ACT B05 Math Q 21-30

ACT B05 Math Q 21-30

by Mrs. Kessler

Multiple Choice

Line l is shown in the standard (x,y) coordinate plane. Alicia drew line p with a slope that is ½ of the

slope of line l and with a y-intercept that is 3 times the y-intercept of line l. One of the following equations represents line p. Which one?

• y = x + 3

• y = -3x + 1

• y = 3x+ 1

• y = -1/2x + 6

• y= 1/2x + 6

​Correct answer: y = 1/2x + 6

Be sure to know the y-intercept form of a line (y = mx + b). You will use that four or five times on every ACT.​

The line on this graph has a y-intercept of 2. 3 x 2 = 6.

​So that eliminates 3 options.

​The slope of this line is positive. Of the two remaining equations, only one has a positive slope. That one is y = 1/2x + 6

Multiple Choice

One angle measure and 2 side lengths, in inches, are

given in the right scalene triangle below. In terms of a and b, what is sin  $$\theta$$  ?

• $$\frac{a}{b}$$  

• $$\frac{b}{a}$$  

• $$\frac{a}{\sqrt[]{a^2\ +b^2}}$$  

• $$\frac{b}{\sqrt[]{a^2\ +\ b^2}}$$  

• $$\frac{\sqrt[]{a^2+b^2}}{b}$$  

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Multiple Choice

Each side of square ABCD has a length of 50 cm. A certain rectangle whose area is equal to the area of ^ABCD has a width of 10 cm. What is the length, in centimeters, of the rectangle?

• 40

• 50

• 60

• 125

• 250

​Correct answer: 250

​The area of a square is side x side. So the area of a square with sides of 50 cm is 50 x 50 = 2500.

​

​The area of a rectangle is length x width. So what time 10 equals 2500? We can write that as 10x = 2500. Divide by ten on both sides to get x = 250

Multiple Choice

If  $$f\left(x\right)=5x^2-6x+1$$  and  $$g\left(x\right)=x^2-2$$  which of the following expressions represents  $$\left(fg\right)\left(x\right)$$  ?

• $$6x^2-6x-1$$  

• $$5x^4\ -26x^2+33$$  

• $$5x^4-20x^2-6x+21$$  

• $$5x^4-6x^3-9x^2+12x-2$$  

• $$25x^4-60x^3+46x^2-12x-1$$  

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​For this problem we need to multiple (5x² - 6x + 1)(x² - 2).

​

​We will get 5x⁴ - 10x² - 6x³ + 12x + x² - 2. We we combine like terms, we get

​

​5x⁴ - 6x³ - 9x² + 12x - 2

Multiple Choice

A bag contains 12 red marbles, 14 yellow marbles, and 8 green marbles.  How many additional red marbles must be added to the 34 marbles already in the bag so that the probability of randomly drawing a red marble is  $$\frac{3}{5}$$   ?

• 16

• 21

• 29

• 34

• 44

​Correct Answer: 21

​Probability is found by taking the desired outcome and placing that over the possible overcomes. In this case that means taking the number of red marbles and put that over the total number of marbles in the bag. So what do we add to the red and the total to make it 3/5?

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