Math STAAR Questions Flashcards

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Questions and Answers

Which expression is equivalent to $(2m^4)(5m^8)$? (Select one)

7m^12
7m^32
10m^32
10m^12 (correct)

The function $f(x) = x$ was transformed to form $g(x) = f(x) - 23$. Which statement is true about the graphs of f and g? (Select one)

The graphs of f and g are not parallel, and the graph of f is translated 23 units up to create the graph of g.
The graphs of f and g are parallel, and the graph of f is translated 23 units down to create the graph of g. (correct)
The graphs of f and g are not parallel, and the graph of f is translated 23 units down to create the graph of g.
The graphs of f and g are parallel, and the graph of f is translated 23 units up to create the graph of g.

What are the x-intercepts of the function?

(-1, 0) and (3, 0)

An artist bought a set of 10 paintbrushes that contained $x$ small paintbrushes and $y$ large paintbrushes. The number of small paintbrushes in the set was 4 times the number of large paintbrushes. Which system of equations can be used to find the numbers of small paintbrushes and large paintbrushes in the set? (Select one)

$x + y = 10$; $x = 4y$ (B) Signup and view all the answers

Which function could represent $f$ given $f(x) = 0$ has solutions $x = 5$ and $x = -2$? (Select one)

$f(x) = 15x^2 - 11x - 14$ (D) Signup and view all the answers

Which expression is equivalent to $ abla 75$? (Select one)

5√3 (B) Signup and view all the answers

What is the solution set for $12 - 4w > 2(w - 18)$? (Select one)

$w < 8$ (D) Signup and view all the answers

What are the factors of $2x^2 + x - 15$? Select TWO correct answers.

$2x - 5$ (B), $x + 3$ (E) Signup and view all the answers

Which value represents the rate of change of $y$ with respect to $x$ for this function: $2/5x - 4/7y = 3/2$? (Select one)

7/10 (C) Signup and view all the answers

A shipping company started with 40 employees. The number of employees at the shipping company increases at a rate of 7.5% each year. Which function can be used to model the number of employees $f(x)$ at the shipping company after $x$ years? (Select one)

$f(x) = 40(1.075)^x$ (A) Signup and view all the answers

Which expression is a factor of $−6x^2 − 19x + 20$? (Select one)

$6x - 5$ (A) Signup and view all the answers

Which statement about $f(x) = 12x^2 - 36x + 27$ is true? (Select one)

The only zero is 3 because $f(x) = 3(2x - 3)^2$. (C) Signup and view all the answers

Which expression is equivalent to $(z + 5)(z^2 - 4z + 6)$? (Select one)

$z^3 + z^2 - 14z + 30$ (A) Signup and view all the answers

Which expression is equivalent to $x^{-6} y^{4}/(x^{3} y)$? (Select one)

$y^{3}/x^{9}$ (A) Signup and view all the answers

What is the solution to $10 - 3(m - 5) = 2(5 - m)$?

15 Signup and view all the answers

What is the slope of the line that passes through the points $(10, 18)$ and $(-5, -12)$? (Select one)

2 (B) Signup and view all the answers

What are the solutions to the equation $x^2 - 2 = -3x$? (Select one)

$-3 ± \sqrt{17}/2$ (A) Signup and view all the answers

What is the simplest form of the expression $(2x^8)(3x^{-1})^2$?

18x^6 Signup and view all the answers

Quadratic function $f$ has vertex (4, 15) and passes through the point (1, 20). Which equation represents $f$? (Select one)

$f(x) = 5/9 (x − 4)^2 + 15$ (B) Signup and view all the answers

Which statement about the graph of the function $f(x) = 35(1.4)^x$ is true? (Select one)

The y-intercept of the function is (0, 35). (D) Signup and view all the answers

Which expression is equivalent to $k^2 - 5k - 6$? (Select one)

$(k - 6)(k + 1)$ (D) Signup and view all the answers

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Study Notes

Algebraic Expressions and Functions

The expression (2m^4)(5m^8) simplifies to 10m^12.
For the transformation of functions, g(x) = f(x) - 23 translates f(x) down by 23 units, confirming that f and g are parallel.
The x-intercepts of a graph indicate points where it crosses the x-axis, specifically at (-1, 0) and (3, 0).

Systems of Equations

A set of paintbrushes combining small (x) and large (y) brushes must satisfy both x + y = 10 and x = 4y.

Quadratic Functions

The quadratic f(x) = x^2 with zeroes at 5 and -2 correlates to the function f(x) = 15x^2 - 11x - 14.
Solutions to the equation f(x) = 0 can also reflect in the factorization with roots leading to expressions like (x + 3) and (2x - 5).

Inequalities and Solutions

To solve 12 - 4w > 2(w - 18), the solution set is w < 8.
The equation (x + 13)(x - 6) = 0 results in solutions x = -13 and x = 6.

Functions, Transformations, and Modeling

A function representing employee growth at a shipping company can be modeled as f(x) = 40(1.075)^x due to yearly 7.5% increases.
When analyzing a quadratic function, transformations such as shifting right by 2 units and up by 5 units are key.

Slope and Line Equations

The slope of the line between points (10, 18) and (-5, -12) is determined as 2.
Parallel lines maintain consistent slopes, as seen with the transformation of y = -x + 17 for line n.

Exponential Decay

A substance's decay can be modeled by the function y = 963(0.73)^x after an initial mass of 963 grams reducing at a 27% rate per hour.

Key Points in Graph Behavior

The function f(x) = 35(1.4)^x shows a y-intercept at (0, 35) and approaches an asymptote of y = 0 as it increases.

Evaluation of Expressions

Simplifying expressions, e.g., ( (2x^8)(3x^{-1})^2 ), results in 18x^6 when written in the form ax^b.
The quadratic expression k^2 - 5k - 6 factors as (k - 6)(k + 1).

Application of Functions

The cost comparison of dance lessons at two studios leads to an equal cost solution after 5 months, illustrating practical use of linear functions.
The vertex form of a quadratic function can help identify characteristics of its graph, such as maximum or minimum values.