SBAC HS Math Prep

Algebra

Algebra 2

Geometry Measurements

Geometry Congruence

Mystery

100

Select the ordered pair that is a solution to the equation represented by the graph.

A. (2.1 , 0)

B. (0 , 0.6)

C. (− 1 , 1.8)

D. (− 2.5 , 3)

100

A student has a savings account with d dollars in it. The student plans to withdraw w dollars each month for n months.

Write an equation for the balance, b, in the account after n months.

b = d – wn

100

Sue wants to buy an air conditioner for her bedroom. She has been told that the air conditioner needs to have 20 BTUs (British thermal units) per square foot to cool her bedroom. Her bedroom measures 15 feet by 12 feet.

What is the number of BTUs needed to cool her bedroom?

3600 BTUs

100

Ron claims that the opposite sides of a quadrilateral are always congruent.

Which quadrilateral could be used to show that Ron’s claim is false?

A. non-square rectangle

B. parallelogram

C. rhombus

D. trapezoid

100

Which inequality represents all possible solutions of

−12d ≥ −6

d ≤ −1/2

d ≥ −1/2

d ≤ 1/2

d ≥ 1/2

d ≤ 1/2

200

The graph shows a quadratic function, f (x), and a cubic function, g (x). Select all values that are approximate solutions to the equation f(x)=g(x).

A. x =2

B. x =1

C. x =0.6

D. x = −0.3

E. x = −0.6

F. x = −1.4

D,F

200

What value of x that makes the equation true?

13/x = 2/(2−x)

26/15

200

Julie has a 20-gallon fish tank full of water that she needs to move from one room to another. She pours out all the water.

* The fish tank is a right rectangular prism.

* The fish tank weighs 225 pounds when it is filled with water.

* The dimensions of the water inside the fish tank are 30 inches by 12 inches by 12 inches.

* 1 cubic foot of water weighs 62.4 pounds.

What is the weight of the fish tank when it is empty, to the nearest pound?

200

Which pair of transformations is the same as a reflection across the y-axis?

A. a rotation of 90° counter-clockwise and a reflection across the x-axis

B. a rotation of 90° clockwise and a reflection across the y-axis

C. a rotation of 180° and a reflection across the x-axis

D. a rotation of 180° and a reflection across the y-axis

C. a rotation of 180° and a reflection across the x-axis

200

What expression is equivalent to

(x + 5)^2−(x − 3)(x + 5)

2x+10

−2(x − 20)

(x + 5)−(x − 3)

(x + 5)[(x+5)-(x-3)]

300

Determine no real solution, one real solution, or infinitely many real solutions for each of the following equations.

\sqrt(x) − 13 = −4

2sqrt(x) + 10 = 8

2/(x−1) = 3/(x+2)

sqrt(x) − 13 = −4

: One real solution

2sqrt(x) + 10 = 8

: No real solution

2/(x−1) = 3/(x+2)

: One real solution

300

Determine whether each function represents exponential growth or decay.\

f (x)= (3/4)^{x/2}

f (x)= (4/3)^x

f (x)= (5/6)^3x

f (x)= (8/3)^{x/3}

f (x)= (3/2)^{2x}

f (x)= (3/4)^{x/2}

: Decay

f (x)= (4/3)^x

: Growth

f (x)=(5/6)^{3x}

: Decay

f (x)= (8/3)^{x/3}

: Growth

f (x)= (3/2)^{2x}

: Growth

300

Lauren is building a swing set on a flat surface.

* The legs of the swing set are each 86 inches long.

* The distance between the legs on the ground is 58 inches.

* The horizontal support bar is 28 inches long and parallel to the ground.

How far from the top and along the legs Lauren should attach the horizontal support bar? Round to the nearest inch.

300

Which type of transformation is described by

(x , y) → (x + 2 , y + 3)

A. a translation 2 units to the right and 3 units down

B. a translation 2 units to the left and 3 units down

C. a translation 2 units to the right and 3 units up

D. a translation 2 units to the left and 3 units up

C. a translation 2 units to the right and 3 units up

300

Which pair of transformations is equivalent to the transformation described by

(x , y) → (x , − y + 1)

A. a reflection across the x−axis followed by a translation of 1 unit up

B. a translation of 1 unit up followed by a reflection across the x−axis

C. a reflection across the y−axis followed by a translation of 1 unit up

D. a translation of 1 unit up followed by a reflection across the y−axis

A. a reflection across the x−axis followed by a translation of 1 unit up

400

A car is tested to determine the speed at which the car achieves the greatest gas mileage. The quadratic model created to fit the experimental data is given as

f (x)= −6.02+1.50x−0.02x^2

where f is the gas mileage in miles per gallon and x is the car's speed in miles per hour.

What information does the quadratic model provide about the car's gas mileage?

A. The car's gas mileage is greatest at a speed of 37.5 miles per hour.

B. The car's gas mileage is capable of being greater than 22.105 miles per gallon.

C. The car's gas mileage decreases after reaching a speed of 22.105 miles per hour.

D. The car's gas mileage increases at a rate of 1.50 miles per gallon for every mile per hour increase in speed.

A. The car's gas mileage is greatest at a speed of 37.5 miles per hour.

400

The equation

f (x)= −(x + 7)^2+3

represents f (x) and the graph represents g (x).

Select whether each statement is True or False about the given functions.

* The line of symmetry of g(x) is x = 1.

* The maximum of g(x) is less than the maximum of f (x) .

* The value of x when f (x) is at its maximum is less than the value of x when g(x) is at its maximum.

False: The line of symmetry of g(x) is x = 1.

False: The maximum of g(x) is less than the maximum of f (x) .

True: The value of x when f (x) is at its maximum is less than the value of x when g(x) is at its maximum.

400

Lauren is designing a metal sculpture that contains a triangle with sides of 4 inches and 11 inches. She is trying to determine possible lengths of the third side of her design. Determine an inequality that shows all possible values, in inches, for the length of the third side of the triangle in Lauren’s sculpture.

A. 7 <x <15

B. 7 ≤x ≤15

C. 11 <x <15

D. 11 ≤x ≤15

A. 7 <x <15

400

Which description of a figure and its image match the transformation described by

(x , y) → (2x , 2y+1)

A. The figure and its image are similar, but not congruent, and then image has been translated 1 unit up.

B. The figure and its image are similar, but not congruent, and the image has been translated 1 unit to the right.

C. The figure and its image are congruent and the image has been translated 1 unit up.

D. The figure and its image are congruent and the image has been translated 1 unit to the right.

A. The figure and its image are similar, but not congruent, and then image has been translated 1 unit up.

400

Consider this function in explicit form.

f (n)=6+2(n − 1);n ≥1

Select the equivalent recursive function.

f (0)=4

f (n)=2f (n − 1); n ≥2

f (1)=4

f (n)=2f (n − 1); n ≥2

f (1)=6

f (n)= f (n − 1)+2; n ≥2

f (0)=6

f (n)=6+2f (n − 1)−1; n ≥2

f (1)=6

f (n)= f (n − 1)+2; n ≥2

500

Rose works a concession stand at a football game that sells whole pretzels and bottles of water.

* Each pretzel sells for $2.50 and each bottle of water sells for $1.00.

* Rose collected $135 in sales.

* Rose sold a total of 87 items at the past game.

What is the number of pretzels Rose sold at the game?

500

Jessica runs a shop that rents canoes and bicycles. Last week, she rented canoes and bicycles for a total of 140 hours. The rental cost for each canoe is $24 per hour, and the rental cost for each bicycle is $8 per hour. Jessica earned a total of $1632 last week from renting canoes for x hours and bicycles for y hours.

Write two equations in terms of x and y Jessica could use to determine how many total hours she rented canoes.

x + y = 140 or equivalent

24x + 8y = 1632 or equivalent

500

Kevin’s grandmother gave him an old lamp that needs a new lampshade. He wants to buy some fabric to make a new lampshade.

* The lampshade is 10 inches tall.

* The diameter of the top is 6 inches.

* The diameter of the bottom is 10 inches.

What is the area that is the best approximation for the amount of fabric he needs to buy?

A. 541.4 square inches

B. 474.1 square inches

C. 321.8 square inches

D. 256.3 square inches

500

Line x is parallel to line y. Line z intersects lines x and y.

Determine whether each statement is Always True, Sometimes True, or Never True:

m∠1+m∠4=180°

m∠5−m∠7=0°

z ⊥ y

∠2≅∠8

m∠2−m∠3=m∠1−m∠4

m∠1+m∠4=180°

: Always True

m∠5−m∠7=0°

: Always True

z ⊥ y

: Sometimes True

∠2≅∠8

: Always True

m∠2−m∠3=m∠1−m∠4

: Sometimes True

500

Consider this right triangle.

Determine whether each equation is correct. Select Yes or No for each equation.

sin(F) = 4.5/7.5

cos(F) = 6/7.5

sin(G) = 4.5/7.5

cos(G) = 6/7.5

sin(F) = 4.5/7.5

: No

cos(F) = 6/7.5

: No

sin(G) = 4.5/7.5

: Yes

cos(G) = 6/7.5

: Yes