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Questions and Answers
Evaluate the expression: 11 + 8 x 3^ - 8.
Evaluate the expression: 11 + 8 x 3^ - 8.
75
Evaluate the expression: 2/3 ((5 + 2)^ - 13).
Evaluate the expression: 2/3 ((5 + 2)^ - 13).
24
Evaluate the expression: 5k^ - 7k when k=3.
Evaluate the expression: 5k^ - 7k when k=3.
24
7x - 11 = 17 is true when x = 4.
7x - 11 = 17 is true when x = 4.
9y + 3 < 13 is true when y = 2.
9y + 3 < 13 is true when y = 2.
5z - 9 >= 7z - 11 is true when z = -2.
5z - 9 >= 7z - 11 is true when z = -2.
Solve: 5 + (-13).
Solve: 5 + (-13).
Solve: -17 + (-21).
Solve: -17 + (-21).
Solve: 15 - (-12).
Solve: 15 - (-12).
Calculate: -7(-11).
Calculate: -7(-11).
Calculate: -1/2(15)(-8).
Calculate: -1/2(15)(-8).
Calculate: 72/-6.
Calculate: 72/-6.
Find the square root of 169.
Find the square root of 169.
Find the negative square root of 9.
Find the negative square root of 9.
Find the positive and negative square roots of 256.
Find the positive and negative square roots of 256.
Find the positive and negative square roots of 0.04.
Find the positive and negative square roots of 0.04.
Solve the equation: x + 7 = 19.
Solve the equation: x + 7 = 19.
Solve the equation: 23 - y = 14.
Solve the equation: 23 - y = 14.
Solve the equation: 7p - 11 = 10.
Solve the equation: 7p - 11 = 10.
Solve the equation: q/4 + 8 = 13.
Solve the equation: q/4 + 8 = 13.
Solve the equation: 15j + 7j = 11.
Solve the equation: 15j + 7j = 11.
Solve the equation: 14m + 7 - 8m = -17.
Solve the equation: 14m + 7 - 8m = -17.
Solve the equation: -3.1t + 4.3 = -1.9t + 3.7.
Solve the equation: -3.1t + 4.3 = -1.9t + 3.7.
Solve the equation: 3(4k - 2) = 16k - 32.
Solve the equation: 3(4k - 2) = 16k - 32.
1/3(9g - 6) = 3/5(5g + 15) has a solution.
1/3(9g - 6) = 3/5(5g + 15) has a solution.
A student can read 4 pages in 5 minutes. How many pages can the student read in 60 minutes?
A student can read 4 pages in 5 minutes. How many pages can the student read in 60 minutes?
What percent of 38 is 15.2?
What percent of 38 is 15.2?
What number is 35% of 150?
What number is 35% of 150?
At your school, 74% of students bought their lunch at the cafeteria. If there are 1250 students, how many bought their lunch?
At your school, 74% of students bought their lunch at the cafeteria. If there are 1250 students, how many bought their lunch?
Solve ax + by = c for a.
Solve ax + by = c for a.
Solve ax - y/b = c for y.
Solve ax - y/b = c for y.
Plot point A(3, 6) on a coordinate plane. Describe its location.
Plot point A(3, 6) on a coordinate plane. Describe its location.
Plot point B(-2, -4) on a coordinate plane. Describe its location.
Plot point B(-2, -4) on a coordinate plane. Describe its location.
Plot point C(0, -3) on a coordinate plane. Describe its location.
Plot point C(0, -3) on a coordinate plane. Describe its location.
Find the slope of the line that passes through the points (4, 8) and (5, 13).
Find the slope of the line that passes through the points (4, 8) and (5, 13).
Find the slope of the line that passes through the points (-3, 6) and (2, 7).
Find the slope of the line that passes through the points (-3, 6) and (2, 7).
Find the slope of the line that passes through the points (-8, -2) and (-5, -2).
Find the slope of the line that passes through the points (-8, -2) and (-5, -2).
Graph y - 2x = -3.
Graph y - 2x = -3.
Graph x = -4.
Graph x = -4.
Graph y = 3/5x + 3.
Graph y = 3/5x + 3.
Evaluate f(x) = -1/2x + 3 when x = -2.
Evaluate f(x) = -1/2x + 3 when x = -2.
Evaluate g(x) = 8x - 7 when x = 0.5.
Evaluate g(x) = 8x - 7 when x = 0.5.
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.
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.
Write an equation in slope-intercept form that passes through (-1, 3) with a slope of 2.
Write an equation in slope-intercept form that passes through (-1, 3) with a slope of 2.
Write an equation in slope-intercept form that passes through (4, -3) with a slope of 3/4.
Write an equation in slope-intercept form that passes through (4, -3) with a slope of 3/4.
Write an equation in slope-intercept form that passes through (2, -7) with a slope of -5.
Write an equation in slope-intercept form that passes through (2, -7) with a slope of -5.
Write an equation in standard form for a line that passes through (3, -7) with a slope of -7.
Write an equation in standard form for a line that passes through (3, -7) with a slope of -7.
Make a scatter plot using the points (0, 7), (2, 16), (4, 25), (6, 38), and (8, 50). Describe the correlation.
Make a scatter plot using the points (0, 7), (2, 16), (4, 25), (6, 38), and (8, 50). Describe the correlation.
Solve and graph the inequality: x - 13 < -8.
Solve and graph the inequality: x - 13 < -8.
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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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.
