CAASPP Math Practice Test (Gr11)
Where x is 4 and y is -2.35, calculate 1.13x + 21.5y + 13.22.
Simply plug the correct values into x and y. 1.13(4) + 21.5(-2.35) + 13.22 = 4.52 — 50.525 + 13.22 = —32.785
Ariel is comparing the costs of two different brands of paper towels, Brand A and Brand B. At $1.74 per roll, Brand B is the more affordable option. Brand A comes in 8-packs, whereas Brand B comes in 12-packs. The cost of a pack of Brand Bis is the same as the cost of a pack of Brand A. How much does Brand A cost each roll?
We must set up an equation to solve for the roll price of Brand A. We know that a pack of Brand B costs 12*1.74 = 20.88. We also know that this is what Brand A costs per pack. To find the per/roll price, we simply divide the pack price by the number of rolls 20.88/8 = 2.61.
For $115, a combat veteran and a senior citizen each purchase the identical vacuum cleaner model. They're both going to use their coupons, which say, "Veterans enjoy 20% off all store purchases!" and "senior discount 550!" respectively. Who has the better bargain?
The veteran pays 115-115*.2 = $92 (or 115*.8 = 92). The senior pays 115 - 50 = $65. The senior gets the better deal.
3 lbs. of ground beef costs $11.52 at one grocery. ”34 per ounce of ground beef,” reads a mistake on a price tag. What is the percentage increase in the price of 3 lbs. ground beef if the buyer calculates his price based on the wrong tag instead of the true price? To the nearest hundredth of a percent, round up.
First, find out the cost of the beef according to the incorrect tag. There are16 ounces per pound, so the correct formula is 16 f 3 = 48 ounces and we multiply this by price per ounce 48 f .34 = $16.32. To find percent increase use the formula:
incorrect value — initial value/ initial vcalue = 16.32-11.52/11.52 = 41.67%
Find the answer to x: 5 (x+3) = 3 (x—5)
First, distribute through both sets of parentheses 5x + 15 = 3x -15. Next, collect like terms 2x = ~30. Finally, x = -15.
Illuminate for the variable: 3x — (2x+3)2 = 5
First, rewrite the problem 3x~2(2x+3) = 5, this is unnecessary, but makes the problem easier to approach. Next, distribute the -2: 3x - 4x —6 = 5. Next, collect like terms: -x = 11. Finally, x = ~11.
Someone's unattended luggage slides out of an open hatchway aboard a helicopter at 30,000 feet. How much time does a recovery crew have to catch the luggage before it lands? (Assume the baggage is falling at 145 feet per second at its final velocity.)
Let y be height and x be seconds. Set up an equation to find how many seconds until the height is zero. 0 = 30000 — 145x, solve for x = 206.897. The provided solutions are given in minutes and seconds, so the 206.897 seconds must be converted. Divide 206.897/60 = 3.448 It is important to remember that the .448 does not represent seconds, but percent of a minute. There are 3 minutes and .448(60) = 26.88 seconds.
Is this a geometric or arithmetic sequence?
A geometric sequence uses multiplication to get from one value to the next. An arithmetic sequence uses addition to get to the next value. This sequence is arrived at by adding 2 to the proceeding value;
In the following sequence, extrapolate the 15th value.
0, 2, 4, 6, 8...
Since 15 is not that large, we can simply continue the series ...10, 12, 14, 16, 18, 20, 22, 24,
until arriving at the 15th value. It is also possible to notice that we have 10 values to project, each one adds 2 and use 10*2+8 = 28, where 8 is the 5th value in the series.
x = 10 and y = 35 in a straight variant. Write a formula for this relationship.
Given that y varies according to x, and that direct variation must pass through the point, (0, O), we can find the slope. m: ?y/?x = rise/run . Plug in 35/10 = 3.5 = m to the equation y=mx+b, where b=0.
What is the y-intercept and what does it represent in the following equation that predicts the revenue of a pizza
store over time?
y = 120x + 1500
To find the y—intercept, we plug 0 in for x. This leaves y = 1500 as the intercept, the answer must be C or D. By convention time is along the x—axis, but we could deduce this without knowing the convention. We have no basis for what 1500 would mean in terms oftime, and so must assume that y represents revenue.
Solve the system of linear equations below.
5.5x + 2 = ~15x ~3 + 4y
6x + 32y = 3
Collect like terms on the first equation to get 20.5x ~4y = 5 Now, find a multiple which allow us to cancel terms from the second equation. If we multiply equation 1 by 8, we get: 164x —32y = —40 we can add this to our other equation.
6x +32y = 3 The collected equation is 170x = -37. Now we simply solve x: -.218, plug this into either of the initial equations for x to get y: .135.
Another approach: Solve both equations in terms of y. Equation 1: y = 5.125x + 1.125.
Equation 2: y = .09375 ~ .1875x. Now set these equations equal to one another and solve for x = -.218 and y = .135.
Who do you think would be the least biased source for an article headed "Are casinos hurting our town?"
The man strolling by is thought to be the individual who is least affected by casinos. All of the other selections are purely personal.
Simon rides his motorcycle around a 4-meter-diameter circular track. His motorcycle wheels are meter in diameter. How many revolutions have his wheels made if he goes around 10 times?
Circumference is 2πr. We first want to find the circumference of the track. Since the diameter is 4, we know the radius is 2. Circumference = 2*π *2 = 4π. Now we want to know the circumference of the wheels. 2* ¼ * π = π/2. Next, since Jack circled the track 10 times, we conclude that he went 10*4π = 40π meters. Finally we divide this amount by how far his wheel travels per revolution 40π/π/2 = 80 revolutions.
Calculate the mean and median of the following collection of numbers:
17.6, 114.3, 13.2, 15.6, 15.7, 16.2, 899.5,
The mean is found with the sum of all values divided by the number of values. In this case:
(17.6 + 114.3 + 13.2 + 15.6 + 15.7 + 16.2 + 899.5 + 615.2 + 1.5)/2 = 1708.8/2 = 189.87 ≈ 190
The median is simply the middle value when they are put in order from least to greatest, in this case the median is the 5th value, or 16.2.
In the interval [0,6], which values are included?
The bracket before 0 indicates that 0 is in the set. The parenthesis after 6 indicates that only values up to, not including, 6 are included. This could also be written: 0 ≤ x < 6. Since no values below 0 are included, we can eliminate (C) as a possible answer because it includes - ½. We can also eliminate (D) because it includes 6. Since 2 π is 6.28, (B) is also eliminated.
Illuminate: 13 ≥ 3- |x+15|
This problem does not require solving completely. Begin by subtracting 3 from both sides to get 10 ≥ -/x+15/ . It is now clear that any input forx will produce a negative value for the right side of the inequality and this will be less than 10.
For the interval [-2, 3) choose the suitable alternative notation.
A bracket [ ] is equivalent to greater than or equal to or less than or equal to. Whereas parentheses ( ) are equivalent to greater than or less than; excluding the value attached to it. X is greater than or equal to -2, and less than 3.
Which of the following functions best fits the data?
Either enter the data points into a graphing calculator and draw a scatterplot, or draw a rough sketch of the data. The resulting graph should look U shaped, indicating a quadratic function.
8!/5! = (8*7*6*5*4*3*2*1/5*4*3*2*1).The 5, 4, 3, 2, and 1 all cancel out which leaves 8*7*6 = 336 for the first term. The second term is 6! = 6*5*4*3*2*1 = 720. The last term reduces to 6*5*4*3 = 360. Perform the indicated operations 336+720-360 = 696.