Praxis study guide Math 5003
Danielle's third-period class began at 10:43 am and ended at 11:38 am. How long was the class? ****
55 minutes NOTE: One option to determine the length of the class period is to see how long it is from the start of class to the next full hour (from 10:43 am to 11:00 am), and then add the minutes part of the end time. In this case, 11:00 am can be thought of as 10:60 am so that subtraction with 10:43 is easy: 10 - 10 = 0, so 0 hours and 60 - 43 = 17, so it is 17 minutes until 11 am. Then, from 11:00 am to 11:38 am is 38 - 0 = 38 minutes. The total length of the class is 17 + 38 = 55 minutes. Another option to determine the length of the class period would be to reason that if it were an hour long and started at 10:43 am, it would end at 11:43 am. But this class ends at 11:38 am, five minutes before 11:43 am (43 - 38 = 5), and so this class is 5 minutes shorter than 1 hour, or 55 minutes long.
Mrs. Fields' science class takes care of a plant at school. The class is responsible for watering the plant and measuring its growth. The students' measurements are charted in the table. Which of the following equations relates the height of the plant, h, and the number of months, m, assuming a constant rate of growth?
5m+3=h NOTE: The difference between the growth of each month is 5 inches; looking at the growth of each month, the plant's height increases 5 inches each month. If the rate of growth is constant, then the beginning height of the plant is 3 inches; the height at the first month (8 inches) minus the growth of that month (5 inches) would equal 3 inches. If the growth of each month is 5 inches, then one can find the height of the plant by the growth of each month (5 inches) multiplied by the month (m) and then add 3 inches to account for the initial height.
Mrs. Smith surveyed her first grade class to ask what their favorite snacks were. She constructed the following pie chart. How many more students prefer ice cream than prefer fruit? Favorite Snacks Ice Cream 47.1% or 8 students Fruit 11.8% 0r 2 students Cookies 23.5% or 4 students Chips 17.6% or 3 students
6 NOTE: Eight students have ice cream as their favorite, while two have fruit as their favorite snack. Therefore six more students prefer ice cream than fruit.
What is the scientific notation of 674.9723? ****
6.749723 × 102 NOTE: 6.749723 × 102 is correct because the 2 notes that the decimal is moved 2 places to the right which is the original number.
What is the value of the expression below when x = 6? 7x + 3x ****
60 7 × 6 = 42 and 3 × 6 = 18 Then, 42 + 18 = 60 Another approach would be to combine like-terms and then multiply: 7x + 3x = 10x = 10 × 6 = 60
The data table shown describes how students get to school each morning at Memorial Middle School. If a student is drawn at random from the walkers and bus riders, what is the probability they are a walker? Transportation Number of Students Bus 148 Carpool 156 Walk 28 Bike 44
7/44 NOTE: The probability is (walk/walk+bus) so 28/176, which simplifies to 7/44.
What is the digit in the hundreds place in the product of 63 × 31? **** 1953
9 NOTE: 63 × 31 = 1953. The digit that occupies the hundreds place is 9.
composite number
A number with more than two factors
prime number
A whole number that has exactly two factors, 1 and itself.
Rational Numbers
All positive and negative integers, fractions and decimal numbers.
A mathematics teacher determines that the median score for the most recent test was 80 percent. Which of the following is the most accurate interpretation of the result?
Half the students scored an 80 percent or below. NOTE: Median is the middle number in a data set. It is calculated by arranging the numbers from least to greatest and finding the number in the middle; if there is not one middle number, then the median is the average of the two numbers. For example, in the data set 1, 2, 3, 4 the median is 2.5 because 2.5 is the average of 2 and 3. If the median score is 80, then it can be assumed half the students scored below 80 and half the students scored above 80.
Maria solved a word problem and correctly gave 72 as the answer. Which of the following could not have been the question asked?****
How many months did Alexa achieve perfect attendance last year? NOTE: The number of months in a year can not exceed 12. Therefore, 72 can not be the answer.
Which terms best describe the triangle shown?
Scalene Scalene triangles have all sides of different length. Right Right triangles contain a right (90 degree) angle.
Ellie is getting a new rug for her room. Her old rectangular rug is 5 ft by 7 ft. Her new rug is circular with a diameter of 7 ft. How is the size of the new rug related to the old one?
The new rug is about 3.5 ft² larger than the old one. NOTE: Ellie's original rectangular rug has an area of 7 × 5 = 35 ft². Her new circular rug has a diameter of 7 ft and, therefore, a radius of 3.5 ft. The area of her new rug will be: A = π(3.5)² ≈ π(12.25) ≈ 38.5 ft². So, the new rug is about 38.5 - 35 = 3.5 square feet larger.
Elona is writing an essay. She writes 3 pages every hour. If her essay is 10 pages long, how many hours did she spend writing? In the situation above, what is the dependent variable?
The number of pages Elona writes. NOTE: The number of pages she writes depends on how long she spent writing. If you think about the number of pages Elona writes and how many hours she spends writing as a cause and effect relationship, the number of hours she spends writing is the cause, which determines the number of pages she wrote, the effect.
The number of tennis shoes, t, in a dorm is 12 more than 5 times the number of dress shoes. Which of the following represents the number of dress shoes in the dorm in terms of t?
d= t−12/5 The problem gives the information in terms of dress shoes: t=5d+12. Subtract 12 from each side: t−12=5d. Divide both sides by 5 for a final answer.
A student was given the following equation. 4(2x+3)+8x=924(2x+3)+8x=92 In solving this problem for x the first step of a student's solution is 4⋅2x+4⋅3+8x=92 4⋅2x+4⋅3+8x=92. Which of the following is the justification for this step? ****
distributive property NOTE: The distributive property allows one to multiply 4 by the sum of 2x + 3 by first multiplying 4 by each term in the sum and adding the result.
real numbers
have a specific value
Students are working with a set of rulers and a collection of objects from around the classroom. Which of the following concepts are these students most likely investigating?****
length Rulers are used to measure length.
Irritational number
must use symbols or be approximated
Solve the inequality: 9x - 8 > 24 - 7x
x > 2 NOTE: Simplification of the expression 9x - 8 > 24 - 7x can begin in multiple ways, but the simplest is to add 7x to each side. Adding a quantity never causes a change in direction of the inequality sign, so the resulting statement is 16x - 8 > 24. Next, 8 can be added to each side of the problem, resulting in 16x > 32. Finally, x will be isolated when 16 is divided from each side. Division by a positive number does not result in a change in the direction of the inequality sign, so the final answer is x > 2.
Which of the following equations is written in slope-intercept form?
y=3x+5 NOTE: Slope-intercept form of the equation of a line is y=mx+b where m and b are numbers representing the slope of the line and its y-intercept, respectively.
Which of the following equations correctly models the relationship in the table? x y 1 -2 3 4 5 10 9 22
y=3x−5 NOTE: This equation correctly models the relationship in the table. Anytime the x value in the table is substituted for the "x" variable in the equation, the y value in the table is the result of the equation. 10 = 3(5) - 5; 22 = 3(9) - 5.
Which of the following linear inequalities best represents the graph shown?
y≥3x−5 NOTE: The graph has a solid line, meaning the points that fall on the line are solutions to the inequality and the inequality symbol contains an "or equal to" line. The area above the line is shaded, meaning the inequality symbol is greater than or equal to, or ≥. Since all the slopes provided are the same (3) this is the only choice that can be correct.
Which of the following is equivalent to the expression below? 2x+4y−3x+6 ****
−x+4y+6 In the expression, 2x and -3x are like terms and therefore can be combined by adding the coefficients and keeping the variables the same: 2x and -3x is -x. The 4y and 6 cannot be combined, and are therefore left as is.
Ari spent half of the money in his checking account. He then deposited $75.00 and later withdrew $15.00. His new balance is $120.00. How much money did Ari have in his account to begin with? (Note: no other transactions were made and no interest accrued.)
$120.00 NOTE: Making an equation out of this would be x+75−15=120x+75−15=120, where x is what remained after spending half of the amount. Therefore, after spending half the amount, x=60. Since he spent half the money, the initial amount is 2 times this amount: 2x=2(60)=120 2x=2(60)=120.
The Booster Club at Martin MS is selling spirit buttons for homecoming. The buttons cost $0.75 to make and will be sold for $2 each. How many buttons, b, must be sold to make a profit of $500? ****
$500 = $2b - $0.75b NOTE: The profit is equal to the selling price minus whatever costs are applicable. So, if the profit is to be $500, then enough buttons must be sold to reach that profit. If we are selling the buttons for $2 each, but it costs $0.75 to make each one, then there is a profit of $2 - .75 or $1.25 on each button.
Which ordered pair is between the x-axis and the line j?
(2, 3) NOTE: Line j is a horizontal line through the point (0,5) on the y-axis. This is the graph of the equation y = 5. Only point (2,3), in quadrant I, is between the x-axis and line j.
What is the prime factorization of 36?
(2²) × (3²) NOTE: The prime factors of a number are the prime numbers that divide the integer exactly. The prime numbers then can be multiplied together to equal that number. The prime factors of 36 are (2²)*(3²). For 36, the factor tree would be: 36 = 4 × 9 = (2²) × (3²).
Simplify the expression: 30−2×50+70
0 NOTE: To simplify the equation, follow the order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction (PEMDAS), and work left to right for each step. There are no parentheses nor exponents, so multiplication/division would come first. The steps to simplify the expression would be: = 30 - 2 × 50 + 70 = 30 - 100 + 70 = -70 + 70 = 0
Which of the following has the least value? ****
0.0518 NOTE: This has the least value of the set. The tenths place has a 0 while the other numerals have a 5 in the tenths place.
Use the following conversion factors to answer the question below. 1 Pa = 0.00750062 mmHg (at 0°C) 1 atm = 1.01375 x 105 Pa During an experiment, a student measures and records a pressure of 1.20 x 105 Pa. What is this pressure in atmospheres and millimeters of mercury at 0°C?
1.18 atm and 900 mmHg NOTE: Set up a ratio to convert units from Pa to atm and another ratio to convert from Pa to mmHg.
Last week, a round-trip plane ticket from New York City to Chicago cost $118. Today, the same ticket costs $130. What is the percent change of the ticket price from last week to today?
10% increase To find percent change, set up and solve a proportion: original/change= 100/%. To go from $118 to $130, there was a $12 increase in price, so the change is 12. The original price of the ticket is $118, so the proportion can be set up as follows: 118/12=100/x. Cross multiply and divide to solve the proportion: 1200 = 118x → 10.17 = x → 10% increase.
The circle graph shows the results of a survey of 150 students. How many students chose basketball as their favorite sport?****
12 NOTE: To find how many students a slice represents, multiply the percentage by the total. According to the graph, 8% of the total (150) students chose basketball as their favorite sport. In decimal form, 8% is represented by .08 so use 150×.08=12150×.08=12 students. To solve using mental math: For the first 100 students, 8% = 8 students. For the remaining 50%, 8% = 4 students. This means 12 students total.
In an omelet made of only cheese and eggs, the ratio of ounces of cheese to omelette is 2 to 7. How many ounces of egg are needed to make the jumbo 21-ounce omelet?
15 ounces NOTE: In every 7 ounces, 2 ounces are cheese and 5 ounces are egg. Multiply by 3 for the jumbo omelet to find that 15 ounces of egg are needed.
During a trip to Mexico, a traveler noticed that 10.00 US dollars were worth 191.42 pesos. Based on this exchange rate, 300.00 pesos are worth approximately how many US dollars?
15.67 Set up a proportion and solve: 10.00 US dollars/191.42 pesos= 300 pesos/191.42 pesos 10.00 US dollars=300 pesosx 3000=191.42 3000=191.42x (divide both sides by 191.42) x≈15.67 US dollars
Which of the following is the greatest common divisor of 3300 and 1050?****
150 NOTE: The prime factors of 3300 are 22 · 3 · 52 · 11 and the prime factors of 1050 are 2 · 3 · 52 · 7. The prime factors that are common to the two numbers are 2 · 3 · 52 = 150.
If the 5th term in a geometric sequence is 162, and the common ratio is 3, what is the first term in the sequence?
2 NOTE: 2 comes from seeing that the sequence is shown to have n = 5, r = 3, and A(5) = 162, where A(n)=a1rn−1 and A(n) is the nth term, a1 is the first term, r is the common ratio and n is the term number. The question is answered correctly by keeping a variable expression in the place of a₁ and inputting all known values so that the formula becomes A(5) = 162 = a₁(3)⁵⁻¹. This equation will be simplified as far as possible and then solved for a₁. When the order of operations is followed correctly, exponents will be simplified before any multiplication occurs. The resulting equation becomes 162 = a₁(3)⁴ and then 162 = a₁(81). The final answer is found by dividing 81 on each side of the equation in order to isolate the unknown a₁. The quotient of 162 and 81 is 2, and so a₁ = 2. KEEP DIVIDING IT DOWN TO THE LAST WHOLE NUMBER
What is the surface area of the figure when folded into a three-dimensional shape? 2cm side of a cube
24 cm2 NOTE: The figure folds into a cube with each side measuring 2 cm. The surface area of a cube is equal to 6 × a². Therefore the surface area is equal to 6 × 2² = 24 cm2.
If the result of performing all four of the steps below is 28, what value was chosen for b? Step 1: Select a number, b Step 2: Divide b by 3 Step 3: Subtract 5 from the result Step 4: Multiply the result by 7 ****
27 NOTE: Work the steps in reverse order from the final answer to find the starting value, using the inverse of the operation presented in each step. From step 4: 28÷7=4 28÷7=4 From step 3: 4+5=9 4+5=9 From step 2: 9×3=27 9×3=27, giving a value of b=27.
What is 5/18 as a percent?
27.78% NOTE: To convert a fraction to a percent, divide the numerator by the denominator and multiply by 100. 5 ÷ 18 = 0.2778 × 100 = 27.78%
Which of the following is an example of the commutative property of multiplication?****
2×8=8×2 NOTE: The commutative property of multiplication states that it does not matter the order of the multiplication sequence, the answer will be the same. This can be represented by the equation a×b×c=c×b×a.
A pancake recipe requires 1 tablespoon of baking powder per 2 cups of flour. If 2 cups of flour make 4 pancakes, how many tablespoons of baking powder are needed to make 12 pancakes?****
3 NOTE: 1 tablespoon of baking powder per 2 cups of flour makes 4 pancakes -> 1 tablespoon of baking powder is used to make 4 pancakes. To make 12 pancakes, 3 tablespoons of baking powder are needed. To find this, divide 12 by 4 to the proportional increase in pancakes. 12 / 4 = 3 -> because the number of pancakes is 3 times as many as the recipe size of 4; multiply 1 tablespoon by 3 to get 3 tablespoons of baking powder.
Consider the algorithm below: Step 1: Select a numerical value for n. Step 2: Subtract 4 from n. Step 3: Square the result Step 4: Multiply the result by 3 Step 5: End Which of the following is an equivalent algebraic expression?
3(n-4)2 NOTE: The key steps are #3 and #4. Only (n-4) is squared and then multiplied by 3.
Jessie draws a marble from the bag shown and then, without replacing the first marble, he draws a second one. Which expression shows the probability that he drew a red marble both times?
3/10 • 2/9 NOTE: This is an example of dependent events. P(red) = 3/10 for the first draw. However, the first marble is not returned to the bag, changing our sample to 9 marbles. If the first marble drawn was red, that leaves only 2 red marbles, so on the second draw, P(red) = 2/9. The probability of both events happening is the product: 3/10 • 2/9.
Put the following fractions in order from least to greatest: 1/2 3/4 5/7 3/16
3/16 1/2 5/7 3/4 NOTE: The easiest way to order these is to convert them to decimals and round to the hundredths place: 1/2 = 0.5 3/4 = 0.75 5/7 = 0.71 3/16 = 0.19 Then order the decimals and pair with their fraction equivalent.
What is the value of the "3" in the number 17,436,825? ****
30,000 NOTE: In a base 10 system, each place location for a number has a value that is a power of 10. Specifically, the ones place is properly understood to be 10⁰ (because any nonzero number raised to the zero power equals 1). The tens place is 10¹, the hundreds place is 10², the thousands place is 10³, etc. When a digit is in a specific position, its value is equal to the product of that digit and the power of 10 that is assigned to its position. Therefore, in the number 17,436,825, the 3 represents 3×104=30,0003×104=30,000.
A field trip to the planetarium is being planned. Mrs. Weir is the principal and needs to know how many buses to take. If each bus will hold 16 people, which equation should she use to reserve the correct number?****
350/16 ≈ 22 NOTE: This is an example of a situation in which an overestimation is required. A bus can carry only 16 people. So, 21 buses will not allow for everyone to have a ride and it does not make sense to take a fraction of a bus. Therefore, 22 buses must be taken.
If the pattern below is continued, how many blocks will be in the 7th term? 1= 3 2= 6 3= 10 4= 15
36 NOTE: The first model is made with three blocks, 1 in column 1, and 2 in column 2; the second term is made of 1 block in column 1, 2 blocks in column 2, and 3 blocks in column 3. So, term #1 = 1 + 2 blocks; term #2 = 1 + 2 + 3 blocks; term #3 = 1 + 2 + 3 + 4 blocks. Each term, n, is the sum of the numbers from 1 to (n + 1); the sum of the consecutive integers from 1 to (n + 1). So, the 7th term would be: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 or 36 blocks. This is a small enough number that you could actually sketch the model and count the blocks.
Kaitlyn wants to call her best friend, Kirby, after Kirby finishes her work at 5:00 PM, but Kaitlyn is on a work trip in another time zone. If Kaitlyn's 4 ½ hour flight took off at 7:45 AM and she landed at 10:15 AM local time, at what local time can she call Kirby?
3:00 PM NOTE: There is a 2 hour time difference because Kaitlyn would have landed at 12:15 PM in her original time zone. Kaitlyn is 2 hours behind, so she can call at 3:00 PM.
Simplify the expression: 4(10)3 ****
4000 NOTE: The 10 must be cubed first (order of operations) and then multiplied by 4. 4(10)3 = 4(1000) = 4000
How many hectoliters are in 45 kiloliters?
450 There are 450 hectoliters in 45 kiloliters because 1 hectoliter is equal to 100 liters.
The west wall of a square room has a length of 13 feet. What is the perimeter of the room?****
52feet NOTE: A square has four sides of equal length. Perimeter is the total distance around an object. To find the perimeter of a square, follow the formula P=4s, where P = perimeter and s = the length of a side of the square. In this case, P=4(13)=52 ft.
