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ACT Math Problems
| Question | Answer |
|---|---|
| What is the equation of a circle with a center of (h, k)? | (x-h)^2+(y-k)^2=r^2 |
| What is the formula for finding the volume of a right cylinder? | V= pi*r^2*h |
| Sine is ___/____? | Opposite/hypotenuse |
| (2(a^3))^4=? | 16(a^12) |
| The formula for calculating permutations is: | n!/(n-r)! |
| A club has 10 members and wants to choose 3 officers, a vise president, a president, and a secretary. How many different slates of officers can be chosen out of ten members? | 10P3= 10*9*8 = 720 |
| How would you express two independent variables, such as rolling a dice and flipping a coin? Hint: (Multiple Events in probability) | P(A and B) -or- P(A) * P(B) |
| Which set of numbers has the lowest Standard Deviation? 1, 5, 6, 9, 15; 1, 2, 5, 6, 7; 1, 9, 17, 23, 24 | 1, 2, 5, 6, 7 |
| What is the Mode of this set of numbers? 2, 6, 5, 3, 4, 7, 6, 2, 6 | 6 |
| Solve this system of equations using inverses (matrix): 2x -y = 4 6x+3y=24 | [A]^-1 * [B] = [3] and [2] |
| How many 3-letter orderings, where no letter is repeated, can be made using the letters of the word POINT? | 60 Explanation: 4 ways of 3 orderings = 12 * 5 letters = 60 |
| Connor cut a rope 35 inches long into 2 pieces. The ratio of the lengths is 2:5. What is the length, to the nearest inch, of the longer piece? | 25 inches Explanation: 2:5 -> 2+5=7 -> (5/7)*35=25 |
| If a and b are positive rational numbers such that a^(2b)=4, then a^(4b)=? | 16 Explanation: a^(4b) can be rewritten as a^2*2b=4^2, and 4 squared is 16. |
| (tanx)/(sinx)(cosx)=? | 1/cos^2x |
| For which of the following values of c will there be 2 distinct solutions to the equation 3x^2+2x+c=0? A. -1 B. 1 C. 2 D. 4 | -1 |
| The graph of y=-2x^2-4 passes through the points (2, 3a) in the standard (x,y) coordinate plane. What is the value of a? | -4 Explanation: substitute (2, 3a) into the equation and solve for a. 3a=-2(2)^2-4 |