Algebraic & Function Expressions

2019 December(C03) Math Question 1

2019 June(72F) Math Question 1

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

2015 June(73C) Math Question 1

2019 April(Z15) Math Question 1

2019 April(B04) Math Question 1

2012 April(70G) 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

Given 4x − 9 = 6x − 15 is true, x = ?

2023 April(F11) Math Question 1

Which of the following expressions is equivalent to a(5 − a) − 8(a + 6)?

2024 June(G20) Math Question 1

Given that f(x) = 3x³ − 7, what is f(−2)?

2024 September(H11) Math Question 1

The function f is defined below. f(x) = |x|. What is(are) the output value(s) of f(2)?

2024 December(H31) Math Question 1

2.Given r = 6, b = 4, and g = -9, (r + b - g)(b + g) =?

2019 June(B02) Math Question 2

2013 April(71G) Math Question 2

2010 April(68G) Math Question 2

2009 December(68A) Math Question 2

2009 June(67C) Math Question 2

2014 April(71H) Math Question 2

2. For what value of x is 6x — 3 = 4x + 7 true?

2013 June(71C) Math Question 2

2. For what value of a is the equation _1_a + 10 = 6 true?

2021 June(D06) Math Question 2

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

2021 April(Z04) Math Question 2

A function, f, is defined by f(x,y) = 3x² − 2y. What is the value of f(2,3)?

35 February(Z14) Math Question 2

2019 April(B04) Math Question 3

2012 April(70G) Math Question 3

2011 June(69F) Math Question 3

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

2016 April(73E) Math Question 3

2009 April(66F) Math Question 3

3. Given f = cd3, f= 450, and d = 10, what is c

2014 June(72C) Math Question 3

Solving equations

2021 April(Z04) Math Question 3

3. The number 312.8 is 34% of x. What is the value of x rounded to the nearest whole number?

Percentages

2020 December(D03) Math Question 3

What is the value of x when 9 − 11x = 13 − 9x is true?

35 February(Z14) Math Question 3

A new operation, ♦, is defined for 2 ordered pairs of integers as follows: (a,b) ♦ (c,d) = (ac + bd)/(ab − cd). What is the value of (4,3) ♦ (1,2)?

2024 December(H31) 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

4. Given that 2x + 1 = 5, what is the value of (x + 3)^3 ?

2014 December(72G) Math Question 4

2013 April(71G) Math Question 4

2010 December(69A) Math Question 4

4. Let the function f be defined as f(x) = 5x2 — 7(4x + 3). What is the value of f(3) ?

2017 April(74F) Math Question 4

2019 June(B02) Math Question 4

2011 April(67F) Math Question 4

2020 July(C01) Math Question 4

2019 December(C03) Math Question 5

2011 June(69F) Math Question 5

5. The sum of 2 numbers is 90. The smaller number is 50 less than the larger number. What is the larger number?

2014 April(71H) Math Question 5

Given that a △ b = a² + b − a/b, what is the value of a △ b when a = 5 and b = 1/2?

35 February(Z14) Math Question 5

2024 April(Z13) Math Question 5

What value of x makes the equation below true? −x + 6 = 3x − 10

2024 June(G20) Math Question 5

6. What value of x makes (2\3)x + 5 = 11 true?

2014 December(72G) Math Question 6

2010 June(68C) Math Question 6

2009 December(68A) Math Question 6

2009 June(67C) Math Question 6

6. A function, f, is defined by f(x,y) = 3Ã—2 â€” 4y. What is the value of f(4,3) ?

2018 June(A11) Math Question 6

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

Brian had $12.80 to spend at the flea market. He bought a portable CD player for $5.50 and wants to buy some CDs that are $0.75 each. Brian can determine n, the number of CDs he can buy, using which of the following inequalities?

2023 September(G01) Math Question 6

(8p − 3q) − (2q + 6p) is equivalent to:

2024 April(Z13) Math Question 6

2012 December(71A) Math Question 7

2011 April(67F) Math Question 7

2010 December(69A) Math Question 7

7. What is the value of x^2 + 2 + y^2 — 3 when x = 3 and y = —3 ?

2014 April(71H) Math Question 7

2009 June(67C) Math Question 7

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

The function f(c) = (9/5)c + 32 gives the temperature, f(c) degrees Fahrenheit, that corresponds to c degrees Celsius. To the nearest 0.1°F, what Fahrenheit temperature corresponds to 13.0°C?

2024 June(G20) Math Question 7

Given x = 100 and y = −20, x + y is equal to the product of −5 and what number?

2024 September(H11) Math Question 7

7. The number of fish, f, in Skipper’s Pond at the beginning of each year can be modeled by the equation f (x) = 3(2x), where x represents the number of years after the beginning of the year 2000. For example, x = 0 represents the beginning of the year 2000, x = 1 represents the beginning of the year 2001, and so forth. According to the model, how many fish were in Skipper’s Pond at the beginning of the year 2006 ?

Exponential Equations

2021 April(Z04) Math Question 7

8. Susan makes holiday wreaths for 4 hours every Saturday. It takes her 20 minutes to make a small wreath and 30 minutes to make a large wreath. This Saturday, Susan will make twice as many large wreaths as small wreaths. How many of the large wreaths will she make this Saturday?

2015 April(73G) Math Question 8

2017 April(74F) Math Question 8

2013 April(71G) Math Question 8

2012 December(71A) Math Question 8

2012 April(70G) Math Question 8

2010 June(68C) Math Question 8

2020 July(C01) Math Question 8

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

2012 June(70C) Math Question 8

8. For what value of x is 2(x − 12) + x = 24 true?

2020 December(D03) Math Question 8

Which of the following values is the solution to the equation below? (2/3)x + 1/4 = 8 1/4

2023 April(F11) Math Question 8

The operation ⊗ is defined by a ⊗ b = a²b. If a = 5 and a ⊗ b = 100, what is the value of b?

2024 September(H11) Math Question 8

What is the product of (3x + 2) and (3x − 2)?

2024 December(H31) Math Question 8

9. Andrea manages a company that currently has 116 customers, which is 8 more than twice the number of customers the company had 1 year ago. How many customers did the company have 1 year ago?

2015 June(73C) Math Question 9

2011 June(69F) Math Question 9

2009 April(66F) Math Question 9

9. If g(x) = 2x^2 — 3x + 4, then g(-3) = ?

2016 April(73E) Math Question 9

Which of the following equations gives a function f(x) that satisfies f(4) = 9?

2024 April(Z13) Math Question 9

For RT shown below, point S is on RT, the length of RS is 6 cm, and the length of ST is 20 cm. What is the distance, in centimeters, between T and the midpoint of RS?

2024 June(G20) Math Question 9

For RT shown below, point S is on RT, the length of RS is 6 cm, and the length of ST is 16 cm. What is the distance, in centimeters, between T and the midpoint of RS?

2024 September(H11) Math Question 9

10. If f(x) 3×2 + 7x — 8, then f(-3) = ?

2018 April(A09) Math Question 10

2010 June(68C) Math Question 10

2010 April(68G) Math Question 10

2020 June(C02) Math Question 10

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

2021 June(D06) Math Question 10

10. Given that f(x) = 3x + 7 and g(x) = x^2/2, what is the
value of f(g(4))?

2017 December(A10) Math Question 10

2014 June(72C) Math Question 10

10. What is the value of 80 – 5(x2 y) + y when x = 4 and y = 6 ?

2013 June(71C) Math Question 10

11. A system of equations is given below. What is the value of b in the (a,b) solution to the system?

2015 April(73G) Math Question 11

2019 April(Z15) Math Question 11

2019 April(B04) Math Question 11

2011 June(69F) Math Question 11

2010 April(68G) Math Question 11

2009 December(68A) Math Question 11

2009 April(66F) Math Question 11

11. Which of the following (x,y) pairs is the solution for the system of equations x + 2y = 2 and −x + y = 7 ?

Algebraic & Function ExpressionsThere are 342 ACT math questions under Algebraic & Function Expressions

Sub-topics

2019 December(C03) Math Question 1

2019 June(72F) Math Question 1