SAT Practice #1 Flashcards: Math

26. Calc Allowed: Katarina is a botanist studying the production of pears by two types of pear trees. She noticed that Type A trees produced 20 percent more pears than Type B trees did. Based on Katarina's observation, if the Type A trees produced 144 pears, how many pears did the Type B trees produce? A) 115 B) 120 C) 124 D) 173

BACKSOLVE: *remember try middle answer choices first (B): 120→ 120 * 0.2 = 24 120+24= 144 pears total, so answer is correct ANSWER: (B) 120

19. Calc Allowed: A food truck sells salads for $6.50 each and drinks for $2.00 each. The food truck's revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day? A) 77 B) 93 C) 99 D) 105

BACKSOLVE: *start with middle answers (b) and (c) to realize whether you need to go bigger or smaller* →start by plugging in (b): 93 salads= 209 total-93= 116 drinks →93 ($6.50) + 116 ($2.00) = $836.50**** *happened to get correct answer, always plug middle answers in first! ANSWER: (B)

10. No calc: g(x) = ax^2 + 24 For the function g defined above, 'a' is a constant and g(4) = 8. What is the value of g(−4) ? A) 8 B) 0 C) −1 D) −8

BACKSOLVING: ***plug in numbers g(x) = ax² + 24 g(4) = 8 therefore, x=4, and entire equation=8 plug in: 8 = a (4)² + 24 (-24)8 = a(16) + 24(-24) *subtract 24* -16 = a (16) *divide by 16* a = -1 plug in: -1(-4)² + 24 -1(16) + 24 -16+24= 8 *ANSWER* CORRECT ANSWER: A. 8

27. Calc Allowed: A square field measures 10 meters by 10 meters. Ten students each mark off a randomly selected region of the field; each region is square and has side lengths of 1 meter, and no two regions overlap. The students count the earthworms contained in the soil to a depth of 5 centimeters beneath the ground's surface in each region. The results are shown in the table below. Which of the following is a reasonable approximation of the number of earthworms to a depth of 5 centimeters beneath the ground's surface in the entire field? A) 150 B) 1,500 C)15,000 D)150,000

**ENTIRE FIELD** →In a square of land 10m x 10m, the total meters is 100m². →In If you took the one region, 1m x 1m the total meters is 1m² " The area of the field is 100 square meters. Each 1-meter- by-1-meter square has an area of 1 square meter. Thus, on average, the earthworm counts to a depth of 5 centimeters for each of the regions investigated by the students should be about _1 of the total number of earthworms to 100 a depth of 5 centimeters in the entire field. Since the counts for the smaller regions are from 107 to 176, the estimate for the entire field should be between 10,700 and 17,600. erefore, of the given choices, 15,000 is a reasonable estimate for the number of earthworms to a depth of 5 centimeters in the entire field." ANSWER: (C) 15,000

25. Calc Allowed: h = − 4.9t² + 25t The equation above expresses the approximate height h, in meters, of a ball t seconds after it is launched vertically upward from the ground with an initial velocity of 25 meters per second. After approximately how many seconds will the ball hit the ground? A) 3.5 B) 4.0 C) 4.5 D) 5.0

*GRAPH ON CALCULATOR TO SEE WHERE THE GRAPH ITS ZERO* ANSWER: (D) 5

11. No calc: b = 2.35 + 0.25x c = 1.75 + 0.40x In the equations above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken? A) $2.60 B) $2.85 C) $2.95 D) $3.35

ALGEBRA/BACKSOLVING: SET EQUATIONS EQUAL TO SOLVE: 2.35 + 0.25x = 1.75 + 0.40x 0.6 = 0.15x *divide by .15 both sides* →change to 60/15 to make easier which =4 *QUESTION ASKS FOR BEEF →plug in 4 for the b=equation (b= beef) b= 2.35 +0.25(4) b = 2.35 + 1 b = 3.35 CORRECT ANSWER: D) $3.35

13. No Calc: If x > 3, which of the following is equivalent to 1 ⁻⁻⁻⁻⁻⁻ (1/x+2) + (1/x+3) A) 2x+5 / x²+5x+6 B) x²+5x+6 / 2x+5 C) 2x+5 D) x²+5x+6

PICK NUMBERS: *plug something in for x x=6 (goes into both 2 and 3) →eventually you get 1/(17/72) which you can divide by (or multiply by reciprocal) 1 * 72 -- -- = 72/17 1 17 *PLUG IN EASIEST TERMS FIRST C) x=17 D) x=72 *** from this you know is HAS to be (B) because you are trying to find 72/17 which is equal to (based on C and D) x²+5x+6 / 2x+5 CORRECT ANSWER: B) x²+5x+6 / 2x+5

7. No calc: m=(r/1,200)(1+r/1,200)^n _________________________________ (1+r/1,200)^n -1 The formula above gives the monthly payment m needed to pay off a loan of P dollars at r percent annual interest over N months. Which of the following gives P in terms of m, r, and N? A) (r/1,200)(1+r/1,200)^n ___________________ m (1+ r/1,200)^n -1 B) (1+ r/1,200)^n -1 ___________________ m (r/1,200) (1+ r/1,200)^n C) p= (r/1,200)m D) p= (1,200/r)m

PICK NUMBERS: r=1,200 n=1 *(no calc so use an exponent that is easy)* m=4 - plug in numbers to original equation to solve for p. - p=2 - now plug in numbers for each answer choice to find which equation lets p=2 CORRECT ANSWER: b.) (1+1)^1 -1 --------------- 4= 2-1 (1)(1+1)^1 ------- 4 = 1/2 (4)= 2 2^1

14. No calc: If 3x − y = 12, what is the value of 8^x / 2^y ? A) 2^12 B) 4^4 C) 8^2 D) The value cannot be determined from the information given.

PICK NUMBERS: remember: → x² * x³ = x⁵ but → (x²)³ = x⁶ STEP 1: *For this equation, you must choose x and y to fit the equation, 3x − y = 12. →X must = 5, and y must = 3 because if you plug them in 3(5) − (3) = 12 and 12=12. STEP 2: you have to plug in numbers to original equation, → 8^5 / 2^3 STEP 3: must give them matching bases. BOTH 2 AND 8 GO INTO 8 → 2^3 = 8, SO: 8^5 / 8^1 = ***8^4*** →THIS IS NOT AN OPTION, so you have to solve, to get 8^4. STEP 4: you know that (2³) is the original (8¹), so you can solve (8⁴) by multiplying (2³)⁴ = ***2^12*** CORRECT ANSWER: A) 2^12

21. Calc Allowed: The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group X consisted of 100 people who observed early bedtimes, and Group Y consisted of 100 people who observed later bedtimes. If a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to Group Y ? A) 68/100 B) 79/100 C) 70/164 D) 164/200

PROBABILITY= DESIRED OUTCOME -------------------------- TOTAL OUTCOME find desire outcome: 79 find total outcome: 39+125 and thats 164 ***79/164 ANSWER: (C) 79/164

7. Calc Allowed: The number of rooftops with solar panel installations in 5 cities is shown in the graph above. If the total number of installations is 27,500, what is an appropriate label for the vertical axis of the graph? A) Number of installations (in tens) B) Number of installations (in hundreds) C) Number of installations (in thousands) D) Number of installations (in tens of thousands

TENS OF THOUSANDS would mean that the 9 on the axis means 90,000, and if there are only 27,500 in total this cannot be correct. →If it were in thousands, a couple thousand added up each time would give you around 27,500 which is why the CORRECT ANSWER: C)

24. Calc Allowed: Which of the following is an equation of a circle in the xy-plane with center (0 , 4) and a radius with an endpoint (4/3 , 5)? A) x²+(y-4)²= 25/9 B) x²+(y+4)²= 25/9 C) x²+(y−4)²=53 D) x²+(y+4)²=53

→ graph on plane, and you'll see that you can use pythagorean theorem to fine 'c': / → (4/3,5) / | --- ↓ (0,4) pythagorean: (4/3)² + (1)² = c √c = 2.77 and 2.77= 25/9 ↓ → therefore it must be (A) OR (B) → In the point for the triangle, it is (0,4) which means in the equation it would be (y-4), making the answer (A) ANSWER: (A) x²+(y-4)²= 25/9

20. Calc Allowed: Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p ? A) 0.88p B) p/0.88 C) (0.8)(1.08)p D) p/(0.8)(1.08)

→Choose original price using 100% to make easier 100-20=pays $80 (with 6% sales tax) so it becomes $86.4 →THEN plug in 86.4 to see what gets you to 100% ANSWER: (D)

14. Calc Allowed: The table above lists the lengths, to the nearest inch, of a random sample of 21 brown bullhead fish. The outlier measurement of 24 inches is an error. Of the mean, median, and range of the values listed, which will change the most if the 24-inch measurement is removed from the data? A) Mean B) Median C) Range D) They will all change by the same amount.

→There are three different 12's on the graph next to each other which means if you are finding the mean even if the '24' is taken away, the mean would STILL be 12. →As for the range, that would mean the range would change from 16 to 8. →As for the mean (average) it would go from 12.47 to 11.3 CORRECT ANSWER: C) Range