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1.

In the figure above, lines l and k intersect at point Q. If $m\degree$ =40 and $p\degree$ =25, what is the value of x?

a)

2 squared

b)

100

c)

solution of the equation 2x=30

d)

4 cubed

e)

square root of 25

2.

Which of the following equations is satisfied by the five pairs of numbers listed in the table above?

a)

$y=x^3+3$

b)

$y=-3x+6$

c)

$y=x^2+6$

d)

$y=3x+3$

e)

$y=\frac{x^2+7}{2}$

3.

If n and k are positive integers and $8^n=2^k$ what is the value of n/k?

a)

one fourth

b)

one third

c)

5/6

d)

two thirds

e)

five sixths

4.

The circle graph shows how David’s monthly expenses are divided. If David spends $450 percent month for food, how much does he spend percent month on his car?

a)

$300+$60

b)

$200-$100

c)

$500

d)

$700

e)

$100+$100

5.

If the function 𝑓 is defined by f(x)=3x+4, then 2f(x)+4=

a)

5x+4

b)

6x+4

c)

5x+8

d)

8x-7

e)

6x+12

6.

Which of the following is the graph of a function f such that f(x) for exactly two values of x between -5 and 5?

a)

b)

c)

d)

e)

7.

The result when a number is divided by 2 is equal to the result when that same number is divided by 4. What is that number?

a)

1 squared

b)

0

c)

square root of 2

d)

an element of the set M={1, 5, 2}

e)

5

8.

The expression $x^2-8x+12$ is equal to 0 when x = 2 and when x= ?

a)

cube root of $6^3$

b)

20

c)

45

d)

index of a root $\sqrt[]{25}$

e)

the base of a logarithm $\log_28$

9.

Triangle BDC, shown above, has an area of 48 square units. If ABCD is a rectangle, what is the area of the circle in square units?

a)

81 square units

b)

49 square units

c)

36 square units

d)

$7^2$ square units

e)

7*7 square units

10.

How called a line segment which connecting the vertex and the midpoint of the opposite side?

a)

a bissectrix

b)

line

c)

midline

d)

a median

e)

ray

11.

Kiki is climbing a mountain. His elevation at the start of today is 900 feet. After 12 hours, Kiki is at an elevation of 1,452 feet. On average, how many feet did Kiki climb per hour today?

a)

an element of M={46,45,55}

b)

a proper fraction

c)

a mixed fraction

d)

the base of a logarithm $\log_28$

e)

cube root of 81

12.

The sum of three consecutive integers is 60. Find the least of these integers.

a)

19

b)

a negative number

c)

75

d)

80

e)

a mixed fraction

13.

Which of the following illustrates a distributive principle?

a)

$\left(6\cdot2\right)+4=4+\left(2\cdot6\right)$

b)

$\left(a\cdot b\right)+c=c+\left(a\cdot b\right)$

c)

$6\cdot\left(2+4\right)=6\cdot2+6\cdot4$

d)

$5+4=4+5$

e)

$\left(3+4\right)+5=3+\left(4+5\right)$

14.

If n is a positive integer, which of the following is always odd?

a)

$19n^2+5$

b)

18n + 4

c)

36n + 10

d)

19n + 6

e)

18n + 5

15.

The average (arithmetic mean) of tand y is 15, and the average of w and x is 15. What is the average of t, w, x and y?

a)

infinity

b)

a negative number

c)

square root of 100

d)

a proper fraction

e)

30/5

16.

For what value(s) of y on the curve shown in figure does y = 4x?

a)

+4 and –12

b)

+3 only

c)

+4 only

d)

–5 only

e)

no value

17.

If (2m)k=6, then mk=

a)

cube root of 27

b)

value of a square root 81

c)

5

d)

infinity

e)

five

18.

If 3 times a number is equal to 3/2, what is the number?

a)

one second

b)

a mixed fraction

c)

index of a root 25

d)

a quotient of two fractions 1/8*2/9

e)

not element of M={1/2, 1/3, 1/8}

19.

Determine so that the system { kx-2y=11 5x+2y=5 has the unique solution.

a)

$k\ne5$

b)

k is equal to 15

c)

k is not equal to 15

d)

k is equal to 5

e)

k is not a proper fraction

20.

Determine so that the system { kx+15y=12 2x+5y=1 has the unique solution.

a)

$k\ne6$

b)

k is equal to 1

c)

$k\ne1$

d)

k is a negative number

e)

k is not a proper fraction

21.

If x=20 and y=30 in the figure above, what is the value of z?

a)

$\frac{\pi}{4}+25\degree$

b)

$\frac{\pi}{4}+15\degree$

c)

$25\degree$

d)

$\frac{\pi}{4}$

e)

$\pi+110\degree$

22.

How called a convex quadrilateral with two parallel and two non-parallel sides

a)

trapezoid

b)

rhombus

c)

parallelogram

d)

square

e)

polygon

23.

Which one of the following is equivalent to the expression ( $\overline{A}$ ∖ $B$ ) $\cup$ ( $A$ ∖ $B$ ) ?

a)

$\overline{B}$

b)

A

c)

$\overline{A}$

d)

∅

e)

B

24.

A student was given a piece of rope and told to cut it into two equal pieces, keep one piece, and pass the other piece to the next student. Each student was to repeat this process until every student in the class had exactly one piece of rope. Which of the following could be the fraction of the original rope that one of the students had?

a)

1/16

b)

a negative number

c)

an improper fraction

d)

a mixed fraction

e)

1/17

25.

Find the root(s) of the equation $y+\sqrt[]{y+5}=7$

a)

4

b)

natural logarithm

c)

trigonometric functions

d)

rational integral functions

e)

base of a power $n^2$

26.

Determine so that the system {kx-2y=11 5x+2y=5 has more then one solution.

a)

k is value of a root $\sqrt[]{81}$

b)

k is equal to 5

c)

k is a proper fraction

d)

k is not equal to 5

e)

k is equal to 1

27.

Point O is the center of both circles in the figure above. If the circumference of the large circle is 36 and the radius of the small circle is half of the radius of the large circle, what is the length of the darkened arc?

a)

infinity

b)

square root of 100

c)

the product of two fractions ½*1/3

d)

a negative number

e)

2 squared

28.

The graph above shows the number of George’s unsold candy bars over a 10-day period. The points on the graph all lie on which of the following lines?

a)

y=120-10x

b)

y-10x+120=0

c)

y=120-12x

d)

y=10x-120

e)

y=10x

29.

Find the equation of the straight line that passes through points (-1, 1) and (0,1).

a)

y + 4x - 3 = 0

b)

y -1 = 0

c)

y - 2x = 0

d)

y = x

e)

y - 4x = 0

30.

Determine so that the system {kx+4y=10 3x+6y=15 has more the one solution.

a)

k = 7

b)

$k\ne5$

c)

k = 2

d)

k = 4

e)

k is value of a root $\sqrt[]{25}$

31.

In how many points do the graphs of the equations $x^2+y^2=25$ and $y^2=4x$ intersect?

a)

the sum of two numbers 1 and 1

b)

the base of a logarithm $\log_58$

c)

radicand of a root $\sqrt[]{7}$

d)

a negative number

e)

a proper fraction

32.

The expression $4x^2-2x+3$ is equal to 3 when x = 0 and when x =

a)

3/4

b)

-1/4

c)

one fourth

d)

a half

e)

-1/2

33.

Which of the following has the greatest value when x= -14?

a)

$x^{-1}$

b)

$4x+3$

c)

$16^x$

d)

$\frac{1}{81^x}$

e)

$-\frac{3}{8x}$

34.

If $x\ne0$ and $y\ne0$ , $\frac{\frac{xy}{y}+xy}{\frac{xy}{x}}=$

a)

$\frac{x}{y}-y$

b)

$\frac{x}{y}+y$

c)

$\frac{2x}{y}+4$

d)

$2\cdot\frac{x}{y}$

e)

$\frac{x}{y}+x$

35.

Find the equation of the straight line that passes through the origin and is parallel to the straight line $y=4x+3$

a)

y = 3x;

b)

y = 4x +1;

c)

y = x - 2;

d)

y = 4x

e)

y-4x=0

36.

Find the equation of the straight line that passes through the origin and is parallel to the straight line $y=\frac{1}{2}x+1$

a)

$y=\frac{1}{2}x$

b)

y=4x+2

c)

y=x-7

d)

y=x

e)

y=4x

37.

A triangle with (at least) two equal sides is called

a)

an equilateral triangle

b)

a right triangle

c)

an isosceles triangle

d)

acute-angled triangle

e)

scalene triangl

38.

Which of the following is an irrational number?

a)

$-\left(\sqrt[]{3}\sqrt[]{3}\right)$

b)

$\sqrt[]{\frac{4}{9}}$

c)

$4^{-3}$

d)

$\left(\sqrt[]{32}\right)^3$

e)

$\sqrt[]{2}\sqrt[]{72}$

39.

In right triangle ABC, DE ⊥ BC . If AB = 6, AC = 8, BC = 10, and DE = 4, find EC.

a)

$5\cdot\frac{5}{3}$

b)

4

c)

$\frac{16}{3}$

d)

$4-4\pi$

e)

15

40.

Which of the following expressions is undefined when x=-2?

a)

$\frac{2x+2}{x-8}$

b)

$y=\frac{x+2}{x-2}$

c)

$y=\frac{2x+4}{x^2+4x+4}$

d)

$\frac{x^2+2x+2}{x^2+6x+8}$

e)

$y=\frac{x^2+3x+2}{-x^2+2}$

41.

If graphed, which of the following pairs of equations would be parallel to each other?

a)

𝑦 = 2𝑥 + 4, 𝑦 = 𝑥 + 4

b)

y = -6x + 6, y = 6x - 6

c)

𝑦 = 3𝑥 + 3, 𝑦 = – 13𝑥 – 3

d)

𝑦 = 4𝑥 + 1, 𝑦 = – 4𝑥 + 1

e)

y = -x + 4, y = -x -10

42.

If $\frac{a}{b-4}=\frac{4b}{a}+1$ , then when a=8, b could be equal to

a)

infinity

b)

-4;6

c)

a mixed fraction

d)

value of a root $\sqrt[]{25}$

e)

-6;4

43.

The average of five consecutive odd integers is –21. What is the least of these integers?

a)

cube root of 8

b)

-25

c)

index of a root $\sqrt[]{25}$

d)

the base of a logarithm $\log_28$

e)

infinity

44.

Line AC is a diagonal of square ABCD. What is the sine of angle ACB?

a)

$\frac{\sqrt[]{3}}{2}$

b)

$\frac{1}{2}$

c)

$\sqrt[]{2}$

d)

$\frac{\sqrt[]{2}}{2}$

e)

2

45.

$\frac{\frac{b}{a}-a}{\frac{1}{a^{-1}}}$ is equivalent to

a)

$\frac{b-1}{a^2}$

b)

$\frac{b}{a^2}-1$

c)

$\frac{b}{a^2}$

d)

$\frac{b-a^2}{ab}$

e)

$\frac{b+a^2-b^2}{a^2}$

46.

Express the infinite decimal .212121… as a common fraction.

a)

5\66

b)

24\33

c)

14\12

d)

4\33

e)

7\33

47.

All of the following are less than 2/5 EXCEPT

a)

3/7

b)

1/5

c)

3/8

d)

0,04

e)

0.0404

48.

If 3x-y=2 and 2y-3x=8, which of the following is equal to $\frac{x}{y}$ ?

a)

a negative number

b)

a mixed fraction

c)

an improper fraction

d)

2/5

e)

value of a root $\sqrt[]{\frac{4}{8}}$

49.

Which of the following sets of numbers contains all and only the roots of the equation $f(x)=x^3+7x^2-8x$ ?

a)

{0, 2, -1}

b)

{0, -8, 1}

c)

{0, 8, 1}

d)

{0, -1}

e)

{0, -7; 1}

50.

An empty crate weighs 8.16 kg and an orange weighs 220 g. If Jon can lift 11,000 g, how many oranges can he pack in the crate before lifting it onto his truck?

a)

thirty

b)

12

c)

fifty

d)

twenty

e)

one hundred and twenty

51.

A box contains five blue pens, three black pens, and two red pens. If every time a pen is selected, it is removed from the box, what is the probability of selecting a black pen followed by a blue pen?

a)

the sum of two unlike fractions 2/7*3/7

b)

cube root of 1/8

c)

the antilogarithm of a logarithm
$\log_28$

d)

an improper fraction

e)

1/6

52.

Two angles are called supplementary angles if the sum of their degree measurements equals

a)

90°

b)

180°

c)

360°

d)

100°

e)

0°

53.

An angle whose measure is greater than 90° but less than 180° is called

a)

a straight angle

b)

an obtuse angle

c)

a right angle

d)

an acute angle

e)

an interior angles

54.

The statement “Raphael runs every Sunday” is always true. Which of the following statements is also true?

a)

If it is Sunday, then Raphael does not
run

b)

If it is Sunday, it is impossible to
determine if Raphael runs

c)

If Raphael runs, then it is Sunday

d)

If it is not Sunday, then Raphael does
not run

e)

If Raphael does not run, then it is not
Sunday

55.

It takes eight people 12 hours to clean an office. How long would it take six people to clean the office?

a)

9 hours

b)

2 hours

c)

16 hours

d)

4 hours

e)

15 hours

56.

Greg has nine paintings. The Hickory Museum has enough space to display three of them. From how many different sets of three paintings does Greg have to choose?

a)

the product of two numbers 12 and 7

b)

value of a root $\sqrt[]{25}$

c)

the sum of two unlike fractions 1\7
and 2\5

d)

the value of a logarithm $\log_28$

e)

27

57.

Given the following figure with one tangent and one secant drawn to the circle, what is the measure of angle ADB?

a)

50 degrees

b)

110 degrees

c)

85 degrees

d)

60 degrees

e)

25 degrees

58.

Balloons are sold according to the chart above. If a customer buys one balloon at a time, the cost is $1.00 per balloon. If a customer buys ten balloons at a time, the cost is $0.90 per balloon. If Carlos wants to buy 2,000 balloons, how much money does he save by buying 1,000 balloons at a time rather than ten balloons at a time?

a)

$300

b)

$500

c)

$600

d)

$800

e)

$200

59.

If $\frac{ab}{c}=d$ and a and c are doubled, what happens to the value of d?

a)

The value of d is four times smaller

b)

The value of d is doubled

c)

The value of d is halved

d)

The value of d remains the same

e)

The value of d is four times greater

60.

In the diagram above, line OA is congruent to line OB. What is the measure of arc CD?

a)

55 degrees

b)

$\pi-110\degree$

c)

27.5 degrees

d)

125 degrees

e)

110 degrees

61.

The volume of a glass of water placed in the sun decreases by 20%. If there are 240 mL of water in the glass now, what was the original volume of water in the glass?

a)

260 mL

b)

300 mL

c)

288 mL

d)

192 mL

e)

360 mL

62.

How does the area of a rectangle change if both the base and the height of the original rectangle are tripled?

a)

The area is nine times larger

b)

The area is six times larger

c)

The area is tripled

d)

The area remains the same

e)

The area cannot be determined

63.

In the diagram above, angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of triangle $BED=5a^2+10$ , what is area of triangle ABC?

a)

$125\sqrt[]{a^4}+250$

b)

$5𝑎^2+10$

c)

$25𝑎^2+50$

d)

$25𝑎^2+100$

e)

$125a^2$

64.

The number p is greater than 0, a multiple of 6, and a factor of 180. How many possibilities are there for the value of p?

a)

8

b)

the sum of two unlike fractions 1\3 and 2\5

c)

base of a power $7^2$

d)

index of a root $\sqrt[]{25}$

e)

the antilogarithm of a logarithm $\log_29$

65.

What is the slope of the line -3y=12x-3?

a)

-3

b)

1

c)

4

d)

12

e)

-4

66.

A spinner is divided into eight equal regions, labeled one through eight. If Jenna spins the wheel, what is the probability that she will spin a number that is less than four and greater than two?

a)

an improper fraction

b)

1\3

c)

a complex number

d)

square root of 7

e)

1\8

67.

The length of an edge of a cube is equal to half the height of a cylinder that has a volume of 160𝜋 cubic units. If the radius of the cylinder is 4 units, what is the surface area of the cube?

a)

100 square units

b)

96 square units

c)

125 square units

d)

64 square units

e)

150 square units

68.

Melissa runs the 50-yard dash five times, with times of 5.4 seconds, 5.6 seconds, 5.4 seconds, 6.3 seconds, and 5.3 seconds. If she runs a sixth dash, which of the following would change the mean and mode of her scores, but not the median?

a)

5.4 seconds

b)

5.5 seconds

c)

5.3 seconds

d)

6.3 seconds

e)

5.6 seconds

69.

A music store offers customized guitars. A buyer has four choices for the neck of the guitar, two choices for the body of the guitar, and six choices for the color of the guitar. The music store offers

a)

24 different guitars

b)

16 different guitars

c)

48 different guitars

d)

12 different guitars

e)

36 different guitars

70.

Which of the following is the set of positive factors of 12 that are NOT multiples of 2?

a)

{2,4, 6,12}

b)

{}

c)

{1}

d)

{1, 3}

e)

{1,2,3}

71.

Define function type $y=kx+b$

a)

Linear function

b)

Logarithmic function

c)

Exponential function

d)

Power function

e)

Trigonometric functions

72.

What is the addition?

a)

It is the operation of finding a number
which gives a measure of the
difference in size between two
quantities or measures.

b)

It is the operation which combines
several equal measures of size giving
the result as a single number.

c)

It is operation inverse to
multiplication

d)

It is the operation of combining
numbers, each of which represents a
separate measure of quantity, so as to
produce a number representing the
measure of all those quantities
together

e)

It is the finding of a quantity, the
quotient, that when multiplied by a
given quantity, the divisor, gives
another given quantity, the dividend

73.

In a class of 25 boys, 17 boys play football, 12 boys play basketball and 5 boys play both games. How many boys don't play any game?

a)

1

b)

4

c)

3

d)

2

e)

0

74.

A survey of 50 students in a college showed the following: 23 students take Maths, 25 take English, 26 take Physics, 11 take Maths and English, 13 take Maths and Physics, 9 take English and Physics, and 2 take Maths and English and Physics. How many students don't take any of the subjects?

a)

7

b)

value of a root $\sqrt[]{81}$

c)

6

d)

8

e)

9

75.

The set A has 6 elements and the set В has 4 elements. What is the least number of subsets of $A\cup B$ ?

a)

value of a root $\sqrt[]{675}$

b)

index of a root $\sqrt[]{25}$

c)

64

d)

24

e)

32

76.

Let $u=\left(-4,3\right)$ , $v=\left(-9,12\right)$ be vectors in $R^2$ . Find the angle between these
vectors

a)

arccos $\frac{1}{4}$

b)

$\frac{\pi}{2}$

c)

arccos $\frac{2}{3}$

d)

0

e)

cube root of 1

77.

Find the slope and the segment cut out on the y-axis of the straight line x+y-5=0.

a)

1;5

b)

4;1

c)

5: -1

d)

-5: 1

e)

-2: 6

78.

Evaluate $\frac{0.01-0.1}{0.27}+\frac{0.01-0.1}{0.9}$ .

a)

The value of expression is equal to ( $-\frac{5}{9}$ )

b)

The value of expression is equal to ( $-\frac{13}{30}$ )

c)

The value of expression is logarithmic
expression

d)

The value of expression is inverse
trigonometric functions

e)

The value of expression is equal to $\frac{2}{3}$

79.

If 40% of j is equal to 50% of k, then 𝑗 is

a)

25 % larger than k

b)

20% larger than k

c)

10% larger than k

d)

80% larger than k

e)

15% larger than k

80.

If a positive integer n is picked at random from the positive integers less than or equal to 10, what is the probability that 5n + 3 ≤ 14?

a)

4/9

b)

the sum of two fractions 1/5+4/5

c)

a quotient of two fractions 1/5*1/6

d)

1/5

e)

square root of 25

81.

If we multiply a number by 2 and add 8, the result is 32. Find the number.

a)

12

b)

10

c)

16

d)

18 cubed

e)

index of a root $\sqrt[]{12}$

82.

a)

$A\cdot B=22$

b)

c)

d)

$A\cdot B=\left(4\ \ 16\ \ 12\right)$

e)

$A\cdot B=0$

83.

Evaluate the determinant of the matrix

a)

a negative number

b)

a complex number

c)

4 squared

d)

4

e)

value of a root $\sqrt[]{4}$

84.

In the sequence above, the first term is 4 and each term after the first is 7 more than the previous term. What is the 12th term of the sequence?

a)

77

b)

the base of a logarithm $\log_28$

c)

index of a root $\sqrt[]{25}$

d)

81

e)

18

85.

Evaluate the determinant of the matrix

a)

a negative number

b)

4

c)

3 squared

d)

a complex number

e)

value of a root $\sqrt[]{36}$

86.

Evaluate the determinant of the matrix

a)

1

b)

a proper fraction

c)

0

d)

a negative number

e)

value of a root $\sqrt[]{4}$

87.

If $\left(x-2\right)^2=9$ , then x could be

a)

a proper fraction

b)

0

c)

6

d)

square root of 25

e)

the value of a logarithm $\log_28$

88.

On Wednesday Heather ran 3 miles in 30 minutes. If she ran for 45 minutes at this rate on Thursday, how far did Heather run on Thursday?

a)

4.5 miles

b)

3.5 miles

c)

5.5 miles

d)

4 miles

e)

5 miles

89.

In the figure above, CDE is an equilateral triangle and ABCE is a square with an area of 1. What is the perimeter of polygon CDE?

a)

a proper fraction

b)

five

c)

radicand of a root $\sqrt[]{25}$

d)

0

e)

6

90.

On the number line above, the tick marks are equally spaced and their coordinates are shown. Of these coordinates, which has the smallest positive value?

a)

a

b)

b

c)

c

d)

d

e)

e

91.

10, 18, 4, 15, 3, 21, x.
If 𝑥 is the median of the 7 numbers listed above, which of the following could be the value of x?

a)

9

b)

a proper fraction

c)

14

d)

the product of two fractions 4/9*3/8

e)

a negative number

92.

In the figure above $\overline{AB}$ , $\overline{CD}$ and $\overline{EF}$ intersect at P. If r=90, s=50, t=60, u=45 and w=50 what is the value of x?

a)

45

b)

$\pi+115$

c)

$\pi$

d)

65

e)

75

93.

Based on the portions of the graphs of the functions f and g shown above, what are all values of x between -6 and 6 for which g(x)>f(x)?

a)

-6<x<-3 only

b)

0<x<3 only

c)

-3<x<0 only

d)

3<x<6 only

e)

-6<x<-3 and 0<x<3

94.

Two spheres, one with radius 7 and one with radius 4, are tangent to each other. If P is any point on one sphere and Q is any point on the other sphere, what is the maximum possible length of PQ?

a)

a negative number

b)

4 squared

c)

value of a root √25

d)

index of a root √25

e)

the product of two numbers 2 and 11

95.

a)

-2

b)

3

c)

4

d)

2

e)

1

96.

a)

3

b)

5

c)

4

d)

0

e)

1

97.

a)

0

b)

3

c)

square root of 25

d)

1

e)

the product of two numbers 1 and 3

98.

A man can do a job in h hours alone and his son can do it in 2h hours alone. Together, how many hours will it take them to do the job?

a)

h*3

b)

2h\3

c)

h\5

d)

h-6

e)

h+5

99.

A dormitory now houses 30 men and allows 42 square feet of space per man. If five more men are put into this dormitory, how much less space will each man have?

a)

4 square feet

b)

6 square feet

c)

8 square feet

d)

7 square feet

e)

5 square feet

100.

In the diagram above, lines EF and GH are parallel, and line AB is perpendicular to lines EF and GH. What is the length of line AB?

a)

$\sqrt[]{75}$

b)

square root of 25

c)

power exponent of $5^2$

d)

radicand of a root $\sqrt[]{25}$

e)

75

кәсіби шет тілі 1рк

Total questions: 100

Worksheet time: 50mins

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