EST1 Math Sample 2026 (50 Questions)

1. Question

Consider the two functions $f(x)=x^{2}-2x+1$ and $g(x)=-x+3$. Which of the following is the correct graph representing $f$ and $g$?

Correct Incorrect Correct answer

2. Question

A box contains 6 plain chocolate bars, 11 chocolates filled with nuts, and 7 chocolates filled with nougat. If Arjun selects one chocolate at random, what is the probability that he chooses a plain chocolate bar?

0.25

Correct Incorrect Correct answer

0.46

Correct Incorrect Correct answer

0.55

Correct Incorrect Correct answer

0.71

Correct Incorrect Correct answer

3. Question

A pencil case contains 4 blue pens, 1 green pen, 2 black pens and 2 red pens. One pen is chosen randomly. What is the probability of not picking a blue pen?

$\dfrac{3}{5}$

Correct Incorrect Correct answer

$\dfrac{5}{9}$

Correct Incorrect Correct answer

$\dfrac{4}{9}$

Correct Incorrect Correct answer

$\dfrac{1}{3}$

Correct Incorrect Correct answer

4. Question

The ratio of men to women in an office is 7 to 4. If there are 66 employees in this office, what is the difference in numbers between the two genders?

12

Correct Incorrect Correct answer

14

Correct Incorrect Correct answer

16

Correct Incorrect Correct answer

18

Correct Incorrect Correct answer

5. Question

What is the value of $x$ in the equation $\dfrac{2x-7}{5}=\dfrac{4x^{2}+7}{10x}$?

1

Correct Incorrect Correct answer

-0.5

Correct Incorrect Correct answer

-1

Correct Incorrect Correct answer

-2

Correct Incorrect Correct answer

6. Question

Given $p=-1+2i$ and $q=2-3i$ then $p+\overline{q}=$

$1-5i$

Correct Incorrect Correct answer

$1+4i$

Correct Incorrect Correct answer

$1+5i$

Correct Incorrect Correct answer

$5-i$

Correct Incorrect Correct answer

7. Question

The bar chart above represents the preferred subject chosen by Grade 10 students in a school.

What is the approximate percentage of students who prefer to study English?

10.8%

Correct Incorrect Correct answer

16.7%

Correct Incorrect Correct answer

28.6%

Correct Incorrect Correct answer

27.5%

Correct Incorrect Correct answer

8. Question

One student is selected at random. What is the probability that the student prefers either Mathematics or Social Studies?

$\dfrac{5}{42}$

Correct Incorrect Correct answer

$\dfrac{3}{14}$

Correct Incorrect Correct answer

$\dfrac{5}{14}$

Correct Incorrect Correct answer

$\dfrac{5}{21}$

Correct Incorrect Correct answer

9. Question

A company manufactures cotton T-shirts. The manufacturing cost for two shirts is \$5 and the average worker's wage to produce one shirt is \$2. Which of the following equations below best represents the total cost $C$ of producing $r$ shirts?

$C=5r$

Correct Incorrect Correct answer

$C=5r-2$

Correct Incorrect Correct answer

$C=4.5r$

Correct Incorrect Correct answer

$C=2.5r+2$

Correct Incorrect Correct answer

10. Question

Which of the following is the remainder when dividing $3x^{4}-4x^{2}+3x-6$ by $(x+2)$?

-15

Correct Incorrect Correct answer

10

Correct Incorrect Correct answer

15

Correct Incorrect Correct answer

20

Correct Incorrect Correct answer

11. Question

If $f(x)=3x-5$ and $g(x)=-2x+1$, which of the following is $f(g(x))$?

$-6x-2$

Correct Incorrect Correct answer

$-2x+5$

Correct Incorrect Correct answer

$4x-2$

Correct Incorrect Correct answer

$6x-1$

Correct Incorrect Correct answer

12. Question

A line passes through the origin and the point $A(2,28)$. What is the y-coordinate of a point $B$ that lies on the same line if $x_{B}=-5$?

-70

Correct Incorrect Correct answer

-7

Correct Incorrect Correct answer

0

Correct Incorrect Correct answer

70

Correct Incorrect Correct answer

13. Question

The line of equation $y-1=7x$ passes through the point $(1, a)$. What is the value of $2a$?

8

Correct Incorrect Correct answer

10

Correct Incorrect Correct answer

16

Correct Incorrect Correct answer

18

Correct Incorrect Correct answer

14. Question

Year	Cars sold
2023	32
2024	40

Based on the data in the table, the owner of a car company estimates that the percentage increase in the number of cars sold between 2023 and 2024 would be half the percentage increase between 2024 and 2025. How many cars are expected to be sold in 2025?

48

Correct Incorrect Correct answer

60

Correct Incorrect Correct answer

65

Correct Incorrect Correct answer

90

Correct Incorrect Correct answer

15. Question

The sum of 5, 15, 2, 18, 7, and $x$ is 50. What is the value of the interquartile range?

12

Correct Incorrect Correct answer

13

Correct Incorrect Correct answer

15

Correct Incorrect Correct answer

16

Correct Incorrect Correct answer

16. Question

What is the value of $x$ if $25^{\dfrac{3}{x}}=125^{\dfrac{5}{x}-4}?$

0.5

Correct Incorrect Correct answer

0.75

Correct Incorrect Correct answer

1.25

Correct Incorrect Correct answer

2.5

Correct Incorrect Correct answer

17. Question

Consider the line defined by the equation $x-3y-12=0$ Let $\overleftrightarrow{AB}$ be a line parallel to $l$, where $A$ has coordinates $(0,-1)$. Which of the following could be the coordinates of point $B$?

(6,-1)

Correct Incorrect Correct answer

(-3,1)

Correct Incorrect Correct answer

(3,0)

Correct Incorrect Correct answer

(-2,1)

Correct Incorrect Correct answer

18. Question

After a 45% discount, Tim bought sweatpants for \$5. What was the original price of the sweatpants before discount?

\$2.25

Correct Incorrect Correct answer

\$7.25

Correct Incorrect Correct answer

\$7.50

Correct Incorrect Correct answer

\$9.09

Correct Incorrect Correct answer

19. Question

James has 3 rings, 4 watches, and 2 necklaces. How many different ways can he wear exactly one accessory from each category?

12

Correct Incorrect Correct answer

20

Correct Incorrect Correct answer

24

Correct Incorrect Correct answer

32

Correct Incorrect Correct answer

20. Question

Given $f(x)=2x^{2}$ and $g(x)=10x-n$, for which value of $n$ is $g$ tangent to $f$?

-18.5

Correct Incorrect Correct answer

-12.5

Correct Incorrect Correct answer

12.5

Correct Incorrect Correct answer

18

Correct Incorrect Correct answer

21. Question

A ball was launched, from the ground, having its trajectory along the curve represented by $y=-3x^{2}+6x+9$, where $x$ and $y$ are measured in meters. How high, above the ground, does the ball get to as it travels?

12 meters

Correct Incorrect Correct answer

10 meters

Correct Incorrect Correct answer

8 meters

Correct Incorrect Correct answer

5 meters

Correct Incorrect Correct answer

22. Question

What is the x-intercept of the line defined by $2x+5y=40$?

2

Correct Incorrect Correct answer

8

Correct Incorrect Correct answer

10

Correct Incorrect Correct answer

20

Correct Incorrect Correct answer

23. Question

Given two points $A(-20,4)$ and $K(12,-3)$ the x-coordinate of the midpoint of $\overline{AK}$ is:

-32

Correct Incorrect Correct answer

-4

Correct Incorrect Correct answer

0.5

Correct Incorrect Correct answer

16

Correct Incorrect Correct answer

24. Question

Which of the following expressions is equivalent to $\dfrac{x^{2}+2x+4}{x+5}$

$x-4-\dfrac{18}{x-5}$

Correct Incorrect Correct answer

$x-3-\dfrac{19}{x+5}$

Correct Incorrect Correct answer

$x-3+\dfrac{19}{x+5}$

Correct Incorrect Correct answer

$x+3+\dfrac{19}{x+5}$

Correct Incorrect Correct answer

25. Question

A student went to the bookstore to buy $x$ notebooks and $y$ copybooks. The price of each notebook is \$5 and the price of each copybook is \$6.

Which of the following expressions represent the total price of buying $y$ copybooks and $x$ notebooks?

$6x+6y$

Correct Incorrect Correct answer

$5x+6y$

Correct Incorrect Correct answer

$5x+y$

Correct Incorrect Correct answer

$x+6y$

Correct Incorrect Correct answer

26. Question

What is the maximum number of copybooks that can be purchased with \$23?

10

Correct Incorrect Correct answer

4

Correct Incorrect Correct answer

3

Correct Incorrect Correct answer

1

Correct Incorrect Correct answer

27. Question

If the student paid \$27 at the counter, how many notebooks and copybooks could he have bought?

1 notebook and 4 copybooks

Correct Incorrect Correct answer

2 notebooks and 4 copybooks

Correct Incorrect Correct answer

3 notebooks and 2 copybooks

Correct Incorrect Correct answer

3 notebooks and 3 copybooks

Correct Incorrect Correct answer

28. Question

What is the exponent of $n$ in the simplified form of the expression $\left[\dfrac{(2m^{10}n^{14})^{4}}{(3m^{4}n^{2})^{3}}\right]^{5}$?

140

Correct Incorrect Correct answer

250

Correct Incorrect Correct answer

300

Correct Incorrect Correct answer

360

Correct Incorrect Correct answer

29. Question

Suppose you have a bag of 12 yellow marbles and 9 blue marbles. If you select 2 marbles randomly and without replacement, what is the probability that both marbles are yellow?

$\dfrac{11}{35}$

Correct Incorrect Correct answer

$\dfrac{16}{49}$

Correct Incorrect Correct answer

$\dfrac{21}{23}$

Correct Incorrect Correct answer

$\dfrac{140}{157}$

Correct Incorrect Correct answer

30. Question

The vertex form of the equation $y=4x^{2}+12x-5$ is $y=4(x+b)^{2}-c$. What is the value of $c-b-3$?

8

Correct Incorrect Correct answer

9.5

Correct Incorrect Correct answer

10.5

Correct Incorrect Correct answer

14

Correct Incorrect Correct answer

31. Question

Amjad and Ali are preparing for a math exam. The probability of Amjad passing his exam is 0.65. The probability of both Ali and Amjad failing is 0.25. Assuming that the events are independent, what is the probability, rounded to the nearest tenth, that both Amjad and Ali pass the exam?

0.6

Correct Incorrect Correct answer

0.3

Correct Incorrect Correct answer

0.2

Correct Incorrect Correct answer

0.1

Correct Incorrect Correct answer

32. Question

A survey was conducted to determine the number of pens owned by employees in a company. The table below shows the number of employees who own 1, 2, 3, and 5 pens. What is the product of the mean, median, and mode of the number of pens?

Number of pens	1	2	3	5
Number of employees	23	17	25	10

10.25

Correct Incorrect Correct answer

13.5

Correct Incorrect Correct answer

14.5

Correct Incorrect Correct answer

14.56

Correct Incorrect Correct answer

33. Question

$9^{2}+4[6\times(-5)+7]+10=$

-2

Correct Incorrect Correct answer

-1

Correct Incorrect Correct answer

2

Correct Incorrect Correct answer

6

Correct Incorrect Correct answer

34. Question

If the point with coordinates $(a, b)$, where $a > 1$ and both $a$ and $b$ integers, lies in the solution set of the system $\begin{cases} x + y < 13 \\ y - x > 7 \end{cases}$, what is the value of $b^a$

100

Correct Incorrect Correct answer

225

Correct Incorrect Correct answer

1,000

Correct Incorrect Correct answer

1,024

Correct Incorrect Correct answer

35. Question

A company sells electric scooters for $\$625$ each. Last month, they decided to apply a $10\%$ tax fee on all products. This month, they reduced the total price of a scooter by $15\%$. Approximately, how much does a scooter cost now?

\$531.2

Correct Incorrect Correct answer

\$584.4

Correct Incorrect Correct answer

\$593.7

Correct Incorrect Correct answer

\$687.5

Correct Incorrect Correct answer

36. Question

To watch a movie at the cinema, Fady bought 4 adult tickets and 1 child ticket for $\$46$, while Samer bought 3 adult tickets and 2 child tickets for $\$42$. What is the price of 1 child ticket?

\$5

Correct Incorrect Correct answer

\$6

Correct Incorrect Correct answer

\$8

Correct Incorrect Correct answer

\$10

Correct Incorrect Correct answer

37. Question

In Turkey, the dollar exchange rate increased from 32.2 TRY in May 2024 to 38.5 TRY in May 2025 due to the recent economic crisis. What was the percentage increase in the value of the dollar in TRY, rounded to the nearest whole percent?

15%

Correct Incorrect Correct answer

19%

Correct Incorrect Correct answer

20%

Correct Incorrect Correct answer

30%

Correct Incorrect Correct answer

38. Question

Consider triangle $ABC$, right-angled at $A$. If $sin(C)=\dfrac{\sqrt{2}}{2},$ what is measure of angle $B$?

$60^{\circ}$

Correct Incorrect Correct answer

$45^{\circ}$

Correct Incorrect Correct answer

$30^{\circ}$

Correct Incorrect Correct answer

$15^{\circ}$

Correct Incorrect Correct answer

39. Question

In the figure above, the area of triangle $ABE$ is $31.5 \text{ cm}^2$. If $FE = \dfrac{2}{3}BE$, what is the area of the parallelogram $ANFE$? (Figure not drawn to scale)

$18~cm^{2}$

Correct Incorrect Correct answer

$21~cm^{2}$

Correct Incorrect Correct answer

$42~cm^{2}$

Correct Incorrect Correct answer

$54~cm^{2}$

Correct Incorrect Correct answer

40. Question

Given $f(x) = \dfrac{2}{x + 4} - 1$. The vertical asymptote of the graph of $f$ is $x = a$, while its horizontal asymptote is $y = b$. What is the value of $|b + a|$

1

Correct Incorrect Correct answer

3

Correct Incorrect Correct answer

4

Correct Incorrect Correct answer

5

Correct Incorrect Correct answer

41. Question

If $\dfrac{13}{8}a+7x=\dfrac{1}{2}$ and $x=1$, what is the value of $a$?

-2

Correct Incorrect Correct answer

-3

Correct Incorrect Correct answer

-4

Correct Incorrect Correct answer

-8

Correct Incorrect Correct answer

42. Question

The interior angles of a hexagon are in the ratio $2:3:4:5:5:6$. What is the measure of the largest angle in this hexagon?

$118.5^{\circ}$

Correct Incorrect Correct answer

$136.0^{\circ}$

Correct Incorrect Correct answer

$172.5^{\circ}$

Correct Incorrect Correct answer

$172.8^{\circ}$

Correct Incorrect Correct answer

43. Question

A company has 6 different stores in Egypt. The number of staff members in each store is represented in the table below. If the store in Giza decided to increase the number of its staff members to 42, which of the following is true regarding the new average number of staff members?

City	Cairo	Alexandria	Port Said	Giza	Aswan	Luxor
Staff	33	37	19	30	11	10

Average decrease

Correct Incorrect Correct answer

Average increase by 2

Correct Incorrect Correct answer

Average increase by 4

Correct Incorrect Correct answer

No change

Correct Incorrect Correct answer

44. Question

What is the value of $x$ if $4\lvert 2x+1 \rvert=10$ and $x<0$?

1.75

Correct Incorrect Correct answer

0.75

Correct Incorrect Correct answer

-1.75

Correct Incorrect Correct answer

-2

Correct Incorrect Correct answer

45. Question

The area of the sector containing the major arc $\overparen{BC}$ in the figure above is: (Figure not drawn to scale)

$\dfrac{\sqrt{17}}{4}\pi$

Correct Incorrect Correct answer

$\dfrac{17}{4}\pi$

Correct Incorrect Correct answer

$\dfrac{51}{4}\pi$

Correct Incorrect Correct answer

$17\pi$

Correct Incorrect Correct answer

46. Question

Which of the points below does not satisfy the system of inequalities $\begin{cases}2x-y\le4\\ y+4x>1\end{cases}$

$(-1,6)$

Correct Incorrect Correct answer

(1,2)

Correct Incorrect Correct answer

$(0,5)$

Correct Incorrect Correct answer

$(-1,1)$

Correct Incorrect Correct answer

47. Question

What is the value of $x$ if $\dfrac{3}{x-3}=\sqrt{3}$

$\sqrt{3}$

Correct Incorrect Correct answer

3

Correct Incorrect Correct answer

$3+\sqrt{3}$

Correct Incorrect Correct answer

$\sqrt{6}$

Correct Incorrect Correct answer

48. Question

In the identity $2x^3 + 2x^2 + 4x - 8 = (x^2 + bx + 4)(2x - a)$, true for every real $x$, $a$and$b$are two integers. Which of the following expressions has the smallest value?

$-4a-b$

Correct Incorrect Correct answer

$a-8$

Correct Incorrect Correct answer

$2b-12$

Correct Incorrect Correct answer

$b^{2}-8$

Correct Incorrect Correct answer

49. Question

The domain of definition of the function $h(x)=\dfrac{6}{\sqrt{-2x+7}}$ is:

$(-\infty,3.5)$

Correct Incorrect Correct answer

$(0,+\infty)$

Correct Incorrect Correct answer

$[3.5,+\infty)$

Correct Incorrect Correct answer

$(3.5,+\infty)$

Correct Incorrect Correct answer

50. Question

$$4\sqrt{x-4}=x.$$ What is the number of real solutions in the equation above?

3

Correct Incorrect Correct answer

2

Correct Incorrect Correct answer

1

Correct Incorrect Correct answer

0

Correct Incorrect Correct answer

EST1 Math Sample 2026 (50 Questions)

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