ACT Questions Math

2 perfect square means squaring it will create an integer

A certain perfect square has exactly 4 digits. The positive square root of the perfect square must have how many digits?

1:1 Work on the AG side only

All three lines are parallel. The two intersect. ABC to AFG perimeter is 1:3. DE to FG is 2:3. What is the ratio of AC to CE?

2 2,3 3,2

Consider all pairs of positive integers w and z whose sum is 5. For how many values of w does that exist a positive integer x that satisfied both 2^w = x and x^z = 64

Walks toward at 2 feet per second Stands still for 5 seconds Walks away at 4 feet per second decreasing distance from motion detector at 2 = -2 and so on

Describe movement in 3 steps

-3/2 (4/5)ⁿ = (5/4)(³/²) n= flip the number and get same -3/2

If (4/5)ⁿ = √(5/4)³ , then n = ?

-21 just divide

If (x-7) is a factor of 2x² -11x + k, what is the value of k?

|a 0 -a | |2a 0 -2a| |3a 0 -3a|

What is the matrix product |a | |1 0 -1| |2a| |3a|

Area of sector with radius r is (x/360)πr^2 r = 1 so linear in equation = (x/360)π(1)

The 2 diagrams below show a circle of radius 1 inch with shaded sectors of angle x°, for 2 different values of x. One of the following is the graph in the standard (x,y) coordinate plane of the area, y, of a shaded sector with angle x°, for all values of x between 0 and 360. Which is that graph?

(x-5)² + (x-5)² = 25 draw out the tangents

A circle in the standard (x,y) coordinate plane is tangent to the x-axis at 5 and tangent to the y-axis at 5. Which of the following is an equation of the circle?

You got the correct answer. The number of inches of wood needed if there were no cuts is 4 + 5 + 6 = 15 feet, or 180 inches. However, you need to add 2(one-eighth) for 2 cuts that are needed so that you have lumber for each of the 3 sides. Since 180 + 2(one-eighth) = 180 + one fourth, the minimum piece needed to construct the flower bed border including the 2 cuts would be 181 inches.

Taher has decided to create a triangular flower bed border. He plans to use 3 pieces of rectangular lumber with lengths 4, 5, and 6 feet, as shown in the figure below. Points A, B, and C are located at the corners of the flower bed. Taher plans to cut the 3 pieces of lumber for the flower bed border from a single piece of lumber. Each cut takes one-eighth inch of wood off the length of the piece of lumber. Among the following lengths, in inches, of pieces of lumber, which is the shortest piece that he can use to cut the pieces for the flower bed border?

This is the correct answer. The angles of the rectangular pieces of lumber measure 90°, so the sum of the measure of the angles at beta is 360°. beta + 90 + x + 90 = 360, or beta = 180 - x.

The measure of angleABC in the figure is x°. Which of the following is an expression for beta° ?

-1/2 formula of a triangle = 1/2base(altitude) Area the same so altitude cannot be different Move in some way that the altitude stays exactly the same to maintain area

Triangle ABC has vertices A(8,2), B(0,6) and C(-3,2). Point C can be moved along a certain line, with points A and B remaining stationary, and the area of triangle ABC will not change. What is the slope of that line?

The product of two even numbers is even

Which of the following statements is true about odd and/or even numbers? The sum of any 2 even numbers is odd The quotient of any 2 even numbers is even The product of any 2 odd numbers is odd The quotient of any 2 even numbers is odd The sum of any 2 even numbers is odd

7/25 remember the angle has to be larger than 90 tan(regular angle) = |tanθ|

For θ, an angle whose measure is between 90 and 180, tanθ = -7/24. Which of the following equals sinθ

2(s+t) the rule of multiplication for logs

If log(a)x = s and log(a)y = t then log(a)(xy)² =?

π/₂ ≤ 2π/₃ unit circle

If the value, to the nearest thousandth, of cosθ is -0.385, which intervals are θ in?

common factor is xy² so it is equal to 45 5 x 9 = 45 5 x 3² = 45 y=3

If x anbd y are positive integers such that the greatest common factor of x²y² and xy³ is 45, then which of the following could y equal?

This is the correct answer. Using matrix multiplication here: [0.5 0.5] · = [0.5b1 + 0.5b2 0.5r1 + 0.5r2] = [p q]. Setting corresponding entries equal, 0.5r1 + 0.5r2 = q. Since 0.5r1 + 0.5r2 is the cost for a half pound of rice flour at Market 1 and a half pound of rice flour at Market 2, K is the correct response.

In the 2 × 2 matrix below, b1 and b2 are the costs per pound of bok choy (Chinese greens) at Market 1 and Market 2, respectively; r1 and r2 are the costs per pound of rice flour at these 2 markets, respectively. In the following matrix product, what does q represent? F. The cost of r1 pounds of rice flour at $0.50 per pound G. The cost of a half-pound of rice flour at Market 1 H. The total cost of a half-pound of bok choy and a half-pound of rice flour at Market 1 J. The total cost of a half-pound of bok choy and a half-pound of rice flour at Market 2 K. The total cost of a half-pound of rice flour at Market 1 and a half-pound of rice flour at Market 2

CE is not congruent to ED The angles C and D need to be equal for the two to exactly the same. The angles are not decided.

In the figure below A, C, F, and D are collinear; B, C , and E are collinear; and the angles at A, E, and F are right angles are marked. Which of the following statements is not justifiable from the given information? AB is parallel to EF DE is perpendicular to BE ∠ACB is congruent to ∠FCE Triangle BAC is similar to triangle EFC CE is congruent to ED

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).

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?

4/5 |cosα| = cosθ α= reference angle

In the standard (x,y) coordinate plane below, an angle is shown whose vertex is the origin. One side of this angle with measure θ passes through (4, -3), and the other side includes the positive x-axis. What is the cosine of θ?

90⁰ two upper triangles are congruent because bottom lines are equal, middle line is equal and bottom line to side lines have same angle Add subtract

In ∆ABC below, D, E, and F are points on line AB, BC and AC and DF is congruent to EF What is the sum of the measures of the angles marked x and y

Since there will be an odd number of terms, the median will have to be the middle number. Write out the numbers in the original set in numerical order. You will see no matter where you place the 5th term, the median will be 14. Ms. Hernandez said that the mean is equal to the median, so the mean is also going to be 14. If x = the 5th number, then the mean is 14 = . So, 14(5) = 52 + x, or x = 18.

Ms. Hernandez began her math class by saying: I'm thinking of 5 numbers such that their mean is equal to their median. If 4 of the numbers are 14, 8, 16, and 14, what is the 5th number? What is the 5th number Ms. Hernandez is thinking of?

1430 24(20) + 5...95 (19 numbers) or 24+ (24+95) = 143 (10 sets of these)

On his first day as a telemarketer, Marshall made 24 calls. His goal was to make 5 more calls on each successive day than he had made the day before. If Marshall met, but did not exceed, his goal, how many calls had he made in all after spending exactly 20 days making calls as a telemarketer?

8.3% (156-144)/144 increase from wk2 not wk 3

Percent of increase from Week 2 to Week 3? Week 2: 144 Week 3: 156

I and II only which equation produce the same results?

Which of the following expressions, if any, are equal for all real numbers x? I. √(-x)² II. | -x | III. - | x |