1)
- E.
  
  (2, 2) and (3, 1)
4.

A company’s profit, P, in dollars, for producing x machines in one day is given by P = 500x - 20x². If the company produces 10 machines in one day, then, according to this formula, what is the profit for that day?
- A.
  
  $5,000
- B.
  
  $4,000
- C.
  
  $3,000
- D.
  
  $2,000
- E.
  
  $1,000
5.

12 - n, 12, 12 + nWhat is the average (arithmetic mean) of the 3 quantities in the list above?
- A.
  
  4
- B.
  
  12
- C.
  
  18
- D.
  
  4 + (n/3)
- E.
  
  12 + (n/3)
6.

In isosceles triangle ABC above, AM and CM are the angle bisectors of angle BAC and angle BCA. What is the measure of angle AMC ?
- A.
  
  110 degrees
- B.
  
  115 degrees
- C.
  
  120 degrees
- D.
  
  125 degrees
- E.
  
  130 degrees
7.

A fruit salad is made from pineapples, pears, and peaches mixed in the ratio of 2 to 3 to 5, respectively, by weight. What fraction of the mixture by weight is pineapple?
- A.
  
  1/5
- B.
  
  3/10
- C.
  
  2/5
- D.
  
  1/2
- E.
  
  2/3
8.

In the figure above, square RSTU is inscribed in the circle. What is the degree measure of arc ST ?
- A.
  
  45 degrees
- B.
  
  60 degrees
- C.
  
  90 degrees
- D.
  
  120 degrees
- E.
  
  180 degrees
9.

If P and Q are two sets of numbers, and if every number in P is also in Q, which of the following CANNOT be true?
- A.
  
  4 is in both P and Q.
- B.
  
  5 is in neither P nor Q.
- C.
  
  6 is in P, but not in Q.
- D.
  
  7 is in Q, but not in P.
- E.
  
  If 8 is not in Q, then 8 is not in P.
10.

What is the maximum number of rectangular blocks measuring 3 inches by 2 inches by 1 inch that can be packed into a cube-shaped box whose interior measures 6 inches on an edge?
- A.
  
  24
- B.
  
  28
- C.
  
  30
- D.
  
  36
- E.
  
  40
11.

If a ≠ 0 and (5/x) = (5 + a)/(x + a), what is the value of x?
- A.
  
  -5
- B.
  
  -1
- C.
  
  1
- D.
  
  2
- E.
  
  5
12.

The figure above is composed of 25 small triangles that are congruent and equilateral. If the area of DFH is 10, what is the area of AFK ?
- A.
  
  40
- B.
  
  42.5
- C.
  
  50
- D.
  
  52.5
- E.
  
  62.5
13.

3x +2y+ 2z = 193x +y +z = 1413. If the equations above are true, which of the followingis the value of y+z? �=+ z ?
- A.
  
  -5
- B.
  
  -4
- C.
  
  0
- D.
  
  4
- E.
  
  5
14.

A boat costs x dollars, and this cost is to be shared equally by a group of people. In terms of x, how many dollars less will each person contribute if there are 4 people in the group instead of 3 ?
- A.
  
  X/12
- B.
  
  X/4
- C.
  
  X/3
- D.
  
  (7x)/12
- E.
  
  7x
15.

If y = 2x+3 and x < 2, which of the followingrepresents all the possible values for y ?
- A.
  
  Y < 7
- B.
  
  Y > 7
- C.
  
  Y < 5
- D.
  
  Y > 5
- E.
  
  5 < y < 7
16.

The graphs of the functions f and g in the interval from x = -2 to x = 2 are shown above.Which of the following could express g in terms of f ?
- A.
  
  G (x) = f (x +1)
- B.
  
  G (x) = f(x) + 1
- C.
  
  G (x) = f(x+1) + 1
- D.
  
  G (x) = f(x - 1)
- E.
  
  G (x) = f(x) - 1
17.

In the figure above, a shaded polygon which has equal sides and equal angles is partially covered with a sheet of blank paper. If x + y = 80, how many sides doesthe polygon have?

Discuss
- A.
  
  Ten
- B.
  
  Nine
- C.
  
  Eight
- D.
  
  Seven
- E.
  
  Six
18.

If s, t, u, and v are the coordinates of the indicated points on the number line above, which of the following is greatest?
- A.
  
  |s+t|
- B.
  
  |s+v|
- C.
  
  |s-t|
- D.
  
  |s-v|
- E.
  
  |s+u|
19.

On the day of a rainstorm, the depth of the water at a certain location along the Winding River was recorded hourly, and the results are indicated in the line graph above. Each unit on the vertical axis represents 1 foot. If the depth of the water decreased 10 percent from3:00 P.M. to 4:00 P.M., what was the depth of the water at 4:00 P.M.?
- A.
  
  3 feet
- B.
  
  15 feet
- C.
  
  18 feet
- D.
  
  20 feet
- E.
  
  30 feet
20.
- A.
  
  I only
- B.
  
  II only
- C.
  
  III only
- D.
  
  I and II only
- E.
  
  I, II, and III