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Mathematics Flashcards

28 cards from real PRAXIS practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. If x= -5, then l x - 7 l =

    Answer: 12

    To evaluate the expression |x - 7| when x = -5, substitute -5 for x. This gives |-5 - 7|. First, perform the subtraction inside the absolute value bars, which results in |-12|. The absolute value of a number is its distance from zero, always a non-negative value. Therefore, |-12| is 12.

  2. Solve and simplify: 2/3 x 3/5 x 5/10 x 6/8

    Answer: 0.15

    To solve this multiplication of fractions, multiply the numerators together and the denominators together. It's often easier to cancel common factors before multiplying. The expression is (2/3) * (3/5) * (5/10) * (6/8). We can cancel the '3' from the first two fractions, and the '5' from the second and third fractions, leaving (2/1) * (1/1) * (1/10) * (6/8). This simplifies to (2 * 6) / (10 * 8) = 12/80. Reducing this fraction by dividing both numerator and denominator by 4 gives 3/20, which as a decimal is 0.15.

  3. If Dave drives at a steady speed of 50 miles per hour, how long will it take him to drive 10 miles?

    Answer: 12 minutes

    To find the time it takes to drive a certain distance at a steady speed, use the formula time = distance / speed. Dave drives 10 miles at 50 miles per hour. So, time = 10 miles / 50 mph = 1/5 of an hour. To convert this to minutes, multiply by 60 (since there are 60 minutes in an hour): (1/5) * 60 minutes = 12 minutes.

  4. John will be x in 7 years. How old was he last year?

    Answer: x - 8

    Let John's current age be C. The problem states that John will be x years old in 7 years, so C + 7 = x. Solving for C, John's current age is x - 7. To find his age last year, subtract 1 from his current age: (x - 7) - 1. Therefore, John was x - 8 years old last year.

  5. Find the slope: 4x - 5y =20

    Answer: 4/5

    To find the slope of a linear equation, rewrite it in the slope-intercept form, y = mx + b, where 'm' is the slope. Starting with 4x - 5y = 20, first isolate the y term by subtracting 4x from both sides: -5y = -4x + 20. Then, divide the entire equation by -5: y = (-4x / -5) + (20 / -5). This simplifies to y = (4/5)x - 4. From this form, the slope 'm' is clearly 4/5.

  6. Rex is four times as old as Ted. If the sum of their ages is 30, how old is Ted?

    Answer: 6

    Let Ted's age be T and Rex's age be R. The problem states that Rex is four times as old as Ted, so R = 4T. It also states that the sum of their ages is 30, so R + T = 30. Substitute the first equation into the second: 4T + T = 30. This simplifies to 5T = 30. Dividing by 5, we find that Ted's age (T) is 6 years.

  7. On a real number line, x =-4 and y = 7. What is the length of the line XY?

    Answer: 11

    The length of a line segment on a real number line between two points x and y is found by taking the absolute difference of their coordinates. Given x = -4 and y = 7, the length is |y - x|. Calculating this, we get |7 - (-4)|, which simplifies to |7 + 4|. This equals |11|, and the absolute value of 11 is 11. Thus, the length of the line segment XY is 11 units.

  8. Regie has enough flour to last for days. If he increases his use of flour by 25%, however, how many day's worth of flour will he have?

    Answer: 32 days

    The question is missing the initial number of days the flour would last. Assuming, based on the answer choices, that Regie initially had enough flour for 40 days, we can calculate the new duration. If he increases his use of flour by 25%, his daily consumption becomes 125% or 1.25 times the original amount. To find how many days the flour will last, divide the original number of days by the new consumption factor: 40 days / 1.25. This calculation yields 32 days.

  9. If x=3 and y = -1, then 3x squared + 2xy - 5 =?

    Answer: 16

    To evaluate the expression 3x^2 + 2xy - 5 with x=3 and y=-1, substitute these values into the expression. This gives 3(3)^2 + 2(3)(-1) - 5. Following the order of operations, first calculate the exponent: 3(9) + 2(3)(-1) - 5. Then perform the multiplications: 27 + (-6) - 5. Finally, perform the additions and subtractions from left to right: 27 - 6 - 5 = 21 - 5 = 16.

  10. 8.5 x 9.07 =

    Answer: 77.095

    To multiply 8.5 by 9.07, perform the multiplication as if they were whole numbers, then place the decimal point in the product. The numbers are 85 and 907. Their product is 77095. Since 8.5 has one decimal place and 9.07 has two decimal places, the total number of decimal places in the product must be 1 + 2 = 3. Counting three places from the right in 77095, the decimal point is placed to get 77.095.

  11. 54 is 75% of what number?

    Answer: 72

    To find the number of which 54 is 75%, set up the equation: Part = Percent × Whole. Here, the Part is 54, and the Percent is 75% (or 0.75 as a decimal). So, 54 = 0.75 × Whole. To find the Whole, divide 54 by 0.75: Whole = 54 / 0.75. This calculation yields 72. Therefore, 54 is 75% of 72.

  12. 8.26 x 76.8

    Answer: 634.368

    To multiply 8.26 by 76.8, perform the multiplication as if they were whole numbers, then place the decimal point in the product. The numbers are 826 and 768. Their product is 634368. Since 8.26 has two decimal places and 76.8 has one decimal place, the total number of decimal places in the product must be 2 + 1 = 3. Counting three places from the right in 634368, the decimal point is placed to get 634.368.

  13. 4 2/3 - 2 ½

    Answer: 2 1/6

    To subtract mixed numbers, first convert them to improper fractions: 4 2/3 becomes 14/3 and 2 1/2 becomes 5/2. Find a common denominator, which is 6, so the fractions become 28/6 and 15/6. Subtracting these gives 13/6, which converts back to the mixed number 2 1/6.

  14. Three people divide up a large pizza. If the first person gets half and the second person gets half as much as the first person, how much is left for the third person?

    Answer: 1/4

    The first person gets 1/2 of the pizza. The second person gets half of what the first person got, which is (1/2) * (1/2) = 1/4 of the pizza. In total, the first two people ate 1/2 + 1/4 = 2/4 + 1/4 = 3/4 of the pizza. To find what's left for the third person, subtract the eaten portion from the whole pizza: 1 - 3/4 = 1/4.

  15. If John scores 20% of his team's oint in a basketball game, how many points does the team score if John scores 14 points?

    Answer: 70

    If John scores 20% of his team's points and that amounts to 14 points, you can set up the equation: 0.20 * Total Points = 14. To find the total points, divide John's score by his percentage contribution. So, 14 / 0.20 equals 70. The team scored 70 points in total.

  16. 3/8 + 1/3 + 1/8 =

    Answer: 5/6

    To add these fractions, first combine the fractions with the same denominator: 3/8 + 1/8 = 4/8, which simplifies to 1/2. Now, add 1/2 to 1/3. Find a common denominator for 2 and 3, which is 6, converting the fractions to 3/6 and 2/6. Adding these gives 3/6 + 2/6 = 5/6.

  17. Written in scientific notation, the number 173,000,000,000 is:

    Answer: 1.73 x 1011

    To write a number in scientific notation, place the decimal point after the first non-zero digit, creating a number between 1 and 10. For 173,000,000,000, this becomes 1.73. Then, count how many places the decimal point moved from its original position (at the end of the number) to its new position. The decimal moved 11 places to the left, so the power of 10 is 11, making the scientific notation 1.73 x 10^11.

  18. If a recipe for cookies calls for ¾ of a cup of sugar, and you want to quadruple the recipe, how many cups of sugar will you need?

    Answer: 3 cups

    To quadruple a recipe means to multiply all ingredients by 4. If the recipe calls for 3/4 of a cup of sugar, you need to calculate (3/4) * 4. Multiplying the fraction by 4 gives (3 * 4) / 4 = 12/4. This simplifies to 3 cups of sugar.

  19. Which of the following numbers has the greatest absolute value: 17, -9, 15.5, -20, 19?

    Answer: - 20

    The absolute value of a number is its distance from zero on the number line, always represented as a positive value. For the given numbers: |17|=17, |-9|=9, |15.5|=15.5, |-20|=20, and |19|=19. Comparing these absolute values, 20 is the greatest, which corresponds to the number -20.

  20. Randy got the following test scores in science class: 76,98,78,80 and 54. What is the median test score?

    Answer: 78

    To find the median of a set of numbers, first arrange them in ascending order. The scores are 54, 76, 78, 80, 98. The median is the middle value in an ordered list. Since there are five scores, the third score (78) is the middle value, representing the median.