ACT Math: Calculator

ACT Math: Calculator

Practice using the calculator for ACT-type questions

Calculator Strategies

• Backsolving

• Plug in

• Pick a number

• Graph

Backsolving

Use your answer choices (consider storing for the variable if appropriate) and work backwards

Multiple Choice

What is the value of x when 2x + 3 = 3x – 4 ?

• -7
• -1/5
• 1/5
• 7

Multiple Choice

What is the smallest positive integer that is divisible by 3, divisible by 5, and divisible by 6 (with no remainders)?

• 15

• 30

• 60

• 90

Plug In

Plug in for the variables. Consider using store here as well.

Multiple Choice

What is the value of the expression (2x + y)(2x - y) when x = 4 and y = -5?

• 39
• 9
• 13
• -9

Multiple Choice

What is the value of 50 - 3(x² -y²) + x when

x= 6, and y = -4?

• -145

• -6

• -4

• 44

Multiple Choice

If q = -1, r = 4, and s = 7, what does (q + r - s) (r - q) equal

• 2

• 17

• 3

• -20

Multiple Choice

When x = 3 and y = 5, by how much does the value of 3x² – 2y exceed the value of 2x² – 3y ?

• 4
• 14
• 16
• 20

Pick a number

Pick a number, not 0 or 1, store it and plug in the question. Then, plug in the answer choices to see which gives you the same result.

Multiple Choice

Find the sum.
(5x² -3x + 4) + (6x -3x² - 3)

• 3x² + 2x + 1
• 2x² + 3x +1
• 2x² + 5x - 7
• 3x² + 4x⁵ -7x

Multiple Choice

(5n-8)(5n+8)

• 25n²-64
• 10n²
• 5n²+16
• 16

Multiple Select

Which of the following should you Never use when using the pick a number strategy? Select all that apply.

• 0

• 1

• 2

• 5

• 10

Multiple Choice

Simplify
(1/3)(21m + 27)

• 63m + 9
• 7m + 9
• 7m + 81
• 7m + 27

Multiple Choice

Which of the following is equivalent to 3m(m² x 2m) for all real values of m?

• 3m² + 6m

• 3m² x 6m

• 3m³ x 6m²

• 6m⁴

Multiple Choice

Which of the following statements must be true for all values of x, y, and z?

I. (x+y) + z = (z+y) + x

II. (x - y) - z = (z - y) - x

III. (x÷y) ÷ z = (z÷y) ÷ x

• I only

• I and II only

• I and III only

• II and III only

Graph

Solve for y and graph using the y= button.

Multiple Choice

What is the x-intercept of the graph of y = x² – 4x + 4 ?

• -2

• -1

• 1

• 2

Multiple Choice

y= x-4

4x-4y=12

The system of equations above consists of two equations, and the graph of each equation in the xy-plane is a line. Which of the following statements is true about these two lines?

• The lines are parallel

• The lines are the same

• The lines are perpendicular

• The lines intersect at (-4, -3)

Pick Your Strategy

Answer the following questions and make a note (on paper or electronic) of what strategy you use for each.

Multiple Choice

For all real numbers x and y, 4x(x) - 3xy(2x) =

• 12x²y(x - 2y)

• 2x²(2 - 3y)

• 2x²(2 + 3y)

• 4xy(x - 3y)

Multiple Choice

For all x<3, (3 - 2x)² = ?

• 9 - x²

• 9 + x²

• 9 - 10x - 4x²

• 9 - 12x + 4x²

Multiple Choice

If [-s + h(t⋅3-w)]r = 1, then which of the following variables CANNOT equal 0?

• h

• r

• s

• t

Multiple Choice

What is the value of the expression (y-x)³ when x =5 and y = 1?

• -64
• 64
• -4
• 16

Multiple Choice

Which one of the following expressions has an even integer value for all integers a and c ?

• 8a+2ac

• 3a+3c

• 2a+c

• ac+a²

Multiple Choice

If x is divisible by 3 and y is divisible by 5, which of the following must be divisible by 15?
I.  xy          
II.  3x + 5y
III.  5x + 3y

• I only
• I and II only
• I and III only
• I, II, and III

Multiple Choice

If 6x= 25, what is the value of 3(x+ 1/2)?

• 53/6

• 51/2

• 13

• 14

Multiple Choice

Which of the following is equivalent to 3(x + 5)-6

• 3x-3

• 3x-1

• 3x+9

• 15x-6

Multiple Choice

Solve .
 $2^{2x+3}=128$  

• -2

•  $-\frac{3}{2}$  

•  $\frac{3}{2}$  

• 2

Multiple Choice

Which of the following is an increasing exponential function whose y-intercept is 50?

• y = 50(.05)^x
• y = 50x - 4
• y = (2)^x + 50
• y = 50(1.4)^x