### Algebra, Functions, and Patterns

- What is the value of
*j*in the formula*j*= 2(4*h*– 3*w*)^{2}where*h*= 3 and*w*= 2? Mark your answer in the circles in the grid. - On an exam, Bart is asked to choose two ways to determine n% of 40. He is given these four choices:
*n*÷ 100 × 40- (
*n*× 0.01) × 40 - (
*n*× 100) ÷ 40 - (
*n*÷ 0.01) × 40

- I and II
- I and IV
- II and III
- II and IV
- III and IV
- Terrell is paying a math tutor a $30 one-time fee plus $40 per hour for time spent tutoring. Which of the following equations tells how to find
*x*, the total amount Terrell will be charged for*h*hours?*x*= $30*h*+ $40*x*= $30 + $40*h**x*= ($30 + $40)*h**x*= $30*h*– $40*x*= ($30 – $40)*h*

- Which expression gives the area of this triangle?
- 7
*x* - 12
*x* - 6
*x*^{2} - 12
*x*^{2} - 12
*x*^{3} - Serena has to choose between two jobs. One is at Books R Us and pays $18,000 with yearly raises of $800. The other, at Readers Galore, pays $16,400 per year with yearly raises of $1,200. In how many years will the two yearly salaries be equal?
- 6
- 5
- 4
- 3
- 2

- When you know the temperature in degrees Celsius (°C), the formula that tells you how to find degrees in Fahrenheit (°F) is °F = C + 32°. According to the formula, which of the following is NOT true?
- 212° F = 100° C
- 86° F = 30° C
- 50° F = 10° C
- 32° F = 0° C
- 0° F = 32° C

- Bernie's monthly rent is
*r*. For each day he pays the rent before it is due, he is given a small discount. Which equation tells how the value of*r*depends on the value of*d*, the number of days early that Bernie pays his rent? *r*= $485*d*– $3*r*= ($485 + $3)*d**r*= ($485 – $3)*d**r*= $485 + 3*d**r*= $485 – $3*d*- The point (2,2) is on a line that passes through the origin (0,0). What is the point on this line that has a
*y*-coordinate of –5? Mark your answer on the following coordinate plane grid. - The simple interest formula is interest earned = principal × rate × time, or
*I*=*prt*. Maria leaves $3,500 in the bank for 1 year and 6 months. If the total interest earned is $210, what is the interest rate?- 2%
- 3%
- 4%
- 5%
- 6%

- Crystal keeps her winter clothes in two storage boxes during the hotter months. Each edge of the larger box, including the height, is 1.25 yards long. Each edge of the smaller box is 1 yard long or high. By about what percent is the volume of the larger box greater than the volume of the smaller box?
- 150%
- 95%
- 66%
- 50%
- 33%

Which two ways are correct?

### Answers

**b.**$224.99 is greater than $220 but less than $225 (i.e., $224.99 is less than halfway between $220 and $230), so $224.99 rounded to the nearest $10 is $220.**d.**Look at the numbers in the tens place: 7, 6, 0, and 8. Placing these numbers on a number line, start at zero to order them from least to greatest.**b.**$589.86 – $18.12 – $50.43 + $40.11 = $561.42.**d.**Add the cost of the shirts (3 × $16), the cost of the sweatshirts (2 × $22), and the shipping cost ($11).**b.**$22 ÷ 4 (Chris plus his three friends) = $5.50.**d.**Denise is the fastest runner because she ran the greatest distance. Rewrite the fractional distances greater than 1 mile using the greatest common denominator: 8. . Now, compare numerators. The greatest numerator is 6, so is the greatest distance.**d.**Round each distance to the nearest whole number: rounds to 0; rounds to 3; rounds to 2. Then, add the numbers: 0 + 3 + 2 = 5.**d.**II: The discounted price = 75% of the original price = 0.75 × $250. IV: The discounted price = (100% – 25%) of the original price = (100% – 25%) × $250 = (1 – 0.25) × $250.**b.**Amount going to taxes = $300 + $100 + $124 = $524; gross earnings = $2,000; percent going to taxes = ($524 ÷ $2,000) × 100 = 26.2%, which rounds to 26%.**d.**You are looking for n, and = or n = × 200,000. 25 of the 200,000 sample population bicycle to work. × 200,000 = 80,000.**a.**(15.5 – 14) ÷ 14 = 0.107 = 10.7%, which rounds to 11%.**d.**Only kilometers is a metric measurement used to measure distances between cities. One kilometer is a distance of about 0.6 miles. A distance of 135 kilometers is equal to a distance of about 81 miles.**a.**10:30 A.M. to 5:30 P.M. is a seven-hour period. Mike can give 13 lessons, each lasting 30 minutes, if he takes 30 minutes for lunch. $20 × 13 = $260.**b.**2 feet = 24 inches = yard = yard. You can also think that 3 feet = 1 yard, so 2 feet = yard.**b.**Total owed = $7,000 + ($7,000 × 0.05 × 1.25) = $7,437.50. For this question, it may be easier to work using fractions, rather than decimals: total owed = $7,000 + ($7,000 × ) = $7,437.50.**d.**Width of copy/width of original = height of copy/height of original: = 3.2.**a.**, or map distance in inches/actual distance in miles.**e.**20 seconds = minutes = minute. Now, divide the available minutes on the CD (75) by the length of one song (2).**c.**Each of the three angles has an equal measure because each of the sides has an equal measure (4 inches). The sum of the three angles is 180 degrees.**c.**An estimate using the Pythagorean relationship gives a length of a little more than 5 meters: .**e.**Number of tiles equals area of pantry (in square feet) divided by area of a single tile (in square feet): area of pantry = 6 × 4 square feet; area of single tile = × square foot.**a.**The volume of a rectangular solid is found by multiplying the length times the width times the height, where each dimension is in the same unit: 25 feet × 16 feet × 0.5 feet (6 inches is written as 0.5 feet).**d.**Slope equals change in y value divided by change in*x*value: (1 – 0) ÷ (5 – 2).**e.**The mean of 80 and 100 is 90; the mean of 80, 90, and 100 is also 90. The median of 80 and 100 is 90; the median of 80, 90, and 100 is also 90. The range of 80 and 100 is 20 (100 – 80); the range of 80, 90, and 100 is also 20. Neither set has a mode.**b.**For the lowest score Avi needs to get an A, assume his final average is 88. Average = (90 + 80 + 85 + a) ÷ 4 = 88. To find a, multiply 88 by 4. Then subtract Avi's first three scores: 88 × 4 = 352; 352 – (90 + 80 + 85) = 352 – 255 = 97.**d.**If you connect the dots, the two lines would cross at about 55° F. The number of sales of each drink at this point is about 375.**e.**This would be about 650 servings, which is halfway between 750 (at 40° F) and 550 (at 50° F).**c.**To determine the average speed, divide the miles traveled during the first 5 hours (175 miles) by the time of travel (5 hours). 175 miles ÷ 5 hours = 35 miles per hour.**c.**You can determine this by finding the point on the graphed line above the 1-hour point on the horizontal axis, which is about 50 miles.**d.**In 2000, 70% of women voted, and 70% of 36,200 = 0.7 × 36,200 = 25,340. In 2000, 60% of men voted, and 60% of 40,400 = 0.6 × 40,400 = 24,240. Female voters – male voters = 1,100, which is closest to 1,000.**a.**Ricardo spends 11% for his car, half of the 22% he saves. (You can use % for the pie chart values without doing any additional math, since the values are out of 100 already.)**a.**Savings and housing together make up 50% of Ricardo's budget: 22% + 28%.**c.**Ricardo spent 6 cents more per dollar on housing than on food: 28 – 22 = 6. 6 cents is 6% of each budgeted dollar. $46,500 × 0.06 = $2,790, which is about $2,800.**d.**Hillary, Mark, and Jomarie together have three chances. Probability = .**b.**Jack is likely to make × 25 = 10 of his next 25 free-throw attempts.**a.**Percent means "out of 100 equal parts." The term*n*% can be written as or as 0.01*n*, which is equal to*n*× 0.01.**b.**The one-time fee is $30, and the charge for working*h*hours is $40*h*. Add $30 and $40*h*to find*x*:*x*= $30 + $40*h*.**c.**The area of a triangle = × base × height = (4*x*)(3*x*) = (12*x*^{2}) = 6*x*^{2}.**c.**Each job will pay $21,200 after 4 years. You can see this by making a chart:**e.**If °C = 32, then (32°) + 32° = F, not 0° F.**e.**This equation matches the table. When d = 0,*r*= $485: $485 – $3(0) = $485. When*d*= 1,*r*= $482:*r*= $485 – $3(1) = $482; and so on.**c.***I*=*prt*can also be written as*r*=*i*÷ (*p*×*t*).*r*= $210 ÷ ($3,500 × 1.5) = $210 ÷ $5,250 = 0.04 = 4%.**b.**The volume of the larger box = 1.25^{3}, which is about 1.95 cubic yards. The volume of the smaller box = 1^{3}, or 1 cubic yard. 1.95 is 95% larger than 1.

Three pounds divided into -pound pieces equals 12: 3 ÷ = 3 × 4 = 12. You can also think about the question this way: Alexia can make four quarter-pound pieces from one pound of chocolate. With three pounds, she gets three times as much: 4 × 3 = 12.

= 37.5% ( × 100% = 37.5%); 80% – 37.5% = 42.5%.

*d* = *r* × *t*; *d* = 4.5 mph × 5 hours = 22.5 miles.

Remember that any two angles whose measures add to 90 degrees are complementary angles. 90° – 55.3° = 34.7°.

A parallelogram has two pairs of parallel sides. You can easily determine the fourth vertex by visually identifying where the lines must meet. Remember, opposite sides are parallel and have equal length.

*j* = 2(4 × 3 – 3 × 2)^{2} = 2(12 – 6)^{2} = 2(6)^{2} = 2(36) = 72.

This line passes through the origin and has a slope of +1. For every point on this line, the *x* value is equal to the *y* value.

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