ACT Test Math Practice 70 Questions with Verified Answers
A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is
... [Show More] closest to how much the gas would cost for this car to travel 2,727 typical miles? - 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.
When x = 3 and y = 5, by how much does the value of 3x 2 - 2y exceed the value of 2x 2 - 3y ? - 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 17 to get 14.
What is the value of x when 2x + 3 = 3x - 4 ? - CORRECT ANSWER 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.
What is the greatest common factor of 42, 126, and 210 ? - CORRECT ANSWER 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.
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? - CORRECT ANSWER 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.
In the figure below, ray was constructed starting from rays and . By using a compas 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: - CORRECT ANSWER 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.
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 + 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? - CORRECT ANSWER If you substitute D with 150 in the expression, you get + 4(150) - 250 = + 600 - 250 = 1,250.
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? - CORRECT ANSWER 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.
In quadrilateral PQRS below, sides PS and QR are parallel for what value of x ? - CORRECT ANSWER 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°.
How many irrational numbers are there between 1 and 6 ? - CORRECT ANSWER 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.
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? - CORRECT ANSWER 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
Quadratic Formula - CORRECT ANSWER -b±[√b²-4ac]/2a
Slope - CORRECT ANSWER (y₂-y₁)/(x₂-x₁)
Slope-Intercept - CORRECT ANSWER y=mx+b
a³-b³ - CORRECT ANSWER (a-b)(a²+ab+b²)
a³+b³ - CORRECT ANSWER (a+b)(a²-ab+b²)
a²-b² - CORRECT ANSWER (a-b)(a+b)
a²-2ab+b² - CORRECT ANSWER (a-b)²
a²+2ab+b² - CORRECT ANSWER (a+b)²
(a+b)(c+d) - CORRECT ANSWER ac+ad+bc+bd
a(b+c) - CORRECT ANSWER ab+ac
sine ratio - CORRECT ANSWER opposite ÷ hypotenuse
cosine ratio - CORRECT ANSWER adjacent ÷ hypotenuse
tangent ratio - CORRECT ANSWER opposite ÷ adjacent
A function is ___________ a relation - CORRECT ANSWER always
Direct Variation - CORRECT ANSWER y=kx
Inverse Variation - CORRECT ANSWER y=k/x
Slope intercept form - CORRECT ANSWER y=mx+b
Point-Slope form - CORRECT ANSWER y-y₁=m(x-x₁)
Standard form - CORRECT ANSWER Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative
Undefined - CORRECT ANSWER When there is a vertical line that has different y points, but the same x point
Zero - CORRECT ANSWER When there is a horizontal line that has different x points, but the same y point
Dividing by a negative number in an inequality - CORRECT ANSWER You must flip the sign
Graphing < or > on a coordinate plane - CORRECT ANSWER dotted line
Graphing ≥ or ≤ on a coordinate plane - CORRECT ANSWER solid line
Graphing ≥ or > on a coordinate plane - CORRECT ANSWER shade upwards or to the right
Graphing ≤ or < on a coordinate plane - CORRECT ANSWER shade downwards or to the left
Infinitely many solutions - CORRECT ANSWER when the system of equations have the same slope and y-intercept
One solution - CORRECT ANSWER when the system of equations have different slopes
No solution - CORRECT ANSWER when the system of equations have the same slope but different y-intercepts
All direct variations are ____________________ - CORRECT ANSWER linear functions
A linear function is a function that _____________ a line - CORRECT ANSWER graphs
A parent function is the simplest ____________ of a function - CORRECT ANSWER equation
Linear parent function - CORRECT ANSWER y=x or f(x)=x
Elimination method - CORRECT ANSWER solving systems by adding or subtracting equations to eliminate a variable
Solution of the system of linear equations - CORRECT ANSWER Any ordered pair in a system that makes all the equations true
Graphing method - CORRECT ANSWER Graphing the system of equations and finding the point at which they intersect
Substitution method - CORRECT ANSWER Replacing one variable with an equivalent expression containing the other variable
Absolute value equation - CORRECT ANSWER A V-shaped graph that points upward of downward
Translation - CORRECT ANSWER A shift of a graph horizontally, vertically, or both, which results in a graph of the same shape and size, but in a different position.
Area of a circle - CORRECT ANSWER Πr²
Area of a square - CORRECT ANSWER s², where s = length of a side
Area of a triangle - CORRECT ANSWER ½(base x height) [or (base x height)÷2]
Area of a trapezoid - CORRECT ANSWER ½(b₁ +b₂) x h [or (b₁ +b₂) x h÷2]
Perimeter of a rectangle - CORRECT ANSWER 2Length + 2width [or (length + width) x 2]
Perimeter of a square - CORRECT ANSWER 4s (where s = length of a side)
Perimeter (circumference) of a circle - CORRECT ANSWER 2 pi r
Area of rectangle, square, parallelogram - CORRECT ANSWER A=bh
Circumference of a circle - CORRECT ANSWER ∏d OR 2∏r
Area of a sector - CORRECT ANSWER x°/360 times (∏r²), where x is the degrees in the angle
length of a sector - CORRECT ANSWER x°/360 times (2 pi r), where x is the degrees in the angle
Circle - CORRECT ANSWER Is the set of points which are all the same distance (its radius) from a certian point( the center).
Radius (Radii) - CORRECT ANSWER A segment connecting the center of a circle to any point on the circle
Diameter - CORRECT ANSWER The distance across the circle through the center of the circle.The diameter is twice the radius.
Chord - CORRECT ANSWER The distance from one point on the circle to another point on the circle.
Sector - CORRECT ANSWER The part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.
Arc - CORRECT ANSWER Part of a circle connecting two points on the circle.
Central Angle - CORRECT ANSWER An ange whose vertex is the center of the circle
Circumference Formula - CORRECT ANSWER C =∏d
Area of Circles - CORRECT ANSWER A=∏r2 [Show Less]