MOCK TEST: SHS
1 1
1. If r ≠ 0 𝑎𝑛𝑑 r + = 2025 and r2 + = s, find the unit digit of s.
𝑟 𝑟2
a. 0
b. 1
c. 2
d. 3
e. 5
2. How many diagonals does a regular 100-sided polygon have?
a. 4850
b. 3200
c. 1800
d. 360
e. 120
3. A fair 6-face die is thrown twice. Find the probability that the product of numbers
obtained is greater than 27.
2
a. 3
1
b. 9
1
c. 6
5
d. 12
1
e. 12
4. What is the minimum value of f(x) = x2 – 12x + 2061
a. 2023
b. 2024
c. 2025
d. 2026
e. 2028
5. Find the remainder for 232025 divided by 24.
a. -1
b. 0
c. 1
d. 23
e. 24
6. What is the next number in the series 6, 9, 15, 21, …
a. 24
b. 26
c. 28
d. 31
e. 33
7. If 4p ≡ 5(mod11), find the least value of p.
a. 4
b. 5
c. 6
d. 15
e. 26
8. The legs of triangle ABC are √81 and √144 units. Find its area.
a. 48 sq. u
b. 52 sq. u
c. 54 sq. u
d. 56 sq. u
e. 60 sq. u
9. A circle has an equation of x2 + y2 + 2x – 4y – 4 =0. How long is its radius?
a. 8 units
b. 6 units
c. 5 units
d. 4 units
e. 3 units
10.Find the remainder when P(x) = x2025 + x2024 + 2026 is divided by x + 1.
a. 2027
b. 2026
c. 2025
d. 2024
e. 2023
11. What is the unit digit of 1! + 2! + 3! + 4! + …+ 2026! ?
a. 1
b. 2
c. 3
d. 4
e. 5
12. It is known that p is rational and greater than zero, find the value of
p = √420 + √420 + √420 + ⋯
a. 18
b. 19
c. 20
d. 21
e. 25
13. From the starting point X, Mike drives West for 15 kms, then drives North for 20 kms.
How far is Mike now from point X?
a. 25
b. 30
c. 35
d. 40
e. 45
14. In how many ways you can arrange Jean, Cathy, Myla and Donna in a row?
a. 36
b. 32
c. 28
d. 24
e. 12
15. Find the product of the first 10 consecutive integers.
a. 1, 290,000
b. 2, 810, 400
c. 3, 628, 800
d. 4, 150, 000
e. 5, 020, 260
16. If x = 900, evaluate 2026sinx + 5cosx
a. 2025
b. 2026
c. 2027
d. 2031
e. 2033
17. 20 is what percent of 30?
a. 66.67%
b. 66.68%
c. 66.69%
d. 66.81%
e. 66.82%
18. The figure shows four congruent circles inscribed in a square. Each circle touches two
sides of the square and two other circles. Find the ratio between the total area of the grey
parts and the area of the black part?
a. 4: 1
b. 3: 2
c. 3:1
d. 4: 3
e. 2: 1
19. In triangle PQR, given that PR = 5√2, QR = 5 and ∠QPR = 30 degrees. Find the smallest
possible measure of ∠PQR?
a. 150
b. 300
c. 450
d. 600
e. 750
20. Find the area of the ellipse given by 49x2 + 36y2 – 490x + 432y + 756 = 2.
a. 36π
b. 42π
c. 49𝜋
d. 54π
e. 60π
a. 2025
b. 2020
c. 1
1
d. 2025
e. 0
22. How many terms does the expansion of (a + b + c + d)3 have?
a. 15
b. 18
c. 20
d. 24
e. 36
23. Dulce has 18 balls in her bag, numbered from 1 to 18. Find the least number of balls she
would have to take ensuring that she takes three primes of them?
a. 10
b. 13
c. 14
d. 16
e. 17
24. Consider the set of positive odd numbers from 1 to 6. How many subsets are there?
a. 2
b. 4
c. 8
d. 16
e. 32
25. If f(x) = x2 + 1 and g(x) = 2 + x2, find f(cos1800)g(sin2700)
a. 6
b. 5
c. 3
d. 2
e. -1
ANSWER KEY
(WITH HINTS)
1. D square the constant minus 2
2. A 𝑛(𝑛−3)
formula:
2
3. E (5,6), (6, 5), (6, 6)
4. C 12
2061 – ( 2 )2
23
5. D = -1 (23 is short by 1 before 24); (−1)2025 = −1; 𝑅: 23
24
6. E Each prime number is multiplied by 3
7. A 5 + 11 = 16; 16/4 = 4
8. C Area of right triangle
9. E (𝑥 − ℎ)2 + (𝑦 − 𝑘)2 = 𝑟 2
10. B x + 1 = 0; x = -1; substitution
11. C from 5! to 2026!, it ends with 0; work only 1! + 2! + 3! + 4!
12. D Transform it into quadratic equation by squaring both sides
13. A Use Pythagorean theorem
14. D Factorial notation
15. C 10!
16. B substitute 900
17. A 20
30
18. C one quarter of square comprises 3 grey areas and 1 black area
19. C Law of sine
20. B Transform into ellipse equation; abπ
21. E log 1 = 0
22. C stars & bars- nonnegative: 6C3
23. C worst scenario: 11 composite numbers + 3 primes
24. C (1, 3, 5); 2𝑛
25. A cos1800 = -1; sin 2700 = 1
