Algebraic & Function Expressions

Simplify Algebraic Expressions

1. Which of the following expressions is equivalent to a(4 — a) — 5(a + 7) ?

2015 June(73C) Math Question 1

1. Which of the following expressions is equivalent to the expression below? −7(5a − b) + 3(−8b + a)

Combining like terms

2020 December(D03) Math Question 1

1. For all nonzero values of x and y, which of the following expressions is equivalent to − ?

Equivalent expressions

Laws of exponents

2021 December(E23) Math Question 1

2010 April(68G) Math Question 2

2. Which of the following expressions is equivalent to −4x3 − 12x3 + 9x2 ?

2021 April(Z04) Math Question 2

3. (9m — 4n) — (2n + 5m) is equivalent to:

2016 April(73E) Math Question 3

4. For all real numbers a, b, and c, the expression ax — bx + cx can be written as the product of x and which of the following?

2015 April(73G) Math Question 4

6. For all real values of p and r, which of the following expressions is equivalent to p(2 − r) + 8( p − r) ?

2021 April(D05) Math Question 6

7. What is the sum of 0.1×2 + 3x + 80 and 0.5×2 — 2x + 60 for all x ?

2017 June(74C) Math Question 7

8. What is the sum of the 4 binomials listed below? x^2 + 2x, 3x + 5, x^2 + 1, 6x — 4

2014 April(71H) Math Question 8

10. (6a3 − 5ac2 + 12c) − (4c − 3a3 − 2ac2) is equivalent to:

2021 June(D06) Math Question 10

2019 June(72F) Math Question 13

2019 December(C03) Math Question 13

15. For the equation 3x + 15y = 9, which of the following expressions represents x in terms of y ?

2015 December(72E) Math Question 15

2011 June(69F) Math Question 18

2012 June(70C) Math Question 19

2010 June(68C) Math Question 19

2011 April(67F) Math Question 21

2009 June(67C) Math Question 21

2009 April(66F) Math Question 21

21. Whenever 4x + 7 = 2x – g, which of the following expressions must be equal to x ?

2014 June(72C) Math Question 21

2019 April(Z15) Math Question 21

2012 December(71A) Math Question 22

23. Which of the following expressions is equivalent to 1/2 y^2(6x + 2y + 12x -2y) ?

2014 June(72C) Math Question 23

24. The sum of (-22 + 2x + 8) and which of the following polynomials is (5x2+ 3) ?

2013 June(71C) Math Question 24

2013 April(71G) Math Question 25

2012 December(71A) Math Question 25

2010 June(68C) Math Question 26

2012 April(70G) Math Question 27

2010 December(69A) Math Question 38

42. Given that the equation 4x-y/x+y = 5/2 is true, what is the value of x/y ?

2021 December(E23) Math Question 42

45. Which of the following expressions is the greatest monomial factor of 80x^3y + 48x^2y^2 ?

2016 April(73E) Math Question 45

45. For all x ≠ ±y, x/(x+y) + y/(x-y) = ?

Using Rational Expressions

2021 April(Z04) Math Question 45

45. For all nonzero values of w, which of the following expressions is equivalent to 4/w + 2/w2?

Fractions

2021 December(E23) Math Question 45

2019 December(C03) Math Question 46

2015 June(73C) Math Question 47

50. Which of the following number properties is illustrated in the statement below?

2016 April(73E) Math Question 50

54. Which of the following expressions is equivalent to __1___ − __1___ ?
x−a x+a

2021 June(D06) Math Question 54

55. For all positive x, which of the following is equal to 2 + 3x/(x+2) − 6/(2x+4) ?

Simplify Algebraic ExpressionsAlgebraic & Function ExpressionsACT math questions

2015 June(73C) Math Question 1

2020 December(D03) Math Question 1