ACT考试数学样题(1)

ACT考试数学样题（1）

DIRECTIONS:Solve each problem, choose t

he correct answer, and then fill in the corresNote: Unless otherwise stated, all of the follponding oval on your answer document. owing should be assumed. Do not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test.

You are permitted to use a calculator on this test. You may use your calculator for any problems you choose, but some of the prob lems may best be done without using a calculator. 1.

A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?

A.$ 44.44 B.$109.08 C.$118.80 D.$408.04 E.$444.40

??Illustrative figures are NOT necessarily drawn to scale.

??Geometric figures lie in a plane.

??The word line indicates a straight line. ??The word average indicates arithmetic mean.

2.

When x = 3 and y = 5, by how much does the value of 3x2 – 2y exceed the value of 2x2 – 3y ? F. 4 G.14 H.16 J.20 K.50

3.

What is the value of x when 2x + 3 = 3x – 4 ? A. –7 B.

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C. 1 D.

E. 7 4.

What is the greatest common factor of 42, 126, and 210 ? F. 2 G. 6 H.14 J.21 K.42

5.

Sales for a business were 3 million dollars more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were 38 million dollars, what were sales, in millions of dollars, for the first year? A.16 B.17.5 C.20.5 D.22 E.35

6.

In the figure below, ray was constructed starting from rays and . By using a compass, D and G were marked equidistant from E on rays and . The compass was then used to locate a point F, distinct from E, so that F is equidistant from D and G. For all constructions defined by the above steps, the measures of DEF and GEF:

F.are equal. G.are NOT equal. H.sum to 30°. J.sum to 45°. K.sum to 60°.

7.

Abandoned mines frequently fill with water. Before an abandoned mine can be reopened, the water must be pumped out. The size of pump required depends on the dept

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h of the mine. If pumping out a mine that is D feet deep requires a pump that pumps a minimum of

+ 4D – 250 gallons per minute, pumping out a mine that is

150 feet deep would require a pump that pumps a minimum of how many gallons per minute? A. 362 B. 500 C. 800 D.1,250 E.1,750

8.

The length, in inches, of a box is 3 inches less than twice its width, in inches. Which of the following gives the length, l inches, in terms of the width, w inches, of the box? F.l =

w + 3

G.l = w + 3 H.l = w – 3 J.l = 2w + 3 K.l = 2w – 3

9.

In quadrilateral PQRS below, sides PS and QR are parallel for what value of x ?

A.158 B.132 C.120 D.110 E. 70

10.

How many irrational numbers are there between 1 and 6 ? F. 1 G. 3 H. 4 J.10

K.Infinitely many

11.

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A typical high school student consumes 67.5 pounds of sugar per year. As part of a new nutrition plan, each member of a track team plans to lower the sugar he or she consumes by at least 20% for the coming year. Assuming each track member had consumed sugar at the level of a typical high school student and will adhere to this plan for the coming year, what is the maximum number of pounds of sugar to be consumed by each track team member in the coming year? A.14 B.44 C.48 D.54 E.66

12.

In the standard (x, y) coordinate plane below, 3 of the vertices of a rectangle are shown. Which of the following is the 4th vertex of the rectangle?

F.(3,–7) G.(4,–8) H.(5,–1) J.(8,–3) K.(9,–3)

keys 1. Correct!

This is the correct answer. If you divide 2,727 miles by 27 miles per gallon you will get the number of gallons: = 101. Then, multiply the number of gallons by the cost per gallon: 101(4.04) = 408.04. This gives the cost of gas for this car to travel 2,727 typical miles. 2. Correct!

14 is the correct answer. When you use x = 3 and y = 5 in the given expressions, 3x2 – 2y = 3(3)2 – 2(5) = 27 – 10 = 17 and 2x2 – 3y = 2(3)2 – 3(5) = 18 – 15 = 3. Then subtract 3 from

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17 to get 14. 3. Correct!

The correct response is E. You can solve this problem by first subtracting 2x from each side of the equation to get 3 = x – 4. Then add 4 to each side, so x = 7. 4. Correct!

42 is the correct answer since it is the largest number that is a factor of all three numbers given. You can find the greatest common factor by writing out the prime factorization of all three numbers, and then taking each of the common prime factors to the lowest power that appears for that factor: 42 = 2 × 3 × 7; 126 = 2 × 32 × 7; and 210 = 2 × 3 × 5 × 7. So the greatest common factor is 2 × 3 × 7 = 42. 5. Correct!

This is the correct answer. If x = sales for the first year, then x + 3 = sales for the second year. Since sales for the third year were double the sales for the second year, sales for the third year = 2(x + 3). Sales for the third year were 38, so 2(x + 3) = 38. To solve this equation, you could first divide each side by 2 to get x + 3 = 19. Then, by subtracting 3 from both sides, x = 16. 6. Correct!

The correct answer is F. If you draw line segments DF and FG, you can show DEF GEF by SSS (side-side-side congruence). So, DEF GEF because corresponding parts of congruent triangles are congruent. 7.Correct!

The correct answer is D. If you substitute D with 150 in the expression, you get + 4(150) – 250 = + 600 – 250 = 1,250. 8. Correct!

You did the problem correctly. Twice a number means to multiply the number by 2, and 3 less than a number means to subtract 3 from the number. Combining these, you get l = 2w – 3. 9. Correct!

The correct answer is D. The question states that PS and QR are parallel. If you treat PQ as a transversal, then P and Q are interior angles on the same side of a transversal, so their measures add up to 180°. Since the measure of P is 70°, the measure of Q is 180° – 70° = 110°. 10. Correct!

This is the correct response. If you chose this answer, you know 1 and 6 are real numbers and that there are an infinite number of irrational numbers between any two real numbers.

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11. Correct!

54 is the correct answer. For each member of the track team to consume 20% less sugar, the track member will consume 100% – 20% = 80% of the level of a typical high school student. 80% of 67.5 = 0.80(67.5) = 54. 12. Correct!

The correct response is F. When moving from (2,1) to (–1,–1), you can go 3 units left and 2 units down. Since you want to form a rectangle, you will need to move in the same pattern from (6,–5) to the 4th vertex. Subtract 3 from the x-value, and subtract 2 from the y-value, and you will find the point needed: (6 – 3, –5 – 2) = (3,–7).

以上由扬格外语考试网整理，更多act考试资料，欢迎查看http://waiyu.kaoshibaike.com/act/ 。

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11. Correct!

54 is the correct answer. For each member of the track team to consume 20% less sugar, the track member will consume 100% – 20% = 80% of the level of a typical high school student. 80% of 67.5 = 0.80(67.5) = 54. 12. Correct!

The correct response is F. When moving from (2,1) to (–1,–1), you can go 3 units left and 2 units down. Since you want to form a rectangle, you will need to move in the same pattern from (6,–5) to the 4th vertex. Subtract 3 from the x-value, and subtract 2 from the y-value, and you will find the point needed: (6 – 3, –5 – 2) = (3,–7).

以上由扬格外语考试网整理，更多act考试资料，欢迎查看http://waiyu.kaoshibaike.com/act/ 。

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