Full-Length Accuplacer Math Practice Test

B. 75 cm

C. 80 cm

D. 85 cm

30- The area of a circle is less than \(121 π\). Which of the following can be the circumference of the circle?

A. \(20 π\)

B. \(24 π\)

C. \(28 π\)

D. \(32 π\)

31- An integer is chosen at random from 5 to 30. Find the probability of not selecting a composite number?

A. \(\frac{1}{5}\)

B. \(\frac{1}{4}\)

C. \(\frac{6}{25}\)

D. \(\frac{8}{25}\)

32- A boat sails 10 miles south and then 24 miles east. How far is the boat from its start point?

A. 18 miles

B. 22 miles

C. 26 miles

D. 30 miles

33- The ratio of boys and girls in a class is 2:5. If there are 56 students in the class, how many more boys should be enrolled to make the ratio 1:1?

A. 16

B. 22

C. 24

D. 32

34- The score of Emma was two-thirds as that of Ava and the score of Mia was twice that of Ava. If the score of Mia was 72, what is the score, Emma?

A. 12

B. 15

C. 24

D. 29

35- three seventh of 21 is equal to \(\frac{3}{5}\) of what number?

A. 15

B. 20

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C. 25

D. 30

36- In 1999, the average worker’s income increased by $1,200 per year starting from a $15,000 annual salary. Which equation represents income greater than average? (I = income, \(x\) = number of years after 1999)

A. \(I<1200x-15000\)

B. \(I>1200x-15000\)

C. \(I>1200x+15000\)

D. \(I<1200x+15000\)

37- The average weight of 15 girls in a class is 50 kg and the average weight of 25 boys in the same class is 60 kg. What is the average weight of all the 40 students in that class?

A. 44.85

B. 48.25

C. 52.5

D. 56.25

38- What is the median of these numbers? \(21,15,13,10,18,6,25\)

A. 8

B. 9

C. 13

D. 15

39- The surface area of a cylinder is \(48π cm^2\). If its height is 5 cm, what is the radius of the cylinder?

A. 3 cm

B. 5 cm

C. 7 cm

D. 9 cm

40- The average of six consecutive numbers is 67.5. What is the smallest number?

A. 60

B. 65

C. 70

D. 75

Section 3: Advanced Algebra and Functions

(Calculator)
20 questions
Total time for this section: No time limit.
You may use a calculator in this Section.
(On a real Accuplacer test, there is an onscreen calculator to use on some questions.)

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41- If \((ax+3)(bx-4)=-6x^2+2cx-12\) for all values of \(x\) and \(a+b=5\), what are the two possible values for c?

A. 13.5, 21

B. 11, 22

C. 10, 13.5

D. 11, 13.5

42- If \(f(x)=7x+2(1-x)\) then \(f(3x)=\)?

A. \(20x+6\)

B. \(15x-6\)

C. \(15x+2\)

D. \(27x+2\)

43- A line in the \(xy\)-plane passes through the origin and has a slope of \(\frac{2}{5}\). Which of the following points lies on the line?

A. \((5,1)\)

B. \((4,-1)\)

C. \((9,10)\)

D. \((15,6)\)

44- Which of the following is equivalent to \((4n^2-5n+12)-(3n^2-4n)\)?

A. \(n+4n^2\)

B. \(n^2-n+12\)

C. \(n^2+2n+12\)

D. \(n+2\)

45- If \(3x+2y=0, 3x-4y=6\), which of the following ordered pairs\( (x,y)\) satisfies both equations?

A. \((\frac{2}{3},-1)\)

B. \((5,-4)\)

C. \((4,-4)\)

D. \((\frac{5}{3},-6)\)

46- John buys a pepper plant that is 8 inches tall. With regular watering, the plant grows 5 inches a year. Writing John’s plant’s height as a function of time, what does the \(y\)-intercept represent?

A. The \(y\)-intercept represents the rate of growth of the plant which is 5 inches

B. The \(y\)-intercept represents the starting height of 6 inches

C. The \(y\)-intercept represents the rate of growth of the plant which is 3 inches per year

D. There is no \(y\)-intercept

47- In the \(xy\)-plane, if (1, 2) is a solution to the system of inequalities above, which of the following relationships between a and b must be true?

A. \(a<b\)

B. \(a>b\)

C. \(a=b\)

D. \(a= b+ a\)

48- Which of the following points lies on the line that goes through the points \((1,-5)\) and \((-3,7)\)?

A. \((2,-3)\)

B. \((5,-12)\)

C. \((-4,10)\)

D. \((3,-6)\)

49- Calculate \(f(-4)\) for the following function \(f\).
\(f(x)=2x^2+4x+1\)

A. 16

B. 17

C. 18

D. 19

50- If \(x≠-4\) and \(x≠9\), which of the following is equivalent to \(\frac{1}{\frac{1}{x+4}+\frac{1}{x-9}}\)?

A. \(\frac{(x-9)-(x+4)}{(x-9)+(x+4)}\)

B. \(\frac{(x-9)(x+4)}{(x+4)+(x-9)}\)

C. \(\frac{(x+4)(x-9)}{(x+4)-(x+5)}\)

D. \(\frac{(x+4)+(x-9)}{(x+4)-(x-9)}\)

51- In the \(xy\)-plane, the line determined by the points (2,m) and (m,10) passes through the origin. Which of the following could be the value of m?

A. \(\sqrt{6}\)

B. \(2\sqrt{5}\)

C. \(6\sqrt{2}\)

D. 9

52- Which of the following is an equation of a circle in the \(xy\)-plane with center \((1,-2)\) and a radius with endpoint \((\frac{1}{3},2)\)?

A. \((x-1)^2+(y+2)^2=\frac{148}{9}\)

B. \(x^2+(y+2)^2=\frac{148}{9}\)

C. \((x-1)^2+(y-2)^2=\frac{148}{9}\)

D. \(x^2+(y-2)^2=\frac{148}{9}\)

53- Given a right triangle \(∆\)ABC whose \(n∠B=90^\circ\),sin⁡C\(=\frac{3}{5}\), find cosA?

A. \(-\frac{1}{2}\)

B. \(\frac{1}{2}\)

C. \(\frac{3}{5}\)

D. \(\frac{4}{5}\)

54- What is the equation of the following graph?

A. \(x^2+6x+5\)

B. \(x^2-3x+1\)

C. \(2x^2-4x+4\)

D. \(x^2-4x+1\)

55- If \(\frac{7}{x}=\frac{21}{(x+4)}\) what is the value of\((-\frac{x}{3}\))?

A. \(-\frac{1}{6}\)

B. \(-\frac{2}{3}\)

C. 1

D. 3

56- A function \(g(6)=8\) and \(g(2)=7\). A function \(f(7)=9\) and \(f(8)=12\). What is the value of \(f(g(6))\)?

A. 5

B. 6

C. 7

D. 12

57- What is the area of the following equilateral triangle if the side AB \(= 14\) cm?

A. \(98\sqrt{3} \)cm\(^2\)

B. \(45\sqrt{3} \)cm\(^2\)

C. \(49\sqrt{3} \)cm\(^2\)

D. \(14\)cm\(^2\)

58- A function \(g(x)\) satisfies \(g(3)=8\) and \(g(4)=10\). A function \(f(x)\) satisfies \(f(8)=12\) and \(f(10)=40\).What is the value of \(f(g(4))\)?

A. 8

B. 10

C. 12

D. 40

59- \(x^2+y^2-6x+4y=4\)
The equation of a circle in the \(xy\)-plane is shown above. What is the radius of the circle?

A. \(\sqrt{17}\)

B. 5

C. \(\sqrt{24}\)

D. \(\sqrt{48}\)

60- Right triangle ABC is shown below. Which of the following is true for all possible values of angle A and B?

A. tan A \(=\) cot B

B. sin A \(= -\)cos B

C. tan\(^2\) A \(=\) tan\(^2\) B

D. tan A \(= \)1

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