### All ACT Math Resources

## Example Questions

### Example Question #41 : How To Find The Solution To An Equation

√(8y) + 18 = 4

What is y?

**Possible Answers:**

**Correct answer:**24.5

First, simplify the equation:

√(8y) + 18 = 4

√(8y) = -14

Then square both sides

(√8y)^{ 2} = -14^{2}

8y = 196

y = 196/8 = 24.5

### Example Question #11 : Linear / Rational / Variable Equations

If y = 4 and 6y = 10z + y, then z = ?

**Possible Answers:**

6

30

24

4

2

**Correct answer:**

2

- Substitute y in the equation for 4.
- You now have 6 * 4 = 10z + 4
- Simplify the equation: 24 = 10z + 4
- Subtract 4 from both sides: 24 – 4 = 10z + 4 – 4
- You now have 20 = 10z
- Divde both sides by 10 to solve for z.
- z = 2.

### Example Question #11 : Algebra

A sequence of numbers is: 2, 5, 8, 11. Assuming it follows the same pattern, what would be the value of the 20th number?

**Possible Answers:**

55

56

61

50

59

**Correct answer:**

59

This goes up at a constant number between values, making it an arthmetic sequence. The first number is 2, with a difference of 3. Plugging this into the arithmetic equation you get A_{n }= 2 + 3 (n – 1). Plugging in 20 for n, you get a value of 59.

### Example Question #12 : Linear / Rational / Variable Equations

The first four numbers of a sequence are 5, 10, 20, 40. Assuming the pattern continues, what is the 6th term of the sequence?

**Possible Answers:**

60

80

50

160

140

**Correct answer:**

160

Looking at the sequence you can see that it doubles each term, making it a geometric sequence. Since it doubles r = 2 and the first term is 5. Plugging this into the geometric equation you get A_{n }= 5(2)^{n–1}. Setting n = 6, you get 160 as the 6th term.

### Example Question #12 : Algebra

Given f(x) = x^{2 }– 9. What are the zeroes of the function?

**Possible Answers:**

0

–3, 3

–3, 0, 3

3

0, 3

**Correct answer:**

–3, 3

The zeroes of the equation are where f(x) = 0 (aka x-intercepts). Setting the equation equal to zero you get x^{2 }=^{ }9. Since a square makes a negative number positive, x can be equal to 3 or –3.

### Example Question #12 : Algebra

Give the lines y = 0.5x+3 and y=3x-2. What is the y value of the point of intersection?

**Possible Answers:**

3

6

2

4

7

**Correct answer:**

4

In order to solve for the x value you set both equations equal to each other (0.5x+3=3x-2). This gives you the x value for the point of intersection at x=2. Plugging x=2 into either equation gives you y=4.

### Example Question #91 : Linear / Rational / Variable Equations

Tommy's and Sara's current ages are represented by t and s, respectively. If in five years, Tommy will be twice as old as Sara, which of the following represents t in terms of s?

**Possible Answers:**

**Correct answer:**

Tommy's current age is represented by t, and Sara's is represented by s. In five years, both Tommy's and Sara's ages will be increased by five. Thus, in five years, we can represent Tommy's age as and Sara's as .

The problem tells us that Tommy's age in five years will be twice as great as Sara's in five years. Thus, we can write an algebraic expression to represent the problem as follows:

In order to solve for t, first simplify the right side by distributing the 2.

Then subtract 5 from both sides.

The answer is .

### Example Question #12 : Algebra

10 gallons of paint will cover 75 ft^{2}.^{ }How many gallons of paint will be required to paint the area of a rectangular wall that has a height of 8 ft and a length of 24 ft?

**Possible Answers:**

17 gallons

14.2 gallons

22.8 gallons

25.6 gallons

31.4 gallons

**Correct answer:**

25.6 gallons

First we need the area or the rectangle. 24 * 8 = 192. So now we know that 10 gallons will cover 75 ft^{2} and *x* gallons will cover 192 ft^{2}. We set up a simple ratio and cross multiply to find that 75*x* = 1920.

*x* = 25.6

### Example Question #13 : How To Find The Solution To An Equation

What number decreased by 7 is equal to 10 increased by 7?

**Possible Answers:**

15

17

10

24

27

**Correct answer:**

24

The best way to solve this problem is to translate it into an equation, "decreased" meaning subtract and "increased" meaning add:

x – 7 = 10 + 7

x = 24

### Example Question #191 : Algebra

If a%b = (2b + 3a)/(6ab), what would have a greater value, 2%3 or 3%2?

**Possible Answers:**

They are the same

3%2

Cannot be determined

2%3

**Correct answer:**

3%2

First find 2%3 = (2 * 3 + 3 * 2)/(6 * 2 * 3) = 12/36 = 1/3, then 3%2 = (2 * 2 + 3 * 3)/(6 * 3 * 2) = 13/36 which is greater.

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