ACT - Math Practice
In the figure below, ray EF^--->(over the EF) was constructed starting from rays ED^--->(over the ED) and EG^---> (over the EG). By using a compass D and G were marked equidistant from E on rays and ED^--->(over ED). 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°. I. sum to 45°. J. sum to 60°.
The answer is F. are equal: If you draw line segments DF and FG, you can show ΔDEF ≅ ΔGEF by SSS (side-side-side congruence). So, ∠DEF ≅ ∠GEF because corresponding parts of congruent triangles are congruent.
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
The correct answer is
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
The correct answer is A. 16: 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.
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
The correct answer is D. $408.04: You get this answer by dividing 2,727 miles by 21: 2,727/27 = 101 Then you multiply the number of gallons by the cost per gallon: 101(4.04) = 408.04
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 depth of the mine. If pumping out a mine that is D feet deep requires a pump that pumps a minimum of D^2/25+ 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
The correct answer is D. 1,250: If you substitute D with 150 in the expression, you get 150^2/25 + 4(150) - 250 = 22,500/25 + 600 - 250 = 1,250
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? Individual Question A. 14 B. 44 C. 48 D. 54 E. 66
The correct answer is D. 54: 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.
What is the value of x when 2x + 3 = 3x - 4 ? A. -7 B. -1/5 C. 1 D. 1/5 E. 7
The correct answer is E. 7: 2x + 3 = 3x - 4 -2x +4 -2x +4 7 = x x = 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? Points on the graph: (2,1) (-1, -1) (6, -5) F. (3,-7) G. (4,-8) H. (5,-1) I. (8,-3) J. (9,-3)
The correct answer is F. (3, -7): 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 they-value, and you will find the point needed: (6 - 3, -5 - 2) = (3,-7).
When x = 3 and y = 5, by how much does the value of 3x^2 - 2y exceed the value of 2x^2 - 3y ? F. 4 G. 14 H. 16 I. 20 J. 50
The correct answer is G. 14: x = 3 y = 5 3(3)^2 - 2(5) 3(9) - 2(5) 27 - 10 =17 2(3)^2 - 3(5) 2(9) - 3(5) 18 - 15 =3 17 - 3 = 14 <= our difference
What is the greatest common factor of 42, 126, and 210 ? Individual Question F. 2 G. 6 H. 14 I. 21 J. 42
The correct answer is J. 42: *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.
How many irrational numbers are there between 1 and 6 ? F. 1 G. 3 H. 4 I. 10 J. Infinitely many
The correct answer is J. Infinitely many: 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.
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 = 1/2w + 3 G. l = w + 3 H. l = w - 3 I. l = 2w + 3 J. l = 2w - 3
The correct answer us J. I = 2w - 3: 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.