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

Let p(x) = 3x² − 15 and q(x) = 5x² + 4. Which of the following polynomials is p(x) + q(x)?

2026 April(R4A) 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)?

2026 February(Z14) Math Question 2

Based on a scatterplot of data, a company uses the quadratic model R = −10p² + 550p to predict the total revenue, R dollars, when the price of the company's product is set at p dollars. What is the predicted total revenue when the price is set at $10?

2026 April(R4A) 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?

2026 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?

2026 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?

Algebraic & Function ExpressionsThere are 347 ACT math questions under Algebraic & Function Expressions

Sub-topics

2019 December(C03) Math Question 1

2019 June(72F) Math Question 1