Full Practice Exams — Exam 14

Questions in this quiz (45)

1. Olivia is mapping her most recent run. She decided to place Elm Street on the x-axis and Oak Street on the y-axis. She ran 50 m at an angle of $$30^\circ$$ relative to Elm Street, then ran 120 m at an angle of $$60^\circ$$ relative to Elm Street and finally ran 40 m directly north on Oak Street. How many meters north of Elm Street did Olivia run?

   • 168.92
   • 120.00
   • 65.92
   • 103.92

2. A large cylindrical tank with a radius of 6 feet feeds water into three smaller tanks of equal size. Each of the smaller tanks allows exactly one-third as much water to flow as the large tank. What is the radius of one of the smaller tanks?

   • $$12$$
   • $$12\sqrt{36}$$
   • $$2\sqrt{3}$$
   • $$\sqrt{3}$$

3. If you add up 5 consecutive even integers that are each greater than 20, what is the smallest possible sum?

   • 124
   • 172
   • 130
   • 128

4. The function $$f(x) = x^3 - 4x^2 + 6x - 3$$ and a line $$k$$ are drawn in the standard $$(x, y)$$ coordinate plane. Line $$k$$ passes through the points $$(-2, 5)$$ and $$(1, -7)$$. Which of the following is the equation of line $$k$$?

   • $$y = -4x - 3$$
   • $$y = -4x + 4$$
   • $$y = 5x - 3$$
   • $$y = 5x - 8$$

5. A certain species of algae is growing in a pond. There were 200000 algae cells per liter during the initial observation. The number of algae cells per liter doubles every 4 hours. How many algae cells per liter will there be 12 hours after the initial observation?

   • $$2,000,000$$
   • $$1,600,000$$
   • $$200,000$$
   • $$160,000$$

6. If $$y$$ is a real number such that $$y^3=27$$, then $$y^2+\sqrt{y}=$$?

   • $$3 + \sqrt{3}$$
   • $$9 + \sqrt{27}$$
   • $$9 + \sqrt{3}$$
   • $$3 - \sqrt{3}$$

7. If there are $$4.5 \times 10^{13}$$ oxygen molecules in a $$3 \times 3 \times 2$$ meter tank, how many oxygen molecules are there per cubic centimeter?

   • $$2.5 \times 10^6$$
   • $$4.5 \times 10^{13}$$
   • $$1.8 \times 10^7$$
   • $$1.8 \times 10^{13}$$

8. Ajit was building a house. He wants to have a $$9 \text{ m} \times 6 \text{ m}$$ sized rectangular base to hold his locker which has some valuable stuff. To ensure uniformity throughout, his builder suggested that he should use square tiles all of the same size, to complete the $$9 \text{ m} \times 6 \text{ m}$$ base. Ajit, being an extravagant, wanted to have the maximum size of such squares to be used. Find out the number of square tiles Ajit had to buy?

   • 6
   • 9
   • 3
   • 12

9. The highest common factor of two consecutive odd numbers is:

   • 0
   • 1
   • 2
   • 3

10. Find the quadratic polynomial whose sum of zeros is $$-7$$ and product of zeros is $$12$$.

    • $$x^2 + 7x + 12$$
    • $$x^2 - 7x - 12$$
    • $$x^2 - 7x + 12$$
    • $$x^2 + 7x - 12$$

11. A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was 1500 dollars after 4 years of service and 1800 dollars after 10 years of service, what was his starting salary and what is the annual increment?

    • The starting salary is 1500 dollars, and the annual increment is 30 dollars.
    • The starting salary is 1300 dollars, and the annual increment is 50 dollars.
    • The starting salary is 1800 dollars, and the annual increment is 30 dollars.
    • The starting salary is 1500 dollars, and the annual increment is 50 dollars.

12. Simplify the given expression:$$\sin\theta \times \cos(90^\circ - \theta) + \tan\theta \times \cot(90^\circ - \theta)$$

    • $$\sin(90^\circ - \theta)$$
    • $$\sin\theta - \cos \theta$$
    • $$\sin^2\theta + \tan^2\theta$$
    • $$ \tan^2(90^\circ - \theta)$$

13. The frequency distribution of scores in mathematics is given in the table. Find the mean.

    • 17
    • 15
    • 18.5
    • 17.38

14. The sum of the fourth and twelfth term of an arithmetic progression is $$20$$. What is the sum of the first $$15$$ terms of the arithmetic progression?

    • 140
    • 110
    • 150
    • 200

15. If tangents $$TA$$ and $$TB$$ are drawn from an external point $$T$$ to a circle with center $$O$$, and the angle between the tangents $$\angle ATB = 70^\circ$$, find the measure of $$\angle AOB$$.

    • $$90^\circ$$
    • $$110^\circ$$
    • $$140^\circ$$
    • $$110^\circ$$

16. The ratio of the length of a flagpole and its shadow is $$1:1$$. What is the angle of elevation (in degrees) of the sun?

    • $$45^\circ$$
    • $$35^\circ$$
    • $$60^\circ$$
    • $$65^\circ$$

17. A circle whose center is the origin passes through the point $$(6,-8)$$. Which point also lies on this circle?

    • $$(-7,7)$$
    • $$(9,-1)$$
    • $$(-6,8)$$
    • $$(10,-6)$$

18. In a certain chip manufacturing company, there are three operating machines A, B, and C. Every day, Machine A produces 30 percent more chips than machine B, and machine B produces twice as many chips as machine C. If on any particular day machine A produces $$x$$ chips, what is the total number of chips produced by machines A, B, and C combined on that day in terms of $$x$$?

    • $$6x$$
    • $$\frac{28}{13}x$$
    • $$\frac{49}{10}x$$
    • $$1.9x$$

19. In the given figure, F is the center of the circle, and J, H, and I are points on the circle, and $$FI=4$$. If $$\angle JHI=\angle JIH=45^\circ$$, what is the area of the shaded region?

    • $$4\pi-8$$
    • $$8\pi+16$$
    • $$2\pi+4$$
    • $$16\pi-32$$

20. In the given figure, triangle ABC is a right triangle with right angle at B. Segment ED is parallel to AB. Given that $$BC=24$$, $$AC=26$$, and $$ED=8$$, what is the length of $$\overline{EC}$$?

    • 16.1
    • 20.8
    • 14.8
    • 15.7

21. A school asks each of its 1550 students whether they use a smartphone, a laptop, or a tablet during online learning. The table below summarizes the results. If a student is selected at random, what is the probability that he or she does not use a tablet given that he or she is not in the secondary section? Round your answer to the nearest tenth.

    • 0.8
    • 0.7
    • 0.55
    • 0.65

22. What is the range of the function $$f(x)=x^2+4x-3$$

    • $$[-7,+\infty)$$
    • $$[-1,+\infty)$$
    • $$(-\infty,1)$$
    • $$(1,+\infty)$$

23. If $$9^{2x-1}=3^8$$ what is the value of $$2x-5$$?

    • 5
    • 10
    • -5
    • 0

24. In the figure below, $$AB=7$$ cm, $$DC=13$$ cm and $$\tan C=\frac{2\sqrt{6}}{13}$$. What is the dimension of segment $$BC$$

    • 12
    • 10
    • 8
    • 5

25. If $$xy$$ is a positive integer and $$xz$$ is a negative integer, which of the following is trueI. $$yz$$ is always positiveII. $$xy - xz$$ is always positiveIII. $$xyz$$ is always negative

    • II and III only
    • I only
    • II only
    • I and II only

26. Joanne is a saleswoman in a TV store. Her salary is 1300 Egyptian pounds per month, in addition to 10 Egyptian pounds for each TV she sells if the quantity sold is less than or equal to 10 TVs per month. If she sells more than 10 TVs in one month, she will get an extra bonus of 10 percent of her initial salary. Last November, she sold 12 TVs. What was her salary at the end of the month?

    • 1600
    • 1350
    • 1550
    • 1650

27. What is the area of the shaded region in the figure below?

    • $$15$$ square units
    • $$24$$ square units
    • $$27$$ square units
    • $$19$$ square units

28. What is the product of the solutions of $$2x^4 = 4x^2 + 6$$

    • -3
    • i
    • 3
    • -i

29. ABCD is a parallelogram such that A(1,2), B(4,4), C(6,1), and D(3,-1). What are the coordinates of E, the center of the parallelogram?

    • $$E(4,1.5)$$
    • $$E(3.5,1.5)$$
    • $$E(3.5,4)$$
    • $$E(3,4)$$

30. Acceleration is a vector quantity that represents the rate of change of velocity over time. In physics, when the velocity of an object is changing, it means the object is either accelerating or decelerating. The formula used to find the velocity $$\vec{v}$$ of an object is $$\vec{v}=\frac{\Delta\vec{r}}{\Delta t}$$ and that of the acceleration is $$\vec{a}=\frac{\Delta\vec{v}}{\Delta t}$$ where $$\Delta\vec{r}$$ is the displacement vector, $$\Delta\vec{v}$$ is the change in velocity vector, and $$\Delta t$$ is the change in time. Which of the following statements is true regarding the given formula?I. If $$\Delta\vec{r}$$ increases and $$\Delta t$$ decreases, the acceleration will increase.II. If $$\Delta\vec{r}$$ decreases and $$\Delta t$$ increases, the acceleration will increase.III. If $$\Delta\vec{r}$$ decreases and $$\Delta t$$ increases, the acceleration will decrease.

    • I
    • II
    • II and III
    • I and III

31. Which point could be the solution for the inequality below?$$-3$$ < $$2x-y\le14$$

    • (3,4)
    • (0,3)
    • (4,-8)
    • (4,12)

32. A football club published on its website the number of entrance tickets sold in 2018 and in 2019. Which of the following equations best represents the relationship between the number of seasonal tickets sold to female customers and the revenue generated from those sales?

    • $$y=\frac{-165}{7}x-66355.7$$
    • $$y=\frac{-165}{7}x+66355.7$$
    • $$y=\frac{165}{7}x+66355.7$$
    • $$y=\frac{165}{7}x-66355.7$$

33. The scatterplot below displays the number of laptops repaired for various companies. Based on the line of best fit shown as a dashed line, what is the average yearly increase in the number of repaired laptops rounded to the nearest tenth?

    • 1.6
    • 0.4
    • 1.2
    • 0.3

34. If $$\sin a=2-\frac{\cos a}{3}$$ what is the value of $$9\sin a+3\cos a$$?

    • 18
    • 9
    • 6
    • 3

35. In planning maintenance for a city's infrastructure, a civil engineer estimates that, starting from the present, the population of the city will decrease by 15 percent every 25 years. If the present population of the city is 40000, which of the following expressions represents the engineer's estimate of the population of the city $$t$$ years from now?

    • $$40,000(0.85)^{\frac{t}{25}}$$
    • $$0.85(40,000)^{\frac{t}{25}}$$
    • $$40,000(0.15)^{25t}$$
    • $$40,000(0.85)^{25t}$$

36. In the xy-plane, the parabola with equation $$y=(x-6)^2$$ intersects the line with equation $$y=4$$ at two points A and B. What is the midpoint of segment AB?

    • $$(8,4)$$
    • $$(2,4)$$
    • $$(6,0)$$
    • $$(6,4)$$

37. The graph above represents the curve of an increasing function f. What is the solution of $$f(x)-1.5=0$$?

    • 4
    • 3
    • 1
    • 0

38. In the right trapezoid above, what is the length of $$x$$?

    • 5
    • 3
    • 4
    • 2

39. What is the solution of the system:$$\frac{2}{3}x+y=-3$$$$\frac{1}{3}x+\frac{1}{2}y=-3$$

    • $$(-6,7)$$
    • $$(-6,-7)$$
    • $$(-6,1)$$
    • No solution

40. The bar chart below shows the scores of a philosophy test over 100. If 5 is subtracted from each score, what do the new mean $$x'$$ and standard deviation $$\alpha'$$ become with respect to the original mean $$x$$ and standard deviation $$\alpha$$?

    • $$x'=x-5$$ ; $$\alpha'=\alpha$$
    • $$x'=x+5$$ ; $$\alpha'=\alpha-5$$
    • $$x'=x-5$$ ; $$\alpha'=\alpha-5$$
    • $$x'=5x$$ ; $$\alpha'=\alpha$$

41. If 40% of a number is equal to three-fifths of another number, what is the ratio of the first number to the second number?

    • $$\frac{40}{21}$$
    • $$\frac{3}{2}$$
    • $$\frac{5}{3}$$
    • $$\frac{21}{40}$$

42. At 8:00 a.m., a patient is given a drip feed containing a particular chemical and its concentration in his blood is measured, in suitable units, at one interval as shown above in the scatterplot. A line of best fit and its equation $$y=1.84x+1.99$$ are also given. Which of the following is the best interpretation of the y-intercept in the equation of the line?

    • Before drip feeding the patient, the concentration of this particular chemical in his blood is expected to be 1.99 units.
    • If $$x$$ increases by 1 unit, then $$y$$ increases by 1.84 units.
    • At 9:00 a.m., the concentration of this particular chemical in his blood is expected to be 1.99 units.
    • If $$x$$ increases by 1 unit, then the concentration of the chemical in his blood is expected to increase by 1.84 units.

43. From the set of equations below, which has a real solution?I. $$\sqrt{2x-1}=-x^2$$II. $$|x+1|=-3$$III. $$(x+1)^2+3=0$$IV. $$\sqrt{2x-1}=x$$

    • IV only
    • I, II, and III
    • III and IV
    • I only

44. What is the best interpretation of the meaning of the slope of the line of best fit?

    • If the price of the slice increases by one dollar, the kiosk expects to sell 8.5 more slices of pizza.
    • If the price of the slice decreases by one dollar, the kiosk expects to sell 8.5 fewer slices of pizza.
    • If the price of the slice increases by one dollar, the kiosk expects to sell 8.5 fewer slices of pizza.
    • If the store sells slices for 0 dollar, 90 people would be expected to accept the free slices of pizza.

45. In a farm, there are 30 rabbits of two sizes small and big and three colors white, brown, and gray as shown in the table below. One rabbit is selected at random from this farm. Suppose that the selected rabbit is not of white color, what is the probability for this rabbit to be from the big size?

    • $$\frac{5}{8}$$
    • $$\frac{3}{8}$$
    • $$\frac{3}{5}$$
    • $$\frac{7}{15}$$