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.
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9y + 3 < 13 is true when y = 2.
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5z - 9 >= 7z - 11 is true when z = -2.
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Solve: 5 + (-13).
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Solve: -17 + (-21).
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Solve: 15 - (-12).
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Calculate: -7(-11).
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Calculate: -1/2(15)(-8).
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Calculate: 72/-6.
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Find the square root of 169.
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Find the negative square root of 9.
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Find the positive and negative square roots of 256.
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Find the positive and negative square roots of 0.04.
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Solve the equation: x + 7 = 19.
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Solve the equation: 23 - y = 14.
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Solve the equation: 7p - 11 = 10.
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Solve the equation: q/4 + 8 = 13.
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Solve the equation: 15j + 7j = 11.
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Solve the equation: 14m + 7 - 8m = -17.
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Solve the equation: -3.1t + 4.3 = -1.9t + 3.7.
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Solve the equation: 3(4k - 2) = 16k - 32.
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1/3(9g - 6) = 3/5(5g + 15) has a solution.
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A student can read 4 pages in 5 minutes. How many pages can the student read in 60 minutes?
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What percent of 38 is 15.2?
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What number is 35% of 150?
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At your school, 74% of students bought their lunch at the cafeteria. If there are 1250 students, how many bought their lunch?
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Solve ax + by = c for a.
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Solve ax - y/b = c for y.
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Plot point A(3, 6) on a coordinate plane. Describe its location.
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Plot point B(-2, -4) on a coordinate plane. Describe its location.
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Plot point C(0, -3) on a coordinate plane. Describe its location.
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Find the slope of the line that passes through the points (4, 8) and (5, 13).
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Find the slope of the line that passes through the points (-3, 6) and (2, 7).
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Find the slope of the line that passes through the points (-8, -2) and (-5, -2).
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Graph y - 2x = -3.
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Graph x = -4.
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Graph y = 3/5x + 3.
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Evaluate f(x) = -1/2x + 3 when x = -2.
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Evaluate g(x) = 8x - 7 when x = 0.5.
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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.
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Write an equation in slope-intercept form that passes through (-1, 3) with a slope of 2.
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Write an equation in slope-intercept form that passes through (4, -3) with a slope of 3/4.
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Write an equation in slope-intercept form that passes through (2, -7) with a slope of -5.
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Write an equation in standard form for a line that passes through (3, -7) with a slope of -7.
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Make a scatter plot using the points (0, 7), (2, 16), (4, 25), (6, 38), and (8, 50). Describe the correlation.
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Solve and graph the inequality: x - 13 < -8.
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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.
Studying That Suits You
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Description
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.
