Critical Thinking Math HS Exit-Level Sample Questions Name: ____________________________________________ 1) Which of the following inequalities best describes the range of the graph below? A) -3 < x < 4 B) y < 4 2) 3) B) 9,000 - 30y 6) C) 2x + 3 D) 2x2 + 3x + 1 D) In the diagram below, two parallel roads, Elm Street and Oak Drive, are crossed by a third road, Walnut Street. Solve the following system of equations algebraically and check: 3x - 2y = 22 2x + 5y = 2 A) (6,2) B) (6,-2) 4) A triangular area of a rectangular parking lot is being turned into a recreational area for children. The dimensions are shown in the diagram below. Which of the following expressions represents the area of the parking lot after the recreational area is formed? A) 9,000 - 60y C) 60(150 - y) C) x < 4 D) -3 < y < 4 The area of a rectangle is 6x3 + 9x2 + 3x and one side is 3x. What is the length of the other side? A) 6x2 + 9x B) 2x2 + 3x 5) C) (-2,6) D) (2,6) As a fundraiser for their club, members sold magazine subscriptions. Juan, Steve, and Beth worked together. Juan sold six more than Steve. Beth sold half as many as Juan. What is an equation that can be used to find the number of subscriptions Steve sold if together they sold 39 subscriptions? 7) A) 2x + 6 + (x + 6) = 39 B) x + 6 + (x + 6) = 39 C) 2x + 6 + 2(x + 6) = 39 D) 2x + 6 + x = 39 8) What is the number of degrees in the acute angle formed by the intersection of Walnut Street and Elm Street? A) 54D B) 45D C) 16D D) 65D What is the slope of the linear equation 5y - 10x = -15? A) 10 C) -15 B) -10 D) 2 Jeannette was given a $100.00 gift certificate to a day spa. Each time she makes a trip to the spa (t) $15.00 is deducted from her gift certificate. What is an equation that can represent her balance (b) in terms of t? A) b = 100t - 15 C) b = 100 - 15t B) b = 100t + 15 D) b = 100 + 5t 9) A surveyor needs to find the width of the Arkansas River just north of Central City, Arkansas. Sighting a flagpole on the riverbank at the campground directly across the river, the surveyor walks 95 yards along the riverbank. If the line of sight to the flagpole from the surveyors new location is 64D, what is the width of the river? [Round to the nearest whole yard.] A) 42 yds C) 85 yds B) 46 yds D) 195 yds 11) Lydia plans to cover the three rectangular faces of a pillow with fabric. The pillow is in the shape of the right triangular prism below. How many square inches of fabric will Lydia need to cover all the rectangular faces of the prism? A) 360 in2 B) 204 in2 C) 300 in2 D) 420 in2 12) Rochelle bought a picnic table on sale for 50% off the original price. The store charged her 10% tax, and her final cost was $22.00. Rochelle would like to know the original price of the picnic table. What is an equation that can be used to solve the problem if x = the original price? A) 0.10(x + 0.50x) = 22 B) 0.10(x - 0.50x) = 22 C) 0.50x + 0.05x = 22 D) 22 + 0.10x = 0.50x 13) A company is making a 5-foot high cylindrical fish tank for the San Antonio Aquarium. The new plan is shown below. 10) What are the coordinates of the vertex of the given parabola after a reflection in the x-axis? A) (-1,4) C) (1,-4) B) (-1,-4) D) (4,1) What is the volume of the fish tank, to the nearest tenth of a cubic foot? 14) 15) Which one of the following histograms represents the table below? A) C) B) D) A forest ranger is trying to determine the distance across Lake Warren from point A to Point C as shown in the diagram below. She has drawn triangles using known distances so that AACB is congruent to ADEB. (a) Explain why hDBE is similar to hABC. (b) Write a proportion that could be used to find the distance between point A and point C. (c) Solve the proportion in part (b) to determine the distance in miles across Lake Warren along AC. [Show all work.]