FC: Mixbook ACT Problems 16-30. | By: Mallory Burman
1: Table of Contents | pg. 2&3 skill #16 pg. 4&5 skill #17 pg. 6&7 skill #18 pg. 8&9 skill #19 pg. 10&11 skill #20 pg. 12&13 skill #21 pg. 14&15 skill #22 pg. 16&17 skill #23 pg.18&19 skill #24 pg. 20&21 skill #25 pg 22&23 skill #26 pg 24&25 skill #27 pg. 26&27 skill #28 pg. 28&29 skill #29 pg. 30&31 skill #30
2: Act skill 16 f(3) means plug 3 in for x f(g(m)) means plug g(m) in for x. | Ex. if f(x)= 2x + 12, what is f(2) -just plug 2 in for x. Answer: 2(2)+12 =16
4: ACT Skill 17 To find the midpoint of two points use the midpoint formula and to find the distance between two points use the distance formula. | Ex: A line in the standard (x,y) coordinate plan contains the points P(3,-5) and Q(-7,9). What point is the midpoint of PQ? -Plug the points into your midpoint formula. Answer: (-2,2)
5: midpoint formula: | Distance formula:
6: ACT skill 18 When a question with variables is way to theoretical, just "Make It Real" | Ex: if c = -2b-2(2c-b), what happened to the value of c when b & e are both increased by 2? - choose reals numbers in place of the variables after work the equation again but add two to the real numbers you chose. Answer: It is decreased by 8
8: Act Skill 19 Memorize basic perimeter, area and volume formulas. To use them, plug in what you know, and solve for the variable. | Ex: A square lot, with area of 625 square feet, is completely fenced. What is the length, in feet, of the fence? -Determine the length of a side of the square. Set up the area formula. Plug in what we know and solve for the variable. Take the square of both sides to get s=25. Since one side = 25, the perimeter is 4*25, which = 100.
9: Volume example
10: ACT skill 20 To find the area of a shaded region, just subtract the area of the smaller figure from the area of the larger figure. | Ex: In the diagram to the right the area of the triangle is 12 meters squared and the the radius of the circle is 3m. What is the area of the shaded region. -first find the area of the circle, which = 28.3 meters squared - Them subtract the area of the triangle from the area of the circle. Answer: 16.3 meters squared
12: ACT skill 21 A ratio can be a reduced version of the real numbers and when you see a proportion on the ACT, cross multiply. | Ex: A triangle with a perimeter has one side that is 19 in. long. The lengths of the other two sides have a ratio of 3:7. What is the length, in inches, of the longest side of the triangle? - if one side of the triangle is 19 and the perimeter is, 89, then the other two sides add up to 89-19=70. One of these must be the largest side, and we know that these two sides must have a ratio of 3:7. Rewrite the ratio as part: total part: part, and set up the proportion. cross multiply your proportion and you get 49.
14: ACT Skill 22 Relax when you see a matrix question; just treat the matrix like a normal chart. To add matrices add corresponding #'s to multiply; and for any other operation, just follow the instructions that the question provides. | Ex: [p q] + [ w x] r s y z Answer: [pw qx] ry sz
16: ACT Skill 23 Use the diagram to estimate the answer. When a diagram is not drawn to scale, redraw it. And when a picture is described, but not shown, draw it. When estimating and answer, translate fractions, square roots or pi into decimals. | Ex: Points A,B,C,D and E are points on a line in order. If B is the midpoint of AC, C is the midpoint of AD, and D is the midpoint of AE, which of the following is the longest segment. -Sketch the diagram to scale, following the instructions in the question -After you do that the answer becomes obvious. Answer= line segment CE
18: ACT Skill 24 When you see a right triangle use the Pythagorean theorem. | Ex: if a=8 and c=17, what is the value of b. -plug a and c into your formula. Answer= 15
20: ACT Skill 25 When you see a 30, 45, 60 angle in a right triangle, try using the special right triangles. | Ex: In the 45, 45, 90 triangle to the right if n= 2 what do the other two sides equal. Answer: 2 and 2 square root of 2
22: ACT Skill 26 Similar triangles have sides that are proportional. | Ex: In the figure to the right are two similar triangles. What does x =? Answer: it equals 20.
24: ACT Skill 27 Translate word problems from English to Math. | Ex: if 5 percent of 20 percent of a number is 24 less than one-quarter of the number, what is the number? -First translate than use algebra to solve. -(0.05)(0.20)=0.25n-24 0.01n=0.25n-24 24=0.24n 100=n Answer: 100
26: ACT Skill 28 Word problems are no problem; translate English to Math and translate fractions to decimals. | Ex: In Seth's refrigerator he found 2 jars of mustard. He estimated it was 1/3 full and the other was 2/5 full. If he combined the 2 jars into one, approximately how full would the one combined jar be. -First translate fractions to decimals: 1/3=0.333 and 2/3=0.4. Now add them together and you get 0.7333,
28: ACT Skill 29 When something can be factored, foiled, reduced or simplified-do it when you have 2 equations in a question, ask how they relate. | Ex: If x2-y2=84 and x-y=6, what is the value of x+y? -factor Answer: 14
30: ACT skill 30 Memorize the Laws of Exponents | Ex: What is the following expression equivalent to (-(2x2y2)3 Answer: -8x6y6.
31: Laws of Exponents