### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Evaluate Algebraic Expressions

If x = y – 3, then (y – x)^{3 }=

**Possible Answers:**

3

–27

–9

27

9

**Correct answer:**

27

Solve for equation for y – x = 3. Then, plug in 3 into (y – x)^{3 }= 27.

### Example Question #2 : How To Evaluate Algebraic Expressions

When graphed in the (x,y) coordinate plane, at what point do the lines -2x + 4y = 5 and y = -2 intersect?

**Possible Answers:**

(-13/2,-2)

(13/2,-2)

(13/2,2)

(2,-2)

**Correct answer:**

(-13/2,-2)

Plugging in y=-2 in the second equation, gives x=-13/2. This is the point where the graphs intersect.

### Example Question #3 : How To Evaluate Algebraic Expressions

The length in cm of a plastic container is 5cm less than triple its width. Which of the following equations is an accurate description of the length, l, as a function of the width, w?

**Possible Answers:**

l = ^{1}/_{3}w – 5

l = 3w + 5

l = ^{1}/_{3}w + 5

l = ^{5}/_{3}w + ^{3}/_{5}

l = 3w – 5

**Correct answer:**

l = 3w – 5

This problem requires the development of an equation. We are told that the length is 5cm less than 3 times its width. So we should set up an equation that describes this situation. The equation l = 3w – 5 demonstrates how the length is 5 cm less than 3 times the width of the container.

### Example Question #4 : How To Evaluate Algebraic Expressions

The expression x(9 + x)(x – 2) = 4 is a polynomial of which degree?

**Possible Answers:**

2

3

0

4

1

**Correct answer:**

3

The highest power this polynomial can achieve is 3.

### Example Question #5 : How To Evaluate Algebraic Expressions

Given that *x* = 2 and *y* = 3, how much less is the value of 3*x*^{2} – 2*y* than the value of 3*y*^{2 }– 2*x*?

**Possible Answers:**

47

6

1

17

29

**Correct answer:**

17

First, we solve each expression by plugging in the given values for *x* and *y*:

3(2^{2}) – 2(3) = 12 – 6 = 6

3(3^{2}) – 2(2) = 27 – 4 = 23

Then we find the difference between the first and second expressions’ values:

23 – 6 = 17

### Example Question #6 : How To Evaluate Algebraic Expressions

Evaluate 4x^{2 }+ 6x – 17, when x = 3.

**Possible Answers:**

30

17

13

37

36

**Correct answer:**

37

Plug in 3 for x, giving you 36 + 18 – 17, which equals 37.

### Example Question #7 : How To Evaluate Algebraic Expressions

John has a motorcycle. He drives it to the store, which is 30 miles away. It takes him 30 minutes to drive there and 60 minutes to drive back, due to traffic. What was his average speed roundtrip in miles per hour?

**Possible Answers:**

40 mph

60 mph

50 mph

45 mph

30 mph

**Correct answer:**

40 mph

The whole trip is 60 miles, and it takes 90 minutes, which is 1.5 hours.

Miles per hour is 60/1.5 = 40 mph

### Example Question #8 : How To Evaluate Algebraic Expressions

If (*xy*/*2*) – 3*w *= –9, what is the value of *w* in terms of *x* and *y*?

**Possible Answers:**

(1/3)*xy *+ 6

(1/2)*xy –* 3

3*xy –* 6

3*xy *+ 6

w = 3 + (*xy*/6)

**Correct answer:**

w = 3 + (*xy*/6)

–3*w* = –9 – (*xy*/2)

w = 3 + (*xy*/6)

### Example Question #9 : How To Evaluate Algebraic Expressions

Evaluate 5*x*^{2 }+ 16*x* + 7 when *x* = 7

**Possible Answers:**

363

365

362

364

361

**Correct answer:**

364

Plug in 7 for *x* and you get 5(49) + 16(7) + 7 = 364

### Example Question #10 : How To Evaluate Algebraic Expressions

Let for all integers and . Which of the following is the value of ?

**Possible Answers:**

**Correct answer:**

In order to solve the expression, replace with and with in the definition given: