1.
Arrange the following fractions and decimals in ascending order.
3
2
0.75, , 0.6, , 0.8
4
3
2.
Arrange the following fractions in descending order:
2 3 1 1 5
3 , ,4 ,3 ,
3 4 2 4 6
3.
1
2
Ernest baked a cake and divided it into 12 equal slices. He ate 3 of the cake, and his brother ate 5 of the
remaining slices. How many slices did his brother eat?
4.
5
A carpenter needs to cut a wooden plank into smaller pieces. He cuts 6 of the plank to make a shelf and
2
uses 3 of the remaining plank to make a table. What fraction of the original plank is left?
3
5.
A classroom has 45 students now, which is 5 of its full capacity. What is the full capacity of the classroom?
6.
A farmer used of a bag of seeds to plant tomatoes and then used of the remaining seeds to plant
1
6
2
5
cucumbers. If there are 1,000 seeds left, how many seeds were there originally in the bag?
7.
Evaluate the expression:
i.
7 − 5 × 2 + 10 ÷ 2
ii.
2 × (7 + 3) − 8 ÷ 4 + 5
iii.
−3 × (2 + 5) + (10 − 4) ÷ 2
iv.
−3 × (7 + 14) + 10 ÷ (6 − 1)
v.
−3 × {[2 + 5 − (3 − 1)] + 4}
vi.
{6 − [4 − (5 − 2)]} × (3 + [12 − (6 − 3)])
8.
Mark the points 𝑃, 𝑄, 𝑅, and 𝑆 on a number line, where 𝑃 represents −6, 𝑄 represents 0, 𝑅 represents
9, and 𝑆 represents −3. Find the distance between points 𝑄 and 𝑅.
9.
Write the number 7, 102, 018 in words.
10.
Write the numeral for the word form: Five million, four hundred and seventy-five thousand, and sixtytwo.
11.
A submarine descends 500 meters below sea level. It then ascends 300 meters and descends another 200
meters. How far below sea level is the submarine now?
12.
Min Yu is training for a marathon. On the first day, he runs 8 miles, and each day, he increases his distance
by 2 miles. If he follows this pattern for five days, how many miles will he run on the fifth day?
13.
A spaceship travels at a speed of 5 × 105 meters per second. How far will it travel in 10 seconds?
14.
Express 3125 in index form, using 5 as the base number.
15.
Express 1024 in index form, using 4 as the base number.
16.
Simplify the expression: 23 × 52 ÷ (5−4 × 2−2 ).
17.
Simplify the expression: 9−2 × 33 ÷ (3−5 × 3−3 ).
18.
Evaluate (2.35 × 106 ) + (1.98 × 105 ), leave your answer in standard form.
19.
Evaluate (7.6 × 10−3 ) + (9.2 × 10−2 ) + (3.7 × 10−1 ), leave your answer in standard form.
20.
Subtract (2.5 × 103 ) from (6.8 × 103 ), leave your answer in standard form.
21.
Evaluate (4.5 × 105 ) × (3.2 × 104 ), leave your answer in standard form.
22.
Evaluate (1.2 × 107 ) × (5.6 × 10−4 ), leave your answer in standard form.
23.
Divide (1.28 × 107 ) by (8 × 103 ), leave your answer in standard form.
24.
A factory produces 2,500.75 kilograms of steel in one day. If they produce the same amount of steel for 7
consecutive days, how much steel will they produce in total?
25.
Brayden earns a commission of 0.025 on the total sales he makes. If his total sales for the month amount
to $6,750.60, how much commission will he earn?
26.
The school has 48 red pens and 60 blue pens. They want to divide the pens into identical packs with the
same number of pens in each pack. What is the largest number of packs they can make?
27.
A farmer has 30 cows, 40 sheep, and 50 goats. He wants to divide them into equal groups, with the same
number of each type of animal in each group. What is the largest possible number of groups he can make?
28.
What is the smallest multiple of 15 that is greater than 100?
29.
Find all the factors of 360.
30.
Find the prime factors of 1260.
31.
Write 315 as a product of its prime factors.
32.
Identify the next three prime numbers after 23.
33.
Find the largest number that will divide 112 and 180, leaving remainders of 5 and 12 respectively.
34.
Find the smallest number that will have a remainder of 3 when divided by 7, 11, and 13.
35.
Write the Roman numeral representation for the number 245.
36.
Subtract the Roman numeral "CXXIX" from "DCCCXC".
37.
A museum has a collection of ancient artifacts. The collection contains XXIV statues, XXXII pottery pieces,
and L sculptures. How many artifacts are there in total?
38.
A Roman empire ruler is building a colosseum and wants to place XXV rows of seats. If each row can
accommodate VIII spectators, how many spectators can the colosseum hold?
39.
Express the year "1984" in Roman numerals.
40.
Kai Jian is investigating twin prime numbers. He finds two prime numbers such that their difference is 2,
and both numbers are less than 40. Can you help him find these twin prime numbers?
41.
𝑥 = 32 × 52 × 7 × 19957 when written as a product of its prime factors.
Write 𝑥 ÷ 315 as a product of its prime factors.