Practice Test 1 - GED Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. A rhombus has diagonals of lengths 16 cm and 12 cm. If each side of the rhombus is extended by 20% while maintaining the rhombus shape, what is the area of the new rhombus?
2. Refer to the figure. A cone has a radius of $5$ cm and a height of $12$ cm. What is the lateral (side) surface area of the cone, in square centimeters? Leave the answer in terms of $\pi$.
3. Which statement best describes the effect of changing the equation $y=\dfrac{1}{3}x-2$ to $y=\dfrac{1}{3}x+4$?
4. A store marks up the wholesale price of an item by 35% to determine the retail price. If the wholesale price is $w$ dollars, which expression represents the retail price?
5. The equation $x^2 + 6x = 16$ can be solved by completing the square. What is the correct form after completing the square?
6. Given the system of equations below, what is the value of the expression $x + y$? $$3x - 2y = 19$$ $$2x + y = 8$$
7. An item's price $P$ is first discounted by $d$ percent. Then, a coupon for $C$ dollars is applied. Finally, a sales tax of $t$ percent is calculated on the new price. Which expression represents the final cost of the item?
8. The two-way frequency table below summarizes survey results of 200 adults about whether they prefer coffee or tea and whether they live in an urban or rural area. Based on the table shown, what is the probability that a randomly selected adult from this survey prefers tea, GIVEN that the adult lives in a rural area?
9. A recipe uses 3 cups of flour for every 5 cups of sugar. If a baker wants to use $s$ cups of sugar, which expression represents the number of cups of flour needed?
10. Use the figure shown. A right triangle has legs of 9 cm and 12 cm. A square is constructed on the hypotenuse, outside the triangle. What is the combined area of the triangle and the square?
11. Refer to the figure. A solid metal sphere of radius $6$ cm is melted and recast into small cylinders, each with radius $1$ cm and height $2$ cm. Assuming no metal is lost, what is the maximum number of complete small cylinders that can be made?
12. The graph shows the cost $C$ (in dollars) of renting a power washer for $h$ hours from two companies, Company A and Company B. Use the graph below to determine: For which number of hours will the two companies charge the same amount?
13. A survey found that 60% of people like coffee, 45% like tea, and 25% like both. If a person is selected randomly and is known to like tea, what is the probability that this person also likes coffee?
14. In a game, you win if you roll a sum of 7 or 11 with two dice, and lose if you roll a sum of 2, 3, or 12. For any other sum, you continue playing. What is the probability that the game ends on the first roll?
15. The coordinate plane below shows line $p$. Line $q$ (not shown) is perpendicular to line $p$ and has the same x-intercept as line $p$. What is the y-intercept of line $q$?
16. The graph of $y = 2x - 3$ is shifted 4 units up and 2 units to the left. What is the slope of the resulting line?
17. Use the table below. The table shows the grade points and credit hours for each course a student took in one semester. What is the student's GPA for the semester (weighted by credit hours), rounded to the nearest hundredth?
18. Carmen is purchasing $50 gift cards to give to each of her employees and also wants to buy one office coffee machine costing $280. If she spends a total of $1,080, which equation could be used to determine $e$, the number of employees?
19. If $g(x)=3x-7$, for which value of $x$ does $g(x)=11$?
20. The graph shown represents a linear function $f(x)$. What is the value of $x$ for which $f(x) = f^{-1}(x)$ (the intersection with the line $y = x$)?

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