Tip #50 to Get a Top ACT Math Score (page 2)
Learning mantras is like learning martial arts. Practice until they become part of you, until you follow them naturally: When you see a proportion, you cross–multiply; when you see a linear pair, you fill in the angles. … This will fundamentally change you as a math student. In fact, after ACT prep, many students begin to like math, they realize that they "get" it, and it stops being intimidating and becomes easy. I've even seen kids overcome serious math phobia with the mantras. Your ACT score and probably even your math class grades will go way up.
Here are the rest of the ACT math mantras. Check the box next to each one when you have mastered it.
- Skill 23. "Use the Diagram" to estimate an answer. When a diagram is not drawn to scale, redraw it. And when a picture is described but not shown, draw it! When estimating an answer, translate fractions, √, or π into decimals.
- Skill 24. When you see a right triangle, try a2 + b2 = c2.
- Skill 25. When you see a 30°, 45°, or 60° angle in a right triangle, try using the pecial right triangles.
- Skill 26. Similar triangles have sides that are proportional.
- Skill 27. Translate word problems from English to math.
- Skill 28. Word problems are no–problems; translate English to math, and translate fractions to decimals.
- Skill 29. When something can be factored, FOILed, reduced, or simplified, do it. When you have two equations in a question, ask how they relate. And convert fractions to decimals.
- Skill 30. Memorize the laws of exponents.
- Skill 32. For the equation y = mx + b, the m is the slope and b is the y intercept.
- Skill 33. When you see an arrangement question, draw a blank for each position, fill in the # of possibilities to fill each position, and multiply. When an arrangement question mentions a "team of two," or specifically points out repeats, divide your result by 2.
- Skill 34. SohCahToa!
- Skill 35. When trig seems tough, "Use the Answers" or "Make It Real."
- Skill 36. When you see the word "probability," use the equation Probability .
- Skill 37. For questions like (x + 4)(x – 3) = 0, just "Use the Answers" or set each parenthesis equal to zero and solve for x.
- Skill 38. For the equation y = ax2 + bx + c, the a tells whether the U shaped graph opens up or down, and the c is the y intercept. For the equation y = (x – h)2 + k, the h and k give the coordinates of the vertex of the graph (h, k). The vertex is the highest or lowest point of the graph and is therefore also called the maximum or minimum point.
- Skill 39. The equation for a circle is (x – h)2 + (y – k)2 = r2, where (h, k) is the center and r is the radius of the circle.
- Skill 40. If one side of a triangle is the diameter of a circle, and the opposite vertex is on the circle, then the triangle is right, with its right angle opposite the diameter.
- Skill 41. When you see absolute value on the ACT, "Use the Answers" or "Make It Real," and remember that absolute value means, "Ditch the negative sign."
- Skill 42. An arithmetic sequence is a sequence of numbers where a certain number is added to each term to arrive at the next, like 3, 7, 11, 15, 19; and a geometric sequence is a sequence of numbers where a certain number is multiplied by each term to arrive at the next, like 3, –6, 12, –24, 48.
- Skill 43. For a Fahrenheit/Celsius conversion question, when you are given degrees Celsius, just plug in and simplify; but when you are given degrees Fahrenheit, you can either do the algebra or "Use the Answers."
- Skill 44. "Careless errors are bad mmmkay," so underline all vocabulary words and remember to distribute the negative.
- Skill 47. A log is just a fancy way of writing exponents. For example, log5 25 = 2 means 52 = 25.
- Skill 48. The key to complex number questions is to treat i like a normal variable, and then in the final step, replace i2 with –1.
Let's look at this question:
Solution: This question would be ranked "medium" or even "hard," but if you just know what "median" means, it's totally easy! Median is the middle number in a list of numbers. To find the median, rewrite the list in order: 79, 80, 82, 85, 90, 92, 94. Then cross out a number on each side until you get to the one in the middle. (If there are two middle numbers, then the median is the average of the two.) Here the middle number is 85.
Correct answer: H
Name the skill(s) that you can use, and then solve each question.
- Which of the following is equivalent to 2(3x4)3 ?
- What is the length of the hypotenuse of a right triangle with legs that are 7 and 24 inches long, respectively?
- Kayla purchased a new phone at 31% off its original price. If she paid $34 for the phone, which of the following is an equation that could be used to find x, the original price of the phone?
- 34 = 1.31x
- 31 = x – 0.34x
- 31 = x – 0.66x
- 34 = x – 0.31x
- x = x – 0.31
- What are the values for x that satisfy the equation x2 – 5x – 14 = 0 ?
- –2 and 9
- –2 and –9
- 2 and –7
- –2 and 7
- In the standard (x, y) coordinate plane, the midpoint of is (–3, 5). If point M is located at (2, 3), what are the coordinates of point N ?
- (–8, 7)
- (7, 1)
- (–6, 15)
- (0, 0)
- For right triangle ΔABC, the sides measure 6, 8, and 10 inches. Which of the following equations could be used to solve for smallest angle, x, which is opposite the smallest side?
- sin x° = 0.6
- sin x° = 0.8
- tan x° = 0.8
- sin x° = 0.75
- tan x° = 0.6
- If m < 0, which of the following is greatest?
- 3 m
- 6 m
- 9 m
- It cannot be determined from the information given.
- If triangle MNO is similar to triangle PQR shown below, which of the following could be the measures of the three sides of triangle MNO ?
- If 4 times a number p is subtracted from 20, the result is negative. Which of the following gives the possible value(s) for p ?
- 0 only
- 5 only
- 20 only
- All p < 5
- All p > 5
- Which of the following could be the equation of the graph below?
- y = x – 1
- y = x2 –1
- y = (x – 1)2
- y = (x +1)2
- y = x2
- The inequality 3(3x – 2) < 6 – (5x – 2) is equivalent to
- x < 7
- x < 5
- x < 3
- x < 1
- x < –1
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