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Mathematics

Sample Questions

TEXAS SUCCESS INITIATIVE ASSESSMENT 2.

College Board

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Texas Success Initiative Assessment 2.

(TSIA 2 ) Mathematics Sample Questions

The TSIA2 Mathematics test covers four main categories:

• Quantitative Reasoning, which includes calculating ratios, proportions, and percents, as well as identifying, manipulating, and interpreting linear equations and expressions.
• Algebraic Reasoning, which includes solving equations (linear, quadratic, polynomial, exponential, rational, and radical), evaluating functions, and solving algebraic problems in context.
• Geometric and Spatial Reasoning, which includes converting units within measurement systems, solving geometric problems (perimeter, area, surface area, and volume), performing transformations, and applying right triangle trigonometry.
• Probabilistic and Statistical Reasoning, which includes classifying data, constructing appropriate representations of data, computing and interpreting probability, and describing measures of center and spread of data.

The Use of Calculators

When you take an actual mathematics test online, a basic, square root, or graphing calculator is allowed for some questions. If a question allows for the use of a calculator, a calculator icon will appear on the screen, along with the question. For each of the sample items in this packet, it is noted which calculator you can use— [basic] , [square root] , or [graphing] —to solve the problem.

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01689-

The area of the triangle above is 21. What is the value of x? [square root]

A. 3 B. 6 C. 7 D. 11

The formula for the volume of the right circular cylinder shown is V = πr^2 h.

If r = 2b and h = 5b + 3, what is the volume of the cylinder in terms of b? [basic]

A. 10 πb^2 + 6πb

B. (^20) πb^3 + 12πb^2

C. 20 π^2 b^3 + 12π^2 b^2

D. 50 πb^3 + 20πb^2 + 90πb

1. In triangle ABC, angle C is a right angle. If cos A = 85 , what is the value of cos B? [graphing]

A.

B. 85

C. 8

D. 8

x

x + 1

r

h

1. For which of the following values of x is the function

f(x) = 4 – x^2 NOT defined as a real number? [square root]

A. − B. 0 C. 2 D. 4

1. Under ideal conditions, the population of a certain

species doubles every nine years. If the population started with 100 individuals, which of the following expressions gives the population of the species t years after the population started, assuming that the population has been living under ideal conditions? [graphing]

A. 2 × 100^9 t

B.

t 2 × 100^9

C. 100 × 2^9 t

D.

t 100 × 2^9

1. If 7p − 4 = 8, what is the value of p? [basic]

A.

B.

C. 7

D.

1. In the xy-plane, the slope of the line y = mx − 4 is

less than the slope of the line y = x − 4. Which of the following must be true about m? [basic] A. m = − 1 B. m = 1 C. m < 1 D. m > 1

The bar graph above shows the number of customers who shopped at a store Monday through Thursday of one week. If the number of customers on Friday was a one-fifth increase from the number of customers on Thursday, how many customers shopped at the store on Friday? [basic]

A. 480 B. 500 C. 525 D. 600

The dot plot above identifies the number of pets living with each of 20 families in an apartment building. What fraction of the families have more than two pets? [basic]

A. 3

B. 1

C. 1

D. 9

Monday Tuesday Wednesday ursday

5 4 3 2 1 0

Number of Customers

(in hundreds)

CUSTOMERS AT A STORE

0 1 2 3 4

1. A history class is made up of 12 tenth graders and 9 eleventh graders. The tenth graders averaged 77 on the midterm exam, and the eleventh graders averaged 91 on the midterm exam. What was the average grade on the midterm exam for the entire class? [basic] A. 82 B. 83 C. 84 D. 85
2. Reyna has 5 coins worth 10 cents each and 4 coins worth 25 cents each. If she chooses two of these coins at random, what is the probability that the two coins combined will be worth at least 35 cents? [basic]

A. 5

B. 5

C. 13

D. 71

Rationales

1. Choice D is the correct answer. If n is the least of two consecutive odd integers, then the greater odd integer is n + 2. It then follows that the sum of the two consecutive odd integers is n + ^n^ + 2 h^ = 2 n + 2. 2. Choice D is the correct answer. Last year, a bakery sold w loaves of bread. This year, the bakery sold three more than twice the number of loaves of bread sold last year, which is 2 w + 3. Next year, the bakery plans on selling twice the number of loaves of bread sold this year, which is 2 2^ w + 3 h = 4 w + 6 loaves of bread. 3. Choice C is the correct answer. To find 25% of $130.00, multiply $130.00 by 0.25, which is $32.50. 4. Choice B is the correct answer. If Xiaoming has 20 eggs, and each batch of cookies uses 3 eggs, the number of batches can be found by dividing 20 by 3. This does not divide evenly, so the number should be rounded down to 6 because Xiaoming does not have enough eggs to make 7 batches ^ 7 # 3 = 21 h. 5. Choice B is the correct answer. The time it would take to fill the tub can be found by dividing the number of gallons the tub can hold by the rate the water runs from the pump. This is represented by 150 gallons ÷ 1.5 gallons per minute = 100. 6. Choice A is the correct answer. The expression 4 ^x + 5 h + 4 x + 8 can be expanded to 4 x + 20 + 4 x + 8 , which is equivalent to 8 x + 28. Since 4 can be factored from each term in this expression, it can be rewritten as 4 2^ x + 7 h. 7. Choice A is the correct answer. The expression ^ 3 x - 12 h ^^ x+ 4 h^ can be rewritten as 3 ^x - 4 h^ x + 4 h = 3 ^x^2 - 16 h, which after applying the distributive property becomes 3 x 2 - 48. Hence, 3 ^x^2 - 16 h^ and 3 x 2 - 48 are equivalent to ^ 3 x - 12 h^ x+ 4 h. A direct application of the distributive property shows that the expression 3 x x ^^ + 4 h - 12 ^x+ 4 h is also equivalent to ^ 3 x - 12 h^ x+ 4 h. By contrast, 3 ^x 2 - 8 x+ 16 h, which is equal to 3 ^ x - 4 h^2 , is not equivalent to ^ 3 x - 12 h^ x+ 4 h. For example, for x = 0 , the value of 3 ^ x - 4 h^2 is 48 and the value of ^ 3 x - 12 h ^ x+ 4 h is - 48. 8. Choice A is the correct answer. The y-intercept of a graph is the y-coordinate of the point where the graph intersects the y-axis. Setting x = 0 in the equation 1 2

y = 6 (^) ( x (^) – ) (x + 3)yields

y = 6 (^) ( – ) (3) = –9. Therefore, the y-intercept of the graph

of the equation is −9.

9. Choice C is the correct answer. The expression inside the parentheses,

x–5y ( (^) y 3 ) ,

can be rewritten as x–5y–2. Since the power of a product is distributed over each

factor, it follows that x–5y–2^ x^5 y^2

( ) =. 10. Choice D is the correct answer. The function f is not defined as a real number if the

expression under the radical is negative. For x = 4 , (^) f (4) = 4 – 42 = –12, which is not a real number. On the other hand, (^) f ( 2) =– f (2) = 4 – 4 =0,, and f (0) = (^4) – 02 = 2. Therefore, of the choices given, the function f is not defined as a real number for x = 4.

11. Choice D is the correct answer. At the start of the population, t = 0 , the population of the species was 100. Under ideal conditions, after nine years, the population will be 100 # 2 = 200 ; after nine more years, the population will be 200 # 2 = 400 ; and so on.

Hence, after 9 p years, where p is a positive integer, the population of the species will be 100 × 2p. Since the number of years elapsed, t, is equal to 9 p, it follows that p^ =^9 t. Therefore, t years after the population started, the population of the species will be t 100 × 2 9.

12. Choice C is the correct answer. If 7 p − 4 = 8 , then 7 p = 12 , so p = 7

13. Choice C is the correct answer. If an equation of a line in the xy - plane is in slope-intercept form, the slope is the coefficient of x, so the slope of the line y = mx - 4 is m, and the slope of the line y = x − 4 is 1. The slope of the line y = mx - 4 is less than the slope of the line y = x − 4 , so it must be true that m < 1. 14. Choice B is the correct answer. The area of a triangle can be calculated as half

the product of its base and height, 1 2

A = bh. Hence, the area of the triangle shown

is (^1) (x + 1)x 2 2 = x^2 +^ x.^ Since the area of the triangle is^21 , it follows that^ =^21 2

x^2 + x (^) ,

which is equivalent to x 2 + x - 42 = 0. Solving x 2 + x - 42 = ^x + 7 h^ x- 6 h = 0 for x gives x = - 7 , x = 6. Since the height of a triangle cannot be −7, the value of x must be 6.

15. Choice B is the correct answer. Substituting the values r = 2 band h = 5 b + 3 into the formula for the volume of the cylinder gives V = π(2b)^2 (5b + 3) = 4πb^2 (5b + 3) = 20 πb^3 + 12πb^2. 16. Choice C is the correct answer. If triangle ABC is defined as a right triangle, where

angle C is the right angle, then the cosine of angle A ^cos^ Ah^ is defined as the ratio

the length of the hypotenuse

the length of the side adjacent to angle A

. Since this ratio is defined as (^8)

, then the

length of the side opposite angle A, which is also the side adjacent to angle B, can be derived from the Pythagorean theorem: a 2 + 5 2 = 82 , where a represents the length of the side opposite angle A. Solving for a yields a 2 = 64 - 25 = 39 , so a = 39. Then, to determine the cosine of angle B, use the same ratio in relation to angle B:

cos B (^8)

the length of the hypotenuse

the length of the side adjacent to angle B = =.

17. Choice A is the correct answer. According to the graph, 400 customers shopped at the store on Thursday. The number of customers at the store on Friday was a one-fifth increase from the number of customers on Thursday. Thus, the number of customers on Friday was 400 + 15 (400) = 400 + 80 = 480.. 18. Choice B is the correct answer. According to the dot plot, families that have more than two pets have either three pets or four pets. Since 3 families have three pets and 1 family has four pets, a total of 4 families have more than two pets. Since there are a total of 20 families, the fraction of families with more than two pets is

20 , which is equivalent to 15.

19. Choice B is the correct answer. Since the 12 tenth graders averaged 77 on the midterm exam, the sum of their scores was 12 # 77 = 924 ; since the 9 eleventh graders averaged 91 on the exam, the sum of their scores was 9 # 91 = 819. Therefore, the sum of the scores of all 12 + 9 = 21 students in the class was 924 + 819 = 1 743, , and their average score on the midterm exam was 1,743 ÷ 21 = 83.