Algebra 1 Midterm Exam Review
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Questions and Answers

Evaluate the expression: 11 + 8 x 3^ - 8.

75

Evaluate the expression: 2/3 ((5 + 2)^ - 13).

24

Evaluate the expression: 5k^ - 7k when k=3.

24

7x - 11 = 17 is true when x = 4.

<p>True</p> Signup and view all the answers

9y + 3 < 13 is true when y = 2.

<p>False</p> Signup and view all the answers

5z - 9 >= 7z - 11 is true when z = -2.

<p>False</p> Signup and view all the answers

Solve: 5 + (-13).

<p>-8</p> Signup and view all the answers

Solve: -17 + (-21).

<p>-38</p> Signup and view all the answers

Solve: 15 - (-12).

<p>27</p> Signup and view all the answers

Calculate: -7(-11).

<p>77</p> Signup and view all the answers

Calculate: -1/2(15)(-8).

<p>60</p> Signup and view all the answers

Calculate: 72/-6.

<p>-12</p> Signup and view all the answers

Find the square root of 169.

<p>13</p> Signup and view all the answers

Find the negative square root of 9.

<p>-3</p> Signup and view all the answers

Find the positive and negative square roots of 256.

<p>16 and -16</p> Signup and view all the answers

Find the positive and negative square roots of 0.04.

<p>0.2 and -0.2</p> Signup and view all the answers

Solve the equation: x + 7 = 19.

<p>12</p> Signup and view all the answers

Solve the equation: 23 - y = 14.

<p>9</p> Signup and view all the answers

Solve the equation: 7p - 11 = 10.

<p>3</p> Signup and view all the answers

Solve the equation: q/4 + 8 = 13.

<p>20</p> Signup and view all the answers

Solve the equation: 15j + 7j = 11.

<p>1/2</p> Signup and view all the answers

Solve the equation: 14m + 7 - 8m = -17.

<p>-4</p> Signup and view all the answers

Solve the equation: -3.1t + 4.3 = -1.9t + 3.7.

<p>1/2</p> Signup and view all the answers

Solve the equation: 3(4k - 2) = 16k - 32.

<p>13/2</p> Signup and view all the answers

1/3(9g - 6) = 3/5(5g + 15) has a solution.

<p>False</p> Signup and view all the answers

A student can read 4 pages in 5 minutes. How many pages can the student read in 60 minutes?

<p>75</p> Signup and view all the answers

What percent of 38 is 15.2?

<p>40%</p> Signup and view all the answers

What number is 35% of 150?

<p>52.5</p> Signup and view all the answers

At your school, 74% of students bought their lunch at the cafeteria. If there are 1250 students, how many bought their lunch?

<p>925</p> Signup and view all the answers

Solve ax + by = c for a.

<p>a = (-by + c)/x</p> Signup and view all the answers

Solve ax - y/b = c for y.

<p>y = abx - bc</p> Signup and view all the answers

Plot point A(3, 6) on a coordinate plane. Describe its location.

<p>(3, 6) is in Quadrant I.</p> Signup and view all the answers

Plot point B(-2, -4) on a coordinate plane. Describe its location.

<p>(-2, -4) is in Quadrant III.</p> Signup and view all the answers

Plot point C(0, -3) on a coordinate plane. Describe its location.

<p>(0, -3) is on the x-axis.</p> Signup and view all the answers

Find the slope of the line that passes through the points (4, 8) and (5, 13).

<p>5</p> Signup and view all the answers

Find the slope of the line that passes through the points (-3, 6) and (2, 7).

<p>1/5</p> Signup and view all the answers

Find the slope of the line that passes through the points (-8, -2) and (-5, -2).

<p>undefined</p> Signup and view all the answers

Graph y - 2x = -3.

<p>Possible points: (0, 3), (1, 5), (2, 7), (-1, 1), (-2, -1)</p> Signup and view all the answers

Graph x = -4.

<p>Possible points: (-4, -2), (-4, -1), (-4, 0), (-4, 1), (-4, 2)</p> Signup and view all the answers

Graph y = 3/5x + 3.

<p>Possible points: (-10, -6), (-5, 0), (0, 3), (5, 6), (10, 9)</p> Signup and view all the answers

Evaluate f(x) = -1/2x + 3 when x = -2.

<p>4</p> Signup and view all the answers

Evaluate g(x) = 8x - 7 when x = 0.5.

<p>-3</p> Signup and view all the answers

The amount of water w (in thousands of gallons) varies directly with time t (in hours). In four hours, six thousand gallons flow over the spillway. Write a direct variation equation and determine how many gallons will be released in twelve hours.

<p>w = 3/2t; 18 thousand gallons</p> Signup and view all the answers

Write an equation in slope-intercept form that passes through (-1, 3) with a slope of 2.

<p>y = 2x + 5</p> Signup and view all the answers

Write an equation in slope-intercept form that passes through (4, -3) with a slope of 3/4.

<p>y = 3/4x - 6</p> Signup and view all the answers

Write an equation in slope-intercept form that passes through (2, -7) with a slope of -5.

<p>y = -5x + 3</p> Signup and view all the answers

Write an equation in standard form for a line that passes through (3, -7) with a slope of -7.

<p>7x + y = 14</p> Signup and view all the answers

Make a scatter plot using the points (0, 7), (2, 16), (4, 25), (6, 38), and (8, 50). Describe the correlation.

<p>To be determined from the scatter plot.</p> Signup and view all the answers

Solve and graph the inequality: x - 13 < -8.

<p>x &lt; 5</p> Signup and view all the answers

Study Notes

Expression Evaluation

  • Order of operations: evaluate exponents, multiplication, and then addition/subtraction.
  • Expression examples:
    • For 11 + 8 x 3^ - 8, the result is 75.
    • For 2/3 ((5 + 2)^ - 13), the result is 24.

Solving for Variables

  • Substitute values to find results:
    • For 5k^ - 7k with k=3, the result is 24.
    • Various equations yield specific variable values:
      • x + 7 = 19 leads to x = 12.
      • 23 - y = 14 leads to y = 9.
      • 7p - 11 = 10 leads to p = 3.

Evaluating Inequalities

  • Check if given numbers satisfy inequalities:
    • 7x-11=17 is true for x=4.
    • 9y + 3 < 13 is false for y=2.

Basic Arithmetic and Operations

  • Basic calculations:
    • 5 + (-13) results in -8.
    • -17 + (-21) results in -38.
    • 15 - (-12) results in 27.

Square Roots

  • Common square roots:
    • Square root of 169 is 13.
    • Negative square root of 9 is -3.
    • Square roots of 256 are ±16.

Graphing Points

  • Points on coordinate plane:
    • A(3, 6) is in Quadrant I.
    • B(-2, -4) is in Quadrant III.
    • C(0, -3) is located on the x-axis.

Finding Slopes

  • Slope formula: (y2 - y1) / (x2 - x1).
  • Examples:
    • Between (4,8) and (5,13) gives a slope of 5.
    • Between (-3,6) and (2,7) gives a slope of 1/5.
    • Between (-8,-2) and (-5,-2) results in an undefined slope.

Writing Equations

  • Slope-intercept form: y = mx + b.
  • Examples:
    • Through (-1, 3) with slope 2 gives y = 2x + 5.
    • Through (4, -3) with slope 3/4 gives y = 3/4x - 6.

Direct Variation and Proportions

  • Direct variation equation: w = kt, where k is a constant.
  • Example: In four hours, six thousand gallons = k(4), solving gives k = 3/2. In twelve hours, water released is 18 thousand gallons.

Inequalities Graphing

  • x - 13 < -8 simplifies to x < 5.

Scatter Plots and Correlation

  • Plot given points and describe correlation:
    • Using points (0, 7), (2, 16), (4, 25), (6, 38), and (8, 50) shows a positive correlation.

No Solutions

  • Some equations yield no solutions:
    • 1/3(9g - 6) = 3/5(5g + 15) results in no solution.

General Notes

  • Practice expressions and equations for reinforcement.
  • Verify answers through substitution and back-calculation.

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Prepare for your Algebra 1 midterm exam with these flashcards that cover essential expression evaluations. Each card challenges you to solve various mathematical expressions, enhancing your problem-solving skills. Perfect for quick revision or deeper understanding of algebra concepts.

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