2014-01-01 15:43 三立在线
SAT考试数学练习题第五套 SAT problem solving practice test 5
1. Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $324 per week. How much does she earn in dollars per hour?
2. ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal. What is the perimeter of the parallelogram?
3. If the product of 6 integers is negative, at most how many of the integers can be negative?
4. If a positive integer n, divided by 5 has a remainder 2, which of the following must be true?
I n is odd
II n + 1 cannot be a prime number
III (n + 2) divided by 7 has remainder 2
B. I only
C. I and II only
D. II and III only
E. I, II and III
5. A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?
6. Line l contains the points (3,1) and (4,4).
If line m is a different line, parallel to line l in the same coordinate plane, which of the following could be the equation of line m?
A. y = 3x - 8
B. y = 1/3x - 3
C. y = -3x - 8
D. y = 3x + 1
E. y = -8x + 3
7. In the figure above the square has two sides which are tangent to the circle. If the area of the circle is 4a2π, what is the area of the square?
8. A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
9. A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles?
10. Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?
A. 1 litre paint
B. 1 litre water
C. litre water and one litre paint
D. litre paint and one litre water
E. litre paint
1.Correct Answer: C
Total hours worked = 8 x 3 + 6 x 2 = 36
Total earned = 324. Hourly wage = 324 / 36 = 9
2.Correct Answer: D
Since the angles of BCD are all equal, it is an equilateral triangle. Therefore. Since one side is 2, BD and CD are also 2. These sides (totaling 4 units) represent half the perimeter of the parallelogram. Total perimeter = 8.
3.Correct Answer: D
Multiplying two negatives (or any even multiple) results in a positive. But multiplying three negatives (or any odd multiple) gives a negative. If the result of multiplying 6 negatives is odd, the largest number of negative integers will be the largest odd number (i.e.5)
4.Correct Answer: A
You can find the integers which when divided by 5 have a remainder 2 by adding 2 to all multiples of 5. So we have n = 9 , 12, 17, 22 etc.
From this series we can see that n does not have to be odd.
Also n + 1 can be a prime because, for example, 12 + 1 = 13
And (n + 2) / 7 has a remainder 2 in some cases but not all.
Remember the question asks us for what MUST be true, and we see that none of the statements are true in all cases.
5.Correct Answer: C
When the larger cube is cut into smaller cubes, the corner cubes will have paint on three sides. The cubes in the middle of the faces will have paint on only one side, but the cubes cut from the edges will have paint on two sides. In this case, there will be only one cube one each edge (excluding the corners), and since there are 12 edges, there will be 12 cubes with paint on two sides. (Drawing a diagram will make this much clearer.)
6.Correct Answer: D
Slope of the line l = (4 – 1) / (4 – 3) = 3/1 = 3
Parallel lines have the same slope. In the equation of a straight line, y = mx + c, m represents the slope, so we are looking for an equation where m = 3
But both answer choices A and D have slope 3.
Now we calculate the intercept, c, for line l. Using the coordinate of one of the points on l, we get: 4 = (3 x 4) + c ; 4 – 12 = c; c = -8
Hence, answer A is the equation of line l, and answer D must be the equation of a parallel line.
7.Correct Answer: D
If the area of the circle is 4a2π , the radius will be the square root of 4a2 (i.e. 2a)
The diameter will be 4a. The diameter is also the side of the square. Area of the square is (4a)2 = 16a2
8.Correct Answer: C
The measure of the third side of a triangle must lie between the sum and the difference of the other two sides. Using this fact along with the answer choices, we can eliminate the wrong answers.
(A) cannot be right because 2 would not be the longest side.
(B) cannot be right because again it would not be the longest side
(C) could be right because the other two sides would be 3 and 4.
(D) and (E) cannot be right because this third side would be greater than the sum of the other two sides.
9.Correct Answer: B
Substitute sensible numbers and work out the problem. Then change the numbers back to letters. For example if the machine puts 6 caps on bottles in 2 minutes, it will put 6 /2 caps on per minute, or (6 /2) x 60 caps per hour. Putting letters back this is 60c/m.If you divide the required number of caps (b) by the caps per hour you will get time taken in hours. This gives bm/60c (Remember dividing by a fraction is the same as multiplying by its inverse.)
10.Correct Answer: A
At the moment the paint is 3 liters of paint and 3 liters of water. We need to add to this to make the new ratio 2 liters paint to 1.5 liters water. As this is equivalent to 4 : 3 we can see that we have the right amount of water, and just need 1 liter of paint to make it correct.