Flex Activity - ACT/FLEX 2013-2014 Schedule



Flex Activity

Sample ACT Problems 13 of 30

Name: ______________________________________ Date: _________ Score: _______

MATHEMATICS TEST

8 Minutes—8 Questions

DIRECTIONS: Solve each problem, choose the correct but some of the problems may best be done without

answer, and then fill in the corresponding oval on your using a calculator.

answer document.

Note:Unless otherwise stated, all of the following should

Do not linger over problems that take too much time. be assumed.

Solve as many as you can; then return to the others in

the time you have left for this test. 1. Illustrative figures are NOT necessarily drawn to scale.

2. Geometric figures lie in a plane.

You are permitted to use a calculator on this test. You 3. The word line indicates a straight line.

may use your calculator for any problems you choose, 4. The word average indicates arithmetic mean.

|Pre-Algebra 23% ~ about 14 out of 60 |

|1. If x is a real number, and if [pic]then x lies between which two |2. One marble is to be drawn randomly from a bag that contains three red |

|consecutive integers? |marbles, two blue marbles, and one green marble. What is the probability of |

|A. 1 and 2 |drawing a blue marble? |

|B. 2 and 3 |F. [pic] |

|C. 3 and 4 |G. [pic] |

|D. 4 and 5 |H. [pic] |

|E. 5 and 6 |J. [pic] |

| |K. [pic] |

| | |

| | |

| | |

| | |

| | |

| | |

|3. If [pic], then y = |

|F. [pic] |

|G. [pic] |

|H. [pic] |

|J. [pic] |

|K. 3 |

| |

|Elementary Algebra 17% ~ about 10 out of 60 |

|4. For all a > 1, the expression [pic] equals: |

|F. [pic] |

|G. [pic] |

|H. [pic] |

|J. [pic] |

|K. [pic] |

| |

|Intermediate Algebra 15% ~ about 9 out of 60 |

|5. If a < b, then | a – b | is equivalent to which of the following? |

|F. a + b |

|G. −(a + b) |

|H. [pic] |

|J. a − b |

|K. −(a − b) |

| |

|Coordinate Geometry 15% ~ about 9 out of 60 |

|6. As shown in the standard (x,y) coordinate plane below, P(6,6) lies on the circle with center (2,3) and radius 5 coordinate units. What are the |

|coordinates of the image of P after the circle is rotated 90° clockwise about the center of the circle? |

|A. (2, 3) |

|B. (3, 2) |

|C. (5,−1) |

|D. (6, 0) |

|E. (7, 3) |

| |

| |

| |

| |

|Plane Geometry 23% ~ about 14 out of 60 |

|7. In isosceles trapezoid ABCD, [pic]is parallel to [pic], |8. In the figure below, the area of the larger square is 50 square |

|∠[pic]BDC measures 25°, and ∠[pic]BCA measures 35°. What |centimeters and the area of the smaller square is 18 square centimeters. What|

|is the measure of ∠[pic]DBC ? |is x, in centimeters? |

|A. 85° |F. 2 |

|B. 95° |G. [pic] |

|C. 105° |H. [pic] |

|D. 115° |J. 16 |

|E. 125° |K. 32 |

| | |

| | |

Answer Key

1. D. Raising a number to the third power means multiplying that number by itself three times. Students should be able to answer this question without looking at the possible responses by creating a simple table of cubes, where 1^3 = 1, 2^3 = 8 and so on.

2. J. There are six total marbles, which will be our denominator. There are two blue marbles, so the probability is [pic]which simplifies to [pic]

3. K.The problem solving strategy is here to cross-multiply and solve for y through algebraic manipulation.

[pic]

which leads to: [pic]

and then: [pic]

finally: [pic]

4. K. The 3 cancels out immediately, and then students need to remember the rules for dividing terms with exponents. The exponents themselves subtract, not divide, so you should be left with an exponent of 2 in the denominator.’

5. K. Absolute value means that all answers would be positive. In the specific case of a < b, a – b will be a negative number. The negative sign in front of (a – b) will cancel the negative result creating a positive number, just as the absolute value would.

6. C. Rotation rules are based on counterclockwise as the standard. So, a 90 clockwise rotation is the same as a 270 deg counterclockwise rotation. The rule for a 270 degree rotation about the origin is (x,y) ( (y,-x), but the center of this circle is not the origin. We can center the circle at the origin and change the coordinates of point P to (6 – 2, 6 – 3) or (4,3). The coordinate of the image after the rotation is now (3,-4), but that has to be moved back to the original circle, so (3+2, -4+3) or (5,-1)

7. B. Because the trapezoid is isosceles, [pic] and both angles are equal to 35 + 25 = 60 degrees. Then triangle DBC has angles of 25 and 60 degrees, missing the 3rd. All angles of a triangle add up to 180 deg., so 180 – 60 – 25 = 95 degrees.

8. G. The side length of the large square is the square root of the area, or √50 and the side of the smaller square is √18. The problem is really asking for √50 - √18. Using a calculator, this equates to ~2.83 which is equivalent to 2√2

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