ACT Math Questions

If x = –6, y = 4, and z = 2, what is the value of xyz – xy ? 

• -72

• -48

• -24

• 12

• 24

Answer explanation

Directly substitute the given values into the corresponding variables and solve.

xyz – xy =

(–6)(4)(2) – (–6)(4) =

–48 + 24 = –24

If a = 9, b = 1, and c = –5, what does (a + b – c)(a – b + c) equal? 

• -25

• 15

• 25

• 45

• 55

Answer explanation

Directly substitute the given values into the corresponding variables and solve.

(a + b – c)(a – b + c) =

(9 + 1 – (–5))(9 – 1 + (–5)) = (15)(3) = 45

What is the value of 2 ∙ 4^(p+q) when p = 3 and q = –1 ? 

• 0

• 1

• 4

• 32

• 64

• -11

• -10

• -4

• 2

• 4

If m = 10, n = 2, and p = –3, what does (m – n + p)(n – p) equal? 

• -11

• -5

• 5

• 11

• 25

Answer explanation

Directly substitute the given values into the corresponding variables and solve.

(m – n + p)(n – p) =

(10 – 2 + (–3))(2 – (–3)) = (5)(5) = 25

Which of the following expressions is equivalent to (a – 4)(4a – 3) ? 

The expression (4x – 6y)(4y + 5x) is equivalent to: 

• 7xy

• 44xy

Answer explanation

Use the FOIL method:

First: 4x · 4y = 16xy

Outer: 4x · 5x = 20x²

Inner: –6y · 4y = –24y²

Last: –6y · 5x = –30xy

Combine like terms:

(4x-6y)(4y+5x)=16xy+20x²-24y²-30xy=20x²-14xy-24y²

The expression (4z – 5)(5z + 4) is equivalent to which of the following? 

• 9z−1

• 9z+1

• -11

• -10

• -4

• 2

• 4

The expression (5a² + 6b)(5a²- 6b) is equivalent to which of the following? 

• 25a⁴−36b²

• 25a⁴−12b²

• 25a⁴+36b²

• 10a⁴−36b²

• 10a⁴−12b²